Unit 2 — End of Topic Tests (reviewer copy: all keys and model answers visible)

[
 "Write down the values in the question:",
 "protons = 12",
 "neutrons = 12",
 "Write down the relationship:",
 "nucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)",
 "Substitute in the values, and calculate:",
 "nucleus mass ≈ 12 + 12",
 "nucleus mass ≈ 24 amu"
]

[
 {
  "value": 12,
  "misconception": "you counted only one kind of particle — the other 12 particles also contribute about 1 amu each",
  "feedback": "This answer is wrong — 12 counts only the protons (or only the neutrons). Each of the magnesium nucleus's 12 protons AND each of its 12 neutrons contributes about 1 amu: 12 + 12 = 24 amu."
 },
 {
  "value": 144,
  "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
  "feedback": "This answer is wrong — you multiplied 12 by 12. Each particle contributes about 1 amu, so the counts add: 12 + 12 = 24 amu."
 },
 {
  "value": 36,
  "misconception": "you added the electrons in as well at about 1 amu each — electrons are about 1/2000 amu and are not counted",
  "feedback": "This answer is wrong — you counted the magnesium atom's 12 electrons at about 1 amu each. Electrons are about 1/2000 amu each, far too light to count: the nucleus's 12 protons and 12 neutrons give 12 + 12 = 24 amu."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 12\nneutrons = 12\nWrite down the relationship:\nnucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)\nSubstitute in the values, and calculate:\nnucleus mass ≈ 12 + 12\nnucleus mass ≈ 24 amu",
 "anticipatedWrong": [
  {
   "value": 12,
   "misconception": "you counted only one kind of particle — the other 12 particles also contribute about 1 amu each",
   "feedback": "This answer is wrong — 12 counts only the protons (or only the neutrons). Each of the magnesium nucleus's 12 protons AND each of its 12 neutrons contributes about 1 amu: 12 + 12 = 24 amu."
  },
  {
   "value": 144,
   "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
   "feedback": "This answer is wrong — you multiplied 12 by 12. Each particle contributes about 1 amu, so the counts add: 12 + 12 = 24 amu."
  },
  {
   "value": 36,
   "misconception": "you added the electrons in as well at about 1 amu each — electrons are about 1/2000 amu and are not counted",
   "feedback": "This answer is wrong — you counted the magnesium atom's 12 electrons at about 1 amu each. Electrons are about 1/2000 amu each, far too light to count: the nucleus's 12 protons and 12 neutrons give 12 + 12 = 24 amu."
  }
 ]
}

[
 {
  "value": 35,
  "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 35 is the entry's decimal value 35.45 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 17 is the atomic number, and it is the proton count."
 },
 {
  "value": 18,
  "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
  "feedback": "This answer is wrong — 18 comes from 35 − 17, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 17 is the atomic number, and the atomic number itself is the proton count."
 }
]

{
 "keyExplanation": "The whole number on the entry is the atomic number: 17. The atomic number is the proton count. Every atom of this element — chlorine — has 17 protons.",
 "anticipatedWrong": [
  {
   "value": 35,
   "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 35 is the entry's decimal value 35.45 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 17 is the atomic number, and it is the proton count."
  },
  {
   "value": 18,
   "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
   "feedback": "This answer is wrong — 18 comes from 35 − 17, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 17 is the atomic number, and the atomic number itself is the proton count."
  }
 ]
}

[
 {
  "value": 73,
  "misconception": "you counted only the protons — the mass number adds the neutrons in too",
  "feedback": "This answer is wrong — 73 counts only the tantalum atom's protons; the mass number adds its 108 neutrons in too: 73 + 108 = 181."
 },
 {
  "value": 108,
  "misconception": "you counted only the neutrons — the mass number adds the protons in too",
  "feedback": "This answer is wrong — 108 counts only the tantalum atom's neutrons; the mass number adds its 73 protons in too: 73 + 108 = 181."
 },
 {
  "value": 254,
  "misconception": "you added the electrons in as well — electrons are nearly 2000 times lighter and are not counted",
  "feedback": "This answer is wrong — you added the electrons in as well; electrons are nearly 2000 times lighter and are not counted. The mass number counts only the tantalum atom's protons and neutrons: 73 + 108 = 181."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 73\nneutrons = 108\nWrite down the relationship:\nmass number = protons + neutrons\nSubstitute in the values, and calculate:\nmass number = 73 + 108\nmass number = 181"
}

[
 "Write down the values in the question:",
 "mass number = 141",
 "atomic number = 59",
 "Write down the relationship:",
 "mass number = atomic number + neutron count",
 "Make the neutron count the subject:",
 "neutron count = mass number − atomic number",
 "Substitute in the values, and calculate:",
 "neutron count = 141 − 59",
 "neutron count = 82 neutrons"
]

[
 {
  "value": 200,
  "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
  "feedback": "This answer is wrong — you added the mass number and the atomic number. The praseodymium atom's mass number 141 already contains its 59 protons, so the neutron count is what is left after subtracting: 141 − 59 = 82 neutrons."
 },
 {
  "value": 59,
  "misconception": "you reported the atomic number, which is the proton count",
  "feedback": "This answer is wrong — 59 is praseodymium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 141 − 59 = 82 neutrons."
 },
 {
  "value": 141,
  "misconception": "you reported the mass number, which counts protons and neutrons together",
  "feedback": "This answer is wrong — 141 is the praseodymium atom's mass number, which counts the protons and neutrons together. Subtract the 59 protons to leave the neutrons: 141 − 59 = 82 neutrons."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass number = 141\natomic number = 59\nWrite down the relationship:\nmass number = atomic number + neutron count\nMake the neutron count the subject:\nneutron count = mass number − atomic number\nSubstitute in the values, and calculate:\nneutron count = 141 − 59\nneutron count = 82 neutrons",
 "anticipatedWrong": [
  {
   "value": 200,
   "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
   "feedback": "This answer is wrong — you added the mass number and the atomic number. The praseodymium atom's mass number 141 already contains its 59 protons, so the neutron count is what is left after subtracting: 141 − 59 = 82 neutrons."
  },
  {
   "value": 59,
   "misconception": "you reported the atomic number, which is the proton count",
   "feedback": "This answer is wrong — 59 is praseodymium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 141 − 59 = 82 neutrons."
  },
  {
   "value": 141,
   "misconception": "you reported the mass number, which counts protons and neutrons together",
   "feedback": "This answer is wrong — 141 is the praseodymium atom's mass number, which counts the protons and neutrons together. Subtract the 59 protons to leave the neutrons: 141 − 59 = 82 neutrons."
  }
 ]
}

[
 {
  "value": "mercury-80",
  "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
  "feedback": "This answer is wrong — you put the proton count 80 after the hyphen. The name form carries the mass number: 80 + 119 = 199, so this atom is mercury-199."
 },
 {
  "value": "mercury-119",
  "misconception": "you used the neutron count alone — the mass number adds the protons in too",
  "feedback": "This answer is wrong — you put the neutron count 119 after the hyphen. The mass number adds the protons in too: 80 + 119 = 199, so the name form is mercury-199."
 },
 {
  "value": "mercury-39",
  "misconception": "you subtracted the counts — the mass number adds them",
  "feedback": "This answer is wrong — you subtracted the counts (119 − 80 = 39). The mass number adds them: 80 + 119 = 199, so the name form is mercury-199."
 },
 {
  "value": "mercury 199",
  "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
  "feedback": "This answer is wrong as written — the mass number 199 is right, but the name form joins the element name to the mass number with a hyphen: mercury-199."
 }
]

{
 "keyExplanation": "The name form is the element name, a hyphen, and the mass number.\nmass number = protons + neutrons\nmass number = 80 + 119 = 199\nSo the name form is mercury-199 — the element name, a hyphen, then the mass number. The number after the hyphen is never the proton count 80 or the neutron count 119 alone.",
 "anticipatedWrong": [
  {
   "value": "mercury-80",
   "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
   "feedback": "This answer is wrong — you put the proton count 80 after the hyphen. The name form carries the mass number: 80 + 119 = 199, so this atom is mercury-199."
  },
  {
   "value": "mercury-119",
   "misconception": "you used the neutron count alone — the mass number adds the protons in too",
   "feedback": "This answer is wrong — you put the neutron count 119 after the hyphen. The mass number adds the protons in too: 80 + 119 = 199, so the name form is mercury-199."
  },
  {
   "value": "mercury-39",
   "misconception": "you subtracted the counts — the mass number adds them",
   "feedback": "This answer is wrong — you subtracted the counts (119 − 80 = 39). The mass number adds them: 80 + 119 = 199, so the name form is mercury-199."
  },
  {
   "value": "mercury 199",
   "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
   "feedback": "This answer is wrong as written — the mass number 199 is right, but the name form joins the element name to the mass number with a hyphen: mercury-199."
  }
 ]
}

[
 "Write down the values in the question:",
 "protons = 10",
 "neutrons = 12",
 "Write down the relationship:",
 "nucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)",
 "Substitute in the values, and calculate:",
 "nucleus mass ≈ 10 + 12",
 "nucleus mass ≈ 22 amu"
]

[
 {
  "value": 10,
  "misconception": "you counted only the protons — the 12 neutrons also contribute about 1 amu each",
  "feedback": "This answer is wrong — 10 counts only the neon nucleus's protons. Its 12 neutrons also contribute about 1 amu each: 10 + 12 = 22 amu."
 },
 {
  "value": 12,
  "misconception": "you counted only the neutrons — the 10 protons also contribute about 1 amu each",
  "feedback": "This answer is wrong — 12 counts only the neon nucleus's neutrons. Its 10 protons also contribute about 1 amu each: 10 + 12 = 22 amu."
 },
 {
  "value": 120,
  "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
  "feedback": "This answer is wrong — you multiplied 10 by 12. Each particle contributes about 1 amu, so the counts add: 10 + 12 = 22 amu."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 10\nneutrons = 12\nWrite down the relationship:\nnucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)\nSubstitute in the values, and calculate:\nnucleus mass ≈ 10 + 12\nnucleus mass ≈ 22 amu",
 "anticipatedWrong": [
  {
   "value": 10,
   "misconception": "you counted only the protons — the 12 neutrons also contribute about 1 amu each",
   "feedback": "This answer is wrong — 10 counts only the neon nucleus's protons. Its 12 neutrons also contribute about 1 amu each: 10 + 12 = 22 amu."
  },
  {
   "value": 12,
   "misconception": "you counted only the neutrons — the 10 protons also contribute about 1 amu each",
   "feedback": "This answer is wrong — 12 counts only the neon nucleus's neutrons. Its 10 protons also contribute about 1 amu each: 10 + 12 = 22 amu."
  },
  {
   "value": 120,
   "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
   "feedback": "This answer is wrong — you multiplied 10 by 12. Each particle contributes about 1 amu, so the counts add: 10 + 12 = 22 amu."
  }
 ]
}

[
 {
  "value": 24,
  "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 24 is the entry's decimal value 24.31 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 12 is the atomic number, and it is the proton count."
 },
 {
  "value": 24.31,
  "misconception": "you copied the decimal number from the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 24.31 is the entry's decimal value, the decimal mass value printed on the tile. The whole number 12 is the atomic number, and it is the proton count."
 }
]

{
 "keyExplanation": "The whole number on the entry is the atomic number: 12. The atomic number is the proton count. Every atom of this element — magnesium — has 12 protons.",
 "anticipatedWrong": [
  {
   "value": 24,
   "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 24 is the entry's decimal value 24.31 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 12 is the atomic number, and it is the proton count."
  },
  {
   "value": 24.31,
   "misconception": "you copied the decimal number from the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 24.31 is the entry's decimal value, the decimal mass value printed on the tile. The whole number 12 is the atomic number, and it is the proton count."
  }
 ]
}

[
 {
  "value": 75,
  "misconception": "you counted only the protons — the mass number adds the neutrons in too",
  "feedback": "This answer is wrong — 75 counts only the rhenium atom's protons; the mass number adds its 110 neutrons in too: 75 + 110 = 185."
 },
 {
  "value": 110,
  "misconception": "you counted only the neutrons — the mass number adds the protons in too",
  "feedback": "This answer is wrong — 110 counts only the rhenium atom's neutrons; the mass number adds its 75 protons in too: 75 + 110 = 185."
 },
 {
  "value": 260,
  "misconception": "you added the electrons in as well — electrons are nearly 2000 times lighter and are not counted",
  "feedback": "This answer is wrong — you added the electrons in as well; electrons are nearly 2000 times lighter and are not counted. The mass number counts only the rhenium atom's protons and neutrons: 75 + 110 = 185."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 75\nneutrons = 110\nWrite down the relationship:\nmass number = protons + neutrons\nSubstitute in the values, and calculate:\nmass number = 75 + 110\nmass number = 185"
}

[
 "Write down the values in the question:",
 "mass number = 175",
 "atomic number = 71",
 "Write down the relationship:",
 "mass number = atomic number + neutron count",
 "Make the neutron count the subject:",
 "neutron count = mass number − atomic number",
 "Substitute in the values, and calculate:",
 "neutron count = 175 − 71",
 "neutron count = 104 neutrons"
]

[
 {
  "value": 246,
  "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
  "feedback": "This answer is wrong — you added the mass number and the atomic number. The lutetium atom's mass number 175 already contains its 71 protons, so the neutron count is what is left after subtracting: 175 − 71 = 104 neutrons."
 },
 {
  "value": 71,
  "misconception": "you reported the atomic number, which is the proton count",
  "feedback": "This answer is wrong — 71 is lutetium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 175 − 71 = 104 neutrons."
 },
 {
  "value": 175,
  "misconception": "you reported the mass number, which counts protons and neutrons together",
  "feedback": "This answer is wrong — 175 is the lutetium atom's mass number, which counts the protons and neutrons together. Subtract the 71 protons to leave the neutrons: 175 − 71 = 104 neutrons."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass number = 175\natomic number = 71\nWrite down the relationship:\nmass number = atomic number + neutron count\nMake the neutron count the subject:\nneutron count = mass number − atomic number\nSubstitute in the values, and calculate:\nneutron count = 175 − 71\nneutron count = 104 neutrons",
 "anticipatedWrong": [
  {
   "value": 246,
   "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
   "feedback": "This answer is wrong — you added the mass number and the atomic number. The lutetium atom's mass number 175 already contains its 71 protons, so the neutron count is what is left after subtracting: 175 − 71 = 104 neutrons."
  },
  {
   "value": 71,
   "misconception": "you reported the atomic number, which is the proton count",
   "feedback": "This answer is wrong — 71 is lutetium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 175 − 71 = 104 neutrons."
  },
  {
   "value": 175,
   "misconception": "you reported the mass number, which counts protons and neutrons together",
   "feedback": "This answer is wrong — 175 is the lutetium atom's mass number, which counts the protons and neutrons together. Subtract the 71 protons to leave the neutrons: 175 − 71 = 104 neutrons."
  }
 ]
}

[
 {
  "value": "osmium-76",
  "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
  "feedback": "This answer is wrong — you put the proton count 76 after the hyphen. The name form carries the mass number: 76 + 116 = 192, so this atom is osmium-192."
 },
 {
  "value": "osmium-116",
  "misconception": "you used the neutron count alone — the mass number adds the protons in too",
  "feedback": "This answer is wrong — you put the neutron count 116 after the hyphen. The mass number adds the protons in too: 76 + 116 = 192, so the name form is osmium-192."
 },
 {
  "value": "osmium-40",
  "misconception": "you subtracted the counts — the mass number adds them",
  "feedback": "This answer is wrong — you subtracted the counts (116 − 76 = 40). The mass number adds them: 76 + 116 = 192, so the name form is osmium-192."
 },
 {
  "value": "osmium 192",
  "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
  "feedback": "This answer is wrong as written — the mass number 192 is right, but the name form joins the element name to the mass number with a hyphen: osmium-192."
 }
]

{
 "keyExplanation": "The name form is the element name, a hyphen, and the mass number.\nmass number = protons + neutrons\nmass number = 76 + 116 = 192\nSo the name form is osmium-192 — the element name, a hyphen, then the mass number. The number after the hyphen is never the proton count 76 or the neutron count 116 alone.",
 "anticipatedWrong": [
  {
   "value": "osmium-76",
   "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
   "feedback": "This answer is wrong — you put the proton count 76 after the hyphen. The name form carries the mass number: 76 + 116 = 192, so this atom is osmium-192."
  },
  {
   "value": "osmium-116",
   "misconception": "you used the neutron count alone — the mass number adds the protons in too",
   "feedback": "This answer is wrong — you put the neutron count 116 after the hyphen. The mass number adds the protons in too: 76 + 116 = 192, so the name form is osmium-192."
  },
  {
   "value": "osmium-40",
   "misconception": "you subtracted the counts — the mass number adds them",
   "feedback": "This answer is wrong — you subtracted the counts (116 − 76 = 40). The mass number adds them: 76 + 116 = 192, so the name form is osmium-192."
  },
  {
   "value": "osmium 192",
   "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
   "feedback": "This answer is wrong as written — the mass number 192 is right, but the name form joins the element name to the mass number with a hyphen: osmium-192."
  }
 ]
}

[
 "Write down the values in the question:",
 "protons = 3",
 "neutrons = 4",
 "Write down the relationship:",
 "nucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)",
 "Substitute in the values, and calculate:",
 "nucleus mass ≈ 3 + 4",
 "nucleus mass ≈ 7 amu"
]

[
 {
  "value": 3,
  "misconception": "you counted only the protons — the 4 neutrons also contribute about 1 amu each",
  "feedback": "This answer is wrong — 3 counts only the lithium nucleus's protons. Its 4 neutrons also contribute about 1 amu each: 3 + 4 = 7 amu."
 },
 {
  "value": 4,
  "misconception": "you counted only the neutrons — the 3 protons also contribute about 1 amu each",
  "feedback": "This answer is wrong — 4 counts only the lithium nucleus's neutrons. Its 3 protons also contribute about 1 amu each: 3 + 4 = 7 amu."
 },
 {
  "value": 12,
  "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
  "feedback": "This answer is wrong — you multiplied 3 by 4. Each particle contributes about 1 amu, so the counts add: 3 + 4 = 7 amu."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 3\nneutrons = 4\nWrite down the relationship:\nnucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)\nSubstitute in the values, and calculate:\nnucleus mass ≈ 3 + 4\nnucleus mass ≈ 7 amu",
 "anticipatedWrong": [
  {
   "value": 3,
   "misconception": "you counted only the protons — the 4 neutrons also contribute about 1 amu each",
   "feedback": "This answer is wrong — 3 counts only the lithium nucleus's protons. Its 4 neutrons also contribute about 1 amu each: 3 + 4 = 7 amu."
  },
  {
   "value": 4,
   "misconception": "you counted only the neutrons — the 3 protons also contribute about 1 amu each",
   "feedback": "This answer is wrong — 4 counts only the lithium nucleus's neutrons. Its 3 protons also contribute about 1 amu each: 3 + 4 = 7 amu."
  },
  {
   "value": 12,
   "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
   "feedback": "This answer is wrong — you multiplied 3 by 4. Each particle contributes about 1 amu, so the counts add: 3 + 4 = 7 amu."
  }
 ]
}

[
 {
  "value": 11,
  "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 11 is the entry's decimal value 10.81 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 5 is the atomic number, and it is the proton count."
 },
 {
  "value": 6,
  "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
  "feedback": "This answer is wrong — 6 comes from 11 − 5, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 5 is the atomic number, and the atomic number itself is the proton count."
 }
]

{
 "keyExplanation": "The whole number on the entry is the atomic number: 5. The atomic number is the proton count. Every atom of this element — boron — has 5 protons.",
 "anticipatedWrong": [
  {
   "value": 11,
   "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 11 is the entry's decimal value 10.81 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 5 is the atomic number, and it is the proton count."
  },
  {
   "value": 6,
   "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
   "feedback": "This answer is wrong — 6 comes from 11 − 5, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 5 is the atomic number, and the atomic number itself is the proton count."
  }
 ]
}

[
 {
  "value": 34,
  "misconception": "you counted only the protons — the mass number adds the neutrons in too",
  "feedback": "This answer is wrong — 34 counts only the selenium atom's protons; the mass number adds its 44 neutrons in too: 34 + 44 = 78."
 },
 {
  "value": 44,
  "misconception": "you counted only the neutrons — the mass number adds the protons in too",
  "feedback": "This answer is wrong — 44 counts only the selenium atom's neutrons; the mass number adds its 34 protons in too: 34 + 44 = 78."
 },
 {
  "value": 112,
  "misconception": "you added the electrons in as well — electrons are nearly 2000 times lighter and are not counted",
  "feedback": "This answer is wrong — you added the electrons in as well; electrons are nearly 2000 times lighter and are not counted. The mass number counts only the selenium atom's protons and neutrons: 34 + 44 = 78."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 34\nneutrons = 44\nWrite down the relationship:\nmass number = protons + neutrons\nSubstitute in the values, and calculate:\nmass number = 34 + 44\nmass number = 78"
}

[
 "Write down the values in the question:",
 "mass number = 173",
 "atomic number = 70",
 "Write down the relationship:",
 "mass number = atomic number + neutron count",
 "Make the neutron count the subject:",
 "neutron count = mass number − atomic number",
 "Substitute in the values, and calculate:",
 "neutron count = 173 − 70",
 "neutron count = 103 neutrons"
]

[
 {
  "value": 243,
  "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
  "feedback": "This answer is wrong — you added the mass number and the atomic number. The ytterbium atom's mass number 173 already contains its 70 protons, so the neutron count is what is left after subtracting: 173 − 70 = 103 neutrons."
 },
 {
  "value": 70,
  "misconception": "you reported the atomic number, which is the proton count",
  "feedback": "This answer is wrong — 70 is ytterbium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 173 − 70 = 103 neutrons."
 },
 {
  "value": 173,
  "misconception": "you reported the mass number, which counts protons and neutrons together",
  "feedback": "This answer is wrong — 173 is the ytterbium atom's mass number, which counts the protons and neutrons together. Subtract the 70 protons to leave the neutrons: 173 − 70 = 103 neutrons."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass number = 173\natomic number = 70\nWrite down the relationship:\nmass number = atomic number + neutron count\nMake the neutron count the subject:\nneutron count = mass number − atomic number\nSubstitute in the values, and calculate:\nneutron count = 173 − 70\nneutron count = 103 neutrons",
 "anticipatedWrong": [
  {
   "value": 243,
   "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
   "feedback": "This answer is wrong — you added the mass number and the atomic number. The ytterbium atom's mass number 173 already contains its 70 protons, so the neutron count is what is left after subtracting: 173 − 70 = 103 neutrons."
  },
  {
   "value": 70,
   "misconception": "you reported the atomic number, which is the proton count",
   "feedback": "This answer is wrong — 70 is ytterbium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 173 − 70 = 103 neutrons."
  },
  {
   "value": 173,
   "misconception": "you reported the mass number, which counts protons and neutrons together",
   "feedback": "This answer is wrong — 173 is the ytterbium atom's mass number, which counts the protons and neutrons together. Subtract the 70 protons to leave the neutrons: 173 − 70 = 103 neutrons."
  }
 ]
}

[
 {
  "value": "selenium-34",
  "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
  "feedback": "This answer is wrong — you put the proton count 34 after the hyphen. The name form carries the mass number: 34 + 43 = 77, so this atom is selenium-77."
 },
 {
  "value": "selenium-43",
  "misconception": "you used the neutron count alone — the mass number adds the protons in too",
  "feedback": "This answer is wrong — you put the neutron count 43 after the hyphen. The mass number adds the protons in too: 34 + 43 = 77, so the name form is selenium-77."
 },
 {
  "value": "selenium-9",
  "misconception": "you subtracted the counts — the mass number adds them",
  "feedback": "This answer is wrong — you subtracted the counts (43 − 34 = 9). The mass number adds them: 34 + 43 = 77, so the name form is selenium-77."
 },
 {
  "value": "selenium 77",
  "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
  "feedback": "This answer is wrong as written — the mass number 77 is right, but the name form joins the element name to the mass number with a hyphen: selenium-77."
 }
]

{
 "keyExplanation": "The name form is the element name, a hyphen, and the mass number.\nmass number = protons + neutrons\nmass number = 34 + 43 = 77\nSo the name form is selenium-77 — the element name, a hyphen, then the mass number. The number after the hyphen is never the proton count 34 or the neutron count 43 alone.",
 "anticipatedWrong": [
  {
   "value": "selenium-34",
   "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
   "feedback": "This answer is wrong — you put the proton count 34 after the hyphen. The name form carries the mass number: 34 + 43 = 77, so this atom is selenium-77."
  },
  {
   "value": "selenium-43",
   "misconception": "you used the neutron count alone — the mass number adds the protons in too",
   "feedback": "This answer is wrong — you put the neutron count 43 after the hyphen. The mass number adds the protons in too: 34 + 43 = 77, so the name form is selenium-77."
  },
  {
   "value": "selenium-9",
   "misconception": "you subtracted the counts — the mass number adds them",
   "feedback": "This answer is wrong — you subtracted the counts (43 − 34 = 9). The mass number adds them: 34 + 43 = 77, so the name form is selenium-77."
  },
  {
   "value": "selenium 77",
   "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
   "feedback": "This answer is wrong as written — the mass number 77 is right, but the name form joins the element name to the mass number with a hyphen: selenium-77."
  }
 ]
}

[
 "Write down the values in the question:",
 "protons = 3",
 "neutrons = 3",
 "Write down the relationship:",
 "nucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)",
 "Substitute in the values, and calculate:",
 "nucleus mass ≈ 3 + 3",
 "nucleus mass ≈ 6 amu"
]

[
 {
  "value": 3,
  "misconception": "you counted only one kind of particle — the other 3 particles also contribute about 1 amu each",
  "feedback": "This answer is wrong — 3 counts only the protons (or only the neutrons). Each of the lithium nucleus's 3 protons AND each of its 3 neutrons contributes about 1 amu: 3 + 3 = 6 amu."
 },
 {
  "value": 9,
  "misconception": "you added the 3 electrons in as if each weighed about 1 amu — electrons weigh only about 1/2000 amu and never count toward the nucleus's mass",
  "feedback": "This answer is wrong — you added the 3 electrons in as if each weighed about 1 amu. An electron weighs only about 1/2000 amu, so the electrons add nothing noticeable: the nucleus's 3 protons + 3 neutrons make the mass about 6 amu."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 3\nneutrons = 3\nWrite down the relationship:\nnucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)\nSubstitute in the values, and calculate:\nnucleus mass ≈ 3 + 3\nnucleus mass ≈ 6 amu",
 "anticipatedWrong": [
  {
   "value": 3,
   "misconception": "you counted only one kind of particle — the other 3 particles also contribute about 1 amu each",
   "feedback": "This answer is wrong — 3 counts only the protons (or only the neutrons). Each of the lithium nucleus's 3 protons AND each of its 3 neutrons contributes about 1 amu: 3 + 3 = 6 amu."
  },
  {
   "value": 9,
   "misconception": "you added the 3 electrons in as if each weighed about 1 amu — electrons weigh only about 1/2000 amu and never count toward the nucleus's mass",
   "feedback": "This answer is wrong — you added the 3 electrons in as if each weighed about 1 amu. An electron weighs only about 1/2000 amu, so the electrons add nothing noticeable: the nucleus's 3 protons + 3 neutrons make the mass about 6 amu."
  }
 ]
}

[
 {
  "value": 64,
  "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 64 is the entry's decimal value 63.55 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 29 is the atomic number, and it is the proton count."
 },
 {
  "value": 35,
  "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
  "feedback": "This answer is wrong — 35 comes from 64 − 29, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 29 is the atomic number, and the atomic number itself is the proton count."
 }
]

{
 "keyExplanation": "The whole number on the entry is the atomic number: 29. The atomic number is the proton count. Every atom of this element — copper — has 29 protons.",
 "anticipatedWrong": [
  {
   "value": 64,
   "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 64 is the entry's decimal value 63.55 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 29 is the atomic number, and it is the proton count."
  },
  {
   "value": 35,
   "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
   "feedback": "This answer is wrong — 35 comes from 64 − 29, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 29 is the atomic number, and the atomic number itself is the proton count."
  }
 ]
}

[
 {
  "value": 77,
  "misconception": "you counted only the protons — the mass number adds the neutrons in too",
  "feedback": "This answer is wrong — 77 counts only the iridium atom's protons; the mass number adds its 114 neutrons in too: 77 + 114 = 191."
 },
 {
  "value": 114,
  "misconception": "you counted only the neutrons — the mass number adds the protons in too",
  "feedback": "This answer is wrong — 114 counts only the iridium atom's neutrons; the mass number adds its 77 protons in too: 77 + 114 = 191."
 },
 {
  "value": 268,
  "misconception": "you added the electrons in as well — electrons are nearly 2000 times lighter and are not counted",
  "feedback": "This answer is wrong — you added the electrons in as well; electrons are nearly 2000 times lighter and are not counted. The mass number counts only the iridium atom's protons and neutrons: 77 + 114 = 191."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 77\nneutrons = 114\nWrite down the relationship:\nmass number = protons + neutrons\nSubstitute in the values, and calculate:\nmass number = 77 + 114\nmass number = 191"
}

[
 "Write down the values in the question:",
 "mass number = 139",
 "atomic number = 57",
 "Write down the relationship:",
 "mass number = atomic number + neutron count",
 "Make the neutron count the subject:",
 "neutron count = mass number − atomic number",
 "Substitute in the values, and calculate:",
 "neutron count = 139 − 57",
 "neutron count = 82 neutrons"
]

[
 {
  "value": 196,
  "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
  "feedback": "This answer is wrong — you added the mass number and the atomic number. The lanthanum atom's mass number 139 already contains its 57 protons, so the neutron count is what is left after subtracting: 139 − 57 = 82 neutrons."
 },
 {
  "value": 57,
  "misconception": "you reported the atomic number, which is the proton count",
  "feedback": "This answer is wrong — 57 is lanthanum's atomic number, which counts the protons. The neutron count is the rest of the mass number: 139 − 57 = 82 neutrons."
 },
 {
  "value": 139,
  "misconception": "you reported the mass number, which counts protons and neutrons together",
  "feedback": "This answer is wrong — 139 is the lanthanum atom's mass number, which counts the protons and neutrons together. Subtract the 57 protons to leave the neutrons: 139 − 57 = 82 neutrons."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass number = 139\natomic number = 57\nWrite down the relationship:\nmass number = atomic number + neutron count\nMake the neutron count the subject:\nneutron count = mass number − atomic number\nSubstitute in the values, and calculate:\nneutron count = 139 − 57\nneutron count = 82 neutrons",
 "anticipatedWrong": [
  {
   "value": 196,
   "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
   "feedback": "This answer is wrong — you added the mass number and the atomic number. The lanthanum atom's mass number 139 already contains its 57 protons, so the neutron count is what is left after subtracting: 139 − 57 = 82 neutrons."
  },
  {
   "value": 57,
   "misconception": "you reported the atomic number, which is the proton count",
   "feedback": "This answer is wrong — 57 is lanthanum's atomic number, which counts the protons. The neutron count is the rest of the mass number: 139 − 57 = 82 neutrons."
  },
  {
   "value": 139,
   "misconception": "you reported the mass number, which counts protons and neutrons together",
   "feedback": "This answer is wrong — 139 is the lanthanum atom's mass number, which counts the protons and neutrons together. Subtract the 57 protons to leave the neutrons: 139 − 57 = 82 neutrons."
  }
 ]
}

[
 {
  "value": "hafnium-72",
  "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
  "feedback": "This answer is wrong — you put the proton count 72 after the hyphen. The name form carries the mass number: 72 + 106 = 178, so this atom is hafnium-178."
 },
 {
  "value": "hafnium-106",
  "misconception": "you used the neutron count alone — the mass number adds the protons in too",
  "feedback": "This answer is wrong — you put the neutron count 106 after the hyphen. The mass number adds the protons in too: 72 + 106 = 178, so the name form is hafnium-178."
 },
 {
  "value": "hafnium-34",
  "misconception": "you subtracted the counts — the mass number adds them",
  "feedback": "This answer is wrong — you subtracted the counts (106 − 72 = 34). The mass number adds them: 72 + 106 = 178, so the name form is hafnium-178."
 },
 {
  "value": "hafnium 178",
  "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
  "feedback": "This answer is wrong as written — the mass number 178 is right, but the name form joins the element name to the mass number with a hyphen: hafnium-178."
 }
]

{
 "keyExplanation": "The name form is the element name, a hyphen, and the mass number.\nmass number = protons + neutrons\nmass number = 72 + 106 = 178\nSo the name form is hafnium-178 — the element name, a hyphen, then the mass number. The number after the hyphen is never the proton count 72 or the neutron count 106 alone.",
 "anticipatedWrong": [
  {
   "value": "hafnium-72",
   "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
   "feedback": "This answer is wrong — you put the proton count 72 after the hyphen. The name form carries the mass number: 72 + 106 = 178, so this atom is hafnium-178."
  },
  {
   "value": "hafnium-106",
   "misconception": "you used the neutron count alone — the mass number adds the protons in too",
   "feedback": "This answer is wrong — you put the neutron count 106 after the hyphen. The mass number adds the protons in too: 72 + 106 = 178, so the name form is hafnium-178."
  },
  {
   "value": "hafnium-34",
   "misconception": "you subtracted the counts — the mass number adds them",
   "feedback": "This answer is wrong — you subtracted the counts (106 − 72 = 34). The mass number adds them: 72 + 106 = 178, so the name form is hafnium-178."
  },
  {
   "value": "hafnium 178",
   "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
   "feedback": "This answer is wrong as written — the mass number 178 is right, but the name form joins the element name to the mass number with a hyphen: hafnium-178."
  }
 ]
}

[
 "Write down the values in the question:",
 "protons = 10",
 "neutrons = 10",
 "Write down the relationship:",
 "nucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)",
 "Substitute in the values, and calculate:",
 "nucleus mass ≈ 10 + 10",
 "nucleus mass ≈ 20 amu"
]

[
 {
  "value": 10,
  "misconception": "you counted only one kind of particle — the other 10 particles also contribute about 1 amu each",
  "feedback": "This answer is wrong — 10 counts only the protons (or only the neutrons). Each of the neon nucleus's 10 protons AND each of its 10 neutrons contributes about 1 amu: 10 + 10 = 20 amu."
 },
 {
  "value": 100,
  "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
  "feedback": "This answer is wrong — you multiplied 10 by 10. Each particle contributes about 1 amu, so the counts add: 10 + 10 = 20 amu."
 },
 {
  "value": 30,
  "misconception": "you added the electrons in as well at about 1 amu each — electrons are about 1/2000 amu and are not counted",
  "feedback": "This answer is wrong — you counted the neon atom's 10 electrons at about 1 amu each. Electrons are about 1/2000 amu each, far too light to count: the nucleus's 10 protons and 10 neutrons give 10 + 10 = 20 amu."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 10\nneutrons = 10\nWrite down the relationship:\nnucleus mass in amu ≈ proton count + neutron count (each proton and each neutron contributes about 1 amu; electrons are about 1/2000 amu and are not counted)\nSubstitute in the values, and calculate:\nnucleus mass ≈ 10 + 10\nnucleus mass ≈ 20 amu",
 "anticipatedWrong": [
  {
   "value": 10,
   "misconception": "you counted only one kind of particle — the other 10 particles also contribute about 1 amu each",
   "feedback": "This answer is wrong — 10 counts only the protons (or only the neutrons). Each of the neon nucleus's 10 protons AND each of its 10 neutrons contributes about 1 amu: 10 + 10 = 20 amu."
  },
  {
   "value": 100,
   "misconception": "you multiplied the counts instead of adding them — each particle contributes about 1 amu, so the counts add",
   "feedback": "This answer is wrong — you multiplied 10 by 10. Each particle contributes about 1 amu, so the counts add: 10 + 10 = 20 amu."
  },
  {
   "value": 30,
   "misconception": "you added the electrons in as well at about 1 amu each — electrons are about 1/2000 amu and are not counted",
   "feedback": "This answer is wrong — you counted the neon atom's 10 electrons at about 1 amu each. Electrons are about 1/2000 amu each, far too light to count: the nucleus's 10 protons and 10 neutrons give 10 + 10 = 20 amu."
  }
 ]
}

[
 {
  "value": 7,
  "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
  "feedback": "This answer is wrong — 7 is the entry's decimal value 6.94 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 3 is the atomic number, and it is the proton count."
 },
 {
  "value": 4,
  "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
  "feedback": "This answer is wrong — 4 comes from 7 − 3, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 3 is the atomic number, and the atomic number itself is the proton count."
 }
]

{
 "keyExplanation": "The whole number on the entry is the atomic number: 3. The atomic number is the proton count. Every atom of this element — lithium — has 3 protons.",
 "anticipatedWrong": [
  {
   "value": 7,
   "misconception": "you rounded the decimal number on the entry — that value is the decimal mass value printed on the tile, not the atomic number",
   "feedback": "This answer is wrong — 7 is the entry's decimal value 6.94 rounded. That decimal is the decimal mass value printed on the tile, not the atomic number. The whole number 3 is the atomic number, and it is the proton count."
  },
  {
   "value": 4,
   "misconception": "you subtracted the atomic number from the rounded decimal value — the atomic number itself is the proton count",
   "feedback": "This answer is wrong — 4 comes from 7 − 3, subtracting the atomic number from the rounded decimal value. No subtraction is needed here: the whole number 3 is the atomic number, and the atomic number itself is the proton count."
  }
 ]
}

[
 {
  "value": 68,
  "misconception": "you counted only the protons — the mass number adds the neutrons in too",
  "feedback": "This answer is wrong — 68 counts only the erbium atom's protons; the mass number adds its 98 neutrons in too: 68 + 98 = 166."
 },
 {
  "value": 98,
  "misconception": "you counted only the neutrons — the mass number adds the protons in too",
  "feedback": "This answer is wrong — 98 counts only the erbium atom's neutrons; the mass number adds its 68 protons in too: 68 + 98 = 166."
 },
 {
  "value": 234,
  "misconception": "you added the electrons in as well — electrons are nearly 2000 times lighter and are not counted",
  "feedback": "This answer is wrong — you added the electrons in as well; electrons are nearly 2000 times lighter and are not counted. The mass number counts only the erbium atom's protons and neutrons: 68 + 98 = 166."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nprotons = 68\nneutrons = 98\nWrite down the relationship:\nmass number = protons + neutrons\nSubstitute in the values, and calculate:\nmass number = 68 + 98\nmass number = 166"
}

[
 "Write down the values in the question:",
 "mass number = 165",
 "atomic number = 67",
 "Write down the relationship:",
 "mass number = atomic number + neutron count",
 "Make the neutron count the subject:",
 "neutron count = mass number − atomic number",
 "Substitute in the values, and calculate:",
 "neutron count = 165 − 67",
 "neutron count = 98 neutrons"
]

[
 {
  "value": 232,
  "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
  "feedback": "This answer is wrong — you added the mass number and the atomic number. The holmium atom's mass number 165 already contains its 67 protons, so the neutron count is what is left after subtracting: 165 − 67 = 98 neutrons."
 },
 {
  "value": 67,
  "misconception": "you reported the atomic number, which is the proton count",
  "feedback": "This answer is wrong — 67 is holmium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 165 − 67 = 98 neutrons."
 },
 {
  "value": 165,
  "misconception": "you reported the mass number, which counts protons and neutrons together",
  "feedback": "This answer is wrong — 165 is the holmium atom's mass number, which counts the protons and neutrons together. Subtract the 67 protons to leave the neutrons: 165 − 67 = 98 neutrons."
 }
]

{
 "keyExplanation": "Write down the values in the question:\nmass number = 165\natomic number = 67\nWrite down the relationship:\nmass number = atomic number + neutron count\nMake the neutron count the subject:\nneutron count = mass number − atomic number\nSubstitute in the values, and calculate:\nneutron count = 165 − 67\nneutron count = 98 neutrons",
 "anticipatedWrong": [
  {
   "value": 232,
   "misconception": "you added the two numbers instead of subtracting — the mass number already contains the protons",
   "feedback": "This answer is wrong — you added the mass number and the atomic number. The holmium atom's mass number 165 already contains its 67 protons, so the neutron count is what is left after subtracting: 165 − 67 = 98 neutrons."
  },
  {
   "value": 67,
   "misconception": "you reported the atomic number, which is the proton count",
   "feedback": "This answer is wrong — 67 is holmium's atomic number, which counts the protons. The neutron count is the rest of the mass number: 165 − 67 = 98 neutrons."
  },
  {
   "value": 165,
   "misconception": "you reported the mass number, which counts protons and neutrons together",
   "feedback": "This answer is wrong — 165 is the holmium atom's mass number, which counts the protons and neutrons together. Subtract the 67 protons to leave the neutrons: 165 − 67 = 98 neutrons."
  }
 ]
}

[
 {
  "value": "erbium-68",
  "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
  "feedback": "This answer is wrong — you put the proton count 68 after the hyphen. The name form carries the mass number: 68 + 99 = 167, so this atom is erbium-167."
 },
 {
  "value": "erbium-99",
  "misconception": "you used the neutron count alone — the mass number adds the protons in too",
  "feedback": "This answer is wrong — you put the neutron count 99 after the hyphen. The mass number adds the protons in too: 68 + 99 = 167, so the name form is erbium-167."
 },
 {
  "value": "erbium-31",
  "misconception": "you subtracted the counts — the mass number adds them",
  "feedback": "This answer is wrong — you subtracted the counts (99 − 68 = 31). The mass number adds them: 68 + 99 = 167, so the name form is erbium-167."
 },
 {
  "value": "erbium 167",
  "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
  "feedback": "This answer is wrong as written — the mass number 167 is right, but the name form joins the element name to the mass number with a hyphen: erbium-167."
 }
]

{
 "keyExplanation": "The name form is the element name, a hyphen, and the mass number.\nmass number = protons + neutrons\nmass number = 68 + 99 = 167\nSo the name form is erbium-167 — the element name, a hyphen, then the mass number. The number after the hyphen is never the proton count 68 or the neutron count 99 alone.",
 "anticipatedWrong": [
  {
   "value": "erbium-68",
   "misconception": "you used the proton count as the number — the name form carries the mass number, protons plus neutrons",
   "feedback": "This answer is wrong — you put the proton count 68 after the hyphen. The name form carries the mass number: 68 + 99 = 167, so this atom is erbium-167."
  },
  {
   "value": "erbium-99",
   "misconception": "you used the neutron count alone — the mass number adds the protons in too",
   "feedback": "This answer is wrong — you put the neutron count 99 after the hyphen. The mass number adds the protons in too: 68 + 99 = 167, so the name form is erbium-167."
  },
  {
   "value": "erbium-31",
   "misconception": "you subtracted the counts — the mass number adds them",
   "feedback": "This answer is wrong — you subtracted the counts (99 − 68 = 31). The mass number adds them: 68 + 99 = 167, so the name form is erbium-167."
  },
  {
   "value": "erbium 167",
   "misconception": "you left out the hyphen — the name form joins the element name to the mass number with a hyphen",
   "feedback": "This answer is wrong as written — the mass number 167 is right, but the name form joins the element name to the mass number with a hyphen: erbium-167."
  }
 ]
}

[
 "Write the percent abundance as a decimal fraction:",
 "fraction of boron-11 = 80.1% → 0.801",
 "Write down the equation:",
 "contribution of boron-11 = fraction × mass",
 "Substitute in the values, and calculate:",
 "contribution of boron-11 = 0.801 × 11.0",
 "contribution of boron-11 = 8.811 amu"
]

[
 {
  "value": 881.1,
  "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
  "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 80.1% → 0.801, and the boron-11 term is 0.801 × 11.0 = 8.811 amu."
 },
 {
  "value": 11.0,
  "misconception": "you reported boron-11's whole mass instead of its fraction × mass share",
  "feedback": "This answer is wrong — you reported boron-11's whole mass. Its term in the average is only its share: the fraction 0.801 times the mass 11.0 amu, which is 8.811 amu."
 },
 {
  "value": 0.8811,
  "misconception": "you shifted the decimal one place too far and turned 80.1% into 0.0801",
  "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 80.1% into 0.0801. Dividing the percent by 100 gives 0.801, and 0.801 × 11.0 = 8.811 amu."
 }
]

{
 "keyExplanation": "Write the percent abundance as a decimal fraction:\nfraction of boron-11 = 80.1% → 0.801\nWrite down the equation:\ncontribution of boron-11 = fraction × mass\nSubstitute in the values, and calculate:\ncontribution of boron-11 = 0.801 × 11.0\ncontribution of boron-11 = 8.811 amu\nAn isotope's fraction is less than 1, so its term must be smaller than its own mass — 8.811 amu sits below 11.0 amu and passes that check; 881.1 does not.",
 "anticipatedWrong": [
  {
   "value": 881.1,
   "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
   "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 80.1% → 0.801, and the boron-11 term is 0.801 × 11.0 = 8.811 amu."
  },
  {
   "value": 11.0,
   "misconception": "you reported boron-11's whole mass instead of its fraction × mass share",
   "feedback": "This answer is wrong — you reported boron-11's whole mass. Its term in the average is only its share: the fraction 0.801 times the mass 11.0 amu, which is 8.811 amu."
  },
  {
   "value": 0.8811,
   "misconception": "you shifted the decimal one place too far and turned 80.1% into 0.0801",
   "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 80.1% into 0.0801. Dividing the percent by 100 gives 0.801, and 0.801 × 11.0 = 8.811 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of neon-20 = 90.0% → 0.900",
 "fraction of neon-22 = 10.0% → 0.100",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.900 × 20.0) + (0.100 × 22.0)",
 "average atomic mass = 18.0 + 2.20",
 "average atomic mass = 20.2 amu"
]

[
 {
  "value": 21.0,
  "misconception": "you averaged the two masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Neon-20 makes up 90.0% of natural neon, so its mass counts for far more: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
 },
 {
  "value": 20.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Neon-22's 10.0% still pulls the average above 20.0: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
 },
 {
  "value": 2020,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write neon-20's 90.0% as 0.900 and neon-22's 10.0% as 0.100 first: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
 },
 {
  "value": 21.8,
  "misconception": "you swapped the two abundances between the isotopes",
  "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Neon-20 carries the 90.0%, not neon-22: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of neon-20 = 90.0% → 0.900\nfraction of neon-22 = 10.0% → 0.100\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.900 × 20.0) + (0.100 × 22.0)\naverage atomic mass = 18.0 + 2.20\naverage atomic mass = 20.2 amu\nThe average must land between 20.0 and 22.0, close to 20.0 because neon-20 dominates — a weighted average is pulled toward the more abundant isotope, never to the halfway point.",
 "anticipatedWrong": [
  {
   "value": 21.0,
   "misconception": "you averaged the two masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Neon-20 makes up 90.0% of natural neon, so its mass counts for far more: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
  },
  {
   "value": 20.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Neon-22's 10.0% still pulls the average above 20.0: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
  },
  {
   "value": 2020,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write neon-20's 90.0% as 0.900 and neon-22's 10.0% as 0.100 first: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
  },
  {
   "value": 21.8,
   "misconception": "you swapped the two abundances between the isotopes",
   "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Neon-20 carries the 90.0%, not neon-22: (0.900 × 20.0) + (0.100 × 22.0) = 20.2 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of silicon-28 = 92.0% → 0.920",
 "fraction of silicon-29 = 5.00% → 0.0500",
 "fraction of silicon-30 = 3.00% → 0.0300",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0)",
 "average atomic mass = 25.76 + 1.45 + 0.900",
 "average atomic mass = 28.11 amu",
 "Rounded to 3 significant figures: 28.1 amu"
]

[
 {
  "value": 29.0,
  "misconception": "you averaged the three masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the three masses as if the isotopes were equally abundant. Silicon-28 carries 92.0% of the weight: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11, which rounds to 28.1 amu."
 },
 {
  "value": 28.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all three isotopes, so it lands just above 28.0: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11 → 28.1 amu."
 },
 {
  "value": 2811,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11 → 28.1 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of silicon-28 = 92.0% → 0.920\nfraction of silicon-29 = 5.00% → 0.0500\nfraction of silicon-30 = 3.00% → 0.0300\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0)\naverage atomic mass = 25.76 + 1.45 + 0.900\naverage atomic mass = 28.11 amu\nRounded to 3 significant figures: 28.1 amu\nSilicon-28 dominates, so the average sits just above 28.0 — not at the plain three-way average of 29.0.",
 "anticipatedWrong": [
  {
   "value": 29.0,
   "misconception": "you averaged the three masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the three masses as if the isotopes were equally abundant. Silicon-28 carries 92.0% of the weight: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11, which rounds to 28.1 amu."
  },
  {
   "value": 28.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all three isotopes, so it lands just above 28.0: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11 → 28.1 amu."
  },
  {
   "value": 2811,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.920 × 28.0) + (0.0500 × 29.0) + (0.0300 × 30.0) = 28.11 → 28.1 amu."
  }
 ]
}

[
 "Write the percent abundance as a decimal fraction:",
 "fraction of ruthenium-102 = 31.5% → 0.315",
 "Write down the equation:",
 "contribution of ruthenium-102 = fraction × mass",
 "Substitute in the values, and calculate:",
 "contribution of ruthenium-102 = 0.315 × 102.0",
 "contribution of ruthenium-102 = 32.13 amu"
]

[
 {
  "value": 3213,
  "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
  "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 31.5% → 0.315, and the ruthenium-102 term is 0.315 × 102.0 = 32.13 amu."
 },
 {
  "value": 102.0,
  "misconception": "you reported ruthenium-102's whole mass instead of its fraction × mass share",
  "feedback": "This answer is wrong — you reported ruthenium-102's whole mass. Its term in the average is only its share: the fraction 0.315 times the mass 102.0 amu, which is 32.13 amu."
 },
 {
  "value": 3.213,
  "misconception": "you shifted the decimal one place too far and turned 31.5% into 0.0315",
  "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 31.5% into 0.0315. Dividing the percent by 100 gives 0.315, and 0.315 × 102.0 = 32.13 amu."
 }
]

{
 "keyExplanation": "Write the percent abundance as a decimal fraction:\nfraction of ruthenium-102 = 31.5% → 0.315\nWrite down the equation:\ncontribution of ruthenium-102 = fraction × mass\nSubstitute in the values, and calculate:\ncontribution of ruthenium-102 = 0.315 × 102.0\ncontribution of ruthenium-102 = 32.13 amu\nAn isotope's fraction is less than 1, so its term must be smaller than its own mass — 32.13 amu sits below 102.0 amu and passes that check; 3213 does not.",
 "anticipatedWrong": [
  {
   "value": 3213,
   "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
   "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 31.5% → 0.315, and the ruthenium-102 term is 0.315 × 102.0 = 32.13 amu."
  },
  {
   "value": 102.0,
   "misconception": "you reported ruthenium-102's whole mass instead of its fraction × mass share",
   "feedback": "This answer is wrong — you reported ruthenium-102's whole mass. Its term in the average is only its share: the fraction 0.315 times the mass 102.0 amu, which is 32.13 amu."
  },
  {
   "value": 3.213,
   "misconception": "you shifted the decimal one place too far and turned 31.5% into 0.0315",
   "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 31.5% into 0.0315. Dividing the percent by 100 gives 0.315, and 0.315 × 102.0 = 32.13 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of sulfur-32 = 85% → 0.85",
 "fraction of sulfur-34 = 15% → 0.15",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.85 × 32.0) + (0.15 × 34.0)",
 "average atomic mass = 27.2 + 5.1",
 "average atomic mass = 32.3 amu"
]

[
 {
  "value": 33.0,
  "misconception": "you averaged the two masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Sulfur-32 makes up 85% of the atoms, so the average sits close to 32.0, not at the halfway point: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
 },
 {
  "value": 3230,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write sulfur-32's 85% as 0.85 and sulfur-34's 15% as 0.15 first: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
 },
 {
  "value": 33.7,
  "misconception": "you swapped the two abundances between the isotopes",
  "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Sulfur-32 carries the 85%, not sulfur-34: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
 },
 {
  "value": 32.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Sulfur-34's 15% still pulls the average above 32.0: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of sulfur-32 = 85% → 0.85\nfraction of sulfur-34 = 15% → 0.15\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.85 × 32.0) + (0.15 × 34.0)\naverage atomic mass = 27.2 + 5.1\naverage atomic mass = 32.3 amu\nThe average must land between 32.0 and 34.0, close to 32.0 because sulfur-32 dominates — 32.3 passes that check.",
 "anticipatedWrong": [
  {
   "value": 33.0,
   "misconception": "you averaged the two masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Sulfur-32 makes up 85% of the atoms, so the average sits close to 32.0, not at the halfway point: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
  },
  {
   "value": 3230,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write sulfur-32's 85% as 0.85 and sulfur-34's 15% as 0.15 first: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
  },
  {
   "value": 33.7,
   "misconception": "you swapped the two abundances between the isotopes",
   "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Sulfur-32 carries the 85%, not sulfur-34: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
  },
  {
   "value": 32.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Sulfur-34's 15% still pulls the average above 32.0: (0.85 × 32.0) + (0.15 × 34.0) = 32.3 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of sulfur-32 = 85% → 0.85",
 "fraction of sulfur-33 = 10% → 0.10",
 "fraction of sulfur-34 = 5% → 0.05",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0)",
 "average atomic mass = 27.2 + 3.3 + 1.7",
 "average atomic mass = 32.2 amu",
 "Rounded to 3 significant figures: 32.2 amu"
]

[
 {
  "value": 33.0,
  "misconception": "you averaged the three masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the three masses as if the isotopes were equally abundant. Sulfur-32 carries 85% of the weight: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
 },
 {
  "value": 32.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all three isotopes, so it lands just above 32.0: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
 },
 {
  "value": 3220,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of sulfur-32 = 85% → 0.85\nfraction of sulfur-33 = 10% → 0.10\nfraction of sulfur-34 = 5% → 0.05\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0)\naverage atomic mass = 27.2 + 3.3 + 1.7\naverage atomic mass = 32.2 amu (already 3 significant figures)\nSulfur-32 dominates, so the average sits just above 32.0 — not at the plain three-way average of 33.0.",
 "anticipatedWrong": [
  {
   "value": 33.0,
   "misconception": "you averaged the three masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the three masses as if the isotopes were equally abundant. Sulfur-32 carries 85% of the weight: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
  },
  {
   "value": 32.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all three isotopes, so it lands just above 32.0: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
  },
  {
   "value": 3220,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.85 × 32.0) + (0.10 × 33.0) + (0.05 × 34.0) = 32.2 amu."
  }
 ]
}

[
 "Write the percent abundance as a decimal fraction:",
 "fraction of titanium-48 = 73.5% → 0.735",
 "Write down the equation:",
 "contribution of titanium-48 = fraction × mass",
 "Substitute in the values, and calculate:",
 "contribution of titanium-48 = 0.735 × 48.0",
 "contribution of titanium-48 = 35.28 amu"
]

[
 {
  "value": 3528,
  "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
  "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 73.5% → 0.735, and the titanium-48 term is 0.735 × 48.0 = 35.28 amu."
 },
 {
  "value": 48.0,
  "misconception": "you reported titanium-48's whole mass instead of its fraction × mass share",
  "feedback": "This answer is wrong — you reported titanium-48's whole mass. Its term in the average is only its share: the fraction 0.735 times the mass 48.0 amu, which is 35.28 amu."
 },
 {
  "value": 3.528,
  "misconception": "you shifted the decimal one place too far and turned 73.5% into 0.0735",
  "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 73.5% into 0.0735. Dividing the percent by 100 gives 0.735, and 0.735 × 48.0 = 35.28 amu."
 }
]

{
 "keyExplanation": "Write the percent abundance as a decimal fraction:\nfraction of titanium-48 = 73.5% → 0.735\nWrite down the equation:\ncontribution of titanium-48 = fraction × mass\nSubstitute in the values, and calculate:\ncontribution of titanium-48 = 0.735 × 48.0\ncontribution of titanium-48 = 35.28 amu\nAn isotope's fraction is less than 1, so its term must be smaller than its own mass — 35.28 amu sits below 48.0 amu and passes that check; 3528 does not.",
 "anticipatedWrong": [
  {
   "value": 3528,
   "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
   "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 73.5% → 0.735, and the titanium-48 term is 0.735 × 48.0 = 35.28 amu."
  },
  {
   "value": 48.0,
   "misconception": "you reported titanium-48's whole mass instead of its fraction × mass share",
   "feedback": "This answer is wrong — you reported titanium-48's whole mass. Its term in the average is only its share: the fraction 0.735 times the mass 48.0 amu, which is 35.28 amu."
  },
  {
   "value": 3.528,
   "misconception": "you shifted the decimal one place too far and turned 73.5% into 0.0735",
   "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 73.5% into 0.0735. Dividing the percent by 100 gives 0.735, and 0.735 × 48.0 = 35.28 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of calcium-40 = 97.5% → 0.975",
 "fraction of calcium-44 = 2.5% → 0.025",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.975 × 40.0) + (0.025 × 44.0)",
 "average atomic mass = 39.0 + 1.10",
 "average atomic mass = 40.1 amu"
]

[
 {
  "value": 42.0,
  "misconception": "you averaged the two masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Calcium-40 makes up 97.5% of the atoms, so the average sits close to 40.0, not at the halfway point: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
 },
 {
  "value": 4010,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write calcium-40's 97.5% as 0.975 and calcium-44's 2.5% as 0.025 first: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
 },
 {
  "value": 43.9,
  "misconception": "you swapped the two abundances between the isotopes",
  "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Calcium-40 carries the 97.5%, not calcium-44: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
 },
 {
  "value": 40.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Calcium-44's 2.5% still pulls the average above 40.0: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of calcium-40 = 97.5% → 0.975\nfraction of calcium-44 = 2.5% → 0.025\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.975 × 40.0) + (0.025 × 44.0)\naverage atomic mass = 39.0 + 1.10\naverage atomic mass = 40.1 amu\nThe average must land between 40.0 and 44.0, close to 40.0 because calcium-40 dominates — 40.1 passes that check.",
 "anticipatedWrong": [
  {
   "value": 42.0,
   "misconception": "you averaged the two masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Calcium-40 makes up 97.5% of the atoms, so the average sits close to 40.0, not at the halfway point: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
  },
  {
   "value": 4010,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write calcium-40's 97.5% as 0.975 and calcium-44's 2.5% as 0.025 first: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
  },
  {
   "value": 43.9,
   "misconception": "you swapped the two abundances between the isotopes",
   "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Calcium-40 carries the 97.5%, not calcium-44: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
  },
  {
   "value": 40.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Calcium-44's 2.5% still pulls the average above 40.0: (0.975 × 40.0) + (0.025 × 44.0) = 40.1 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of tungsten-182 = 27.0% → 0.270",
 "fraction of tungsten-183 = 12.0% → 0.120",
 "fraction of tungsten-184 = 32.5% → 0.325",
 "fraction of tungsten-186 = 28.5% → 0.285",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0)",
 "average atomic mass = 49.14 + 21.96 + 59.80 + 53.01",
 "average atomic mass = 183.91 amu",
 "Rounded to 4 significant figures: 183.9 amu"
]

[
 {
  "value": 183.75,
  "misconception": "you averaged the four masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the four masses as if the isotopes were equally abundant. Each mass must be weighted by its fraction: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91, which rounds to 183.9 amu."
 },
 {
  "value": 184.0,
  "misconception": "you reported a single isotope mass (or over-rounded the true average) instead of the unrounded 4-significant-figure weighted average",
  "feedback": "This answer is wrong — 184.0 amu is what you get by reporting the most abundant isotope’s mass, or by rounding the correct average too far. Weight each mass by its fraction and keep 4 significant figures: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91, reported as 183.9 amu."
 },
 {
  "value": 18391,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91 → 183.9 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of tungsten-182 = 27.0% → 0.270\nfraction of tungsten-183 = 12.0% → 0.120\nfraction of tungsten-184 = 32.5% → 0.325\nfraction of tungsten-186 = 28.5% → 0.285\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0)\naverage atomic mass = 49.14 + 21.96 + 59.80 + 53.01\naverage atomic mass = 183.91 amu\nRounded to 4 significant figures: 183.9 amu\nThe average must land between 182.0 and 186.0, pulled toward the more abundant tungsten-184 — 183.9 passes that check, dragged just below 184.0 by the lighter isotopes.",
 "anticipatedWrong": [
  {
   "value": 183.75,
   "misconception": "you averaged the four masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the four masses as if the isotopes were equally abundant. Each mass must be weighted by its fraction: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91, which rounds to 183.9 amu."
  },
  {
   "value": 184.0,
   "misconception": "you reported a single isotope mass (or over-rounded the true average) instead of the unrounded 4-significant-figure weighted average",
   "feedback": "This answer is wrong — 184.0 amu is what you get by reporting the most abundant isotope’s mass, or by rounding the correct average too far. Weight each mass by its fraction and keep 4 significant figures: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91, reported as 183.9 amu."
  },
  {
   "value": 18391,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.270 × 182.0) + (0.120 × 183.0) + (0.325 × 184.0) + (0.285 × 186.0) = 183.91 → 183.9 amu."
  }
 ]
}

[
 "Write the percent abundance as a decimal fraction:",
 "fraction of erbium-166 = 33.5% → 0.335",
 "Write down the equation:",
 "contribution of erbium-166 = fraction × mass",
 "Substitute in the values, and calculate:",
 "contribution of erbium-166 = 0.335 × 166.0",
 "contribution of erbium-166 = 55.61 amu"
]

[
 {
  "value": 5561,
  "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
  "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 33.5% → 0.335, and the erbium-166 term is 0.335 × 166.0 = 55.61 amu."
 },
 {
  "value": 166.0,
  "misconception": "you reported erbium-166's whole mass instead of its fraction × mass share",
  "feedback": "This answer is wrong — you reported erbium-166's whole mass. Its term in the average is only its share: the fraction 0.335 times the mass 166.0 amu, which is 55.61 amu."
 },
 {
  "value": 5.561,
  "misconception": "you shifted the decimal one place too far and turned 33.5% into 0.0335",
  "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 33.5% into 0.0335. Dividing the percent by 100 gives 0.335, and 0.335 × 166.0 = 55.61 amu."
 }
]

{
 "keyExplanation": "Write the percent abundance as a decimal fraction:\nfraction of erbium-166 = 33.5% → 0.335\nWrite down the equation:\ncontribution of erbium-166 = fraction × mass\nSubstitute in the values, and calculate:\ncontribution of erbium-166 = 0.335 × 166.0\ncontribution of erbium-166 = 55.61 amu\nAn isotope's fraction is less than 1, so its term must be smaller than its own mass — 55.61 amu sits below 166.0 amu and passes that check; 5561 does not.",
 "anticipatedWrong": [
  {
   "value": 5561,
   "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
   "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 33.5% → 0.335, and the erbium-166 term is 0.335 × 166.0 = 55.61 amu."
  },
  {
   "value": 166.0,
   "misconception": "you reported erbium-166's whole mass instead of its fraction × mass share",
   "feedback": "This answer is wrong — you reported erbium-166's whole mass. Its term in the average is only its share: the fraction 0.335 times the mass 166.0 amu, which is 55.61 amu."
  },
  {
   "value": 5.561,
   "misconception": "you shifted the decimal one place too far and turned 33.5% into 0.0335",
   "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 33.5% into 0.0335. Dividing the percent by 100 gives 0.335, and 0.335 × 166.0 = 55.61 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of cerium-140 = 95% → 0.95",
 "fraction of cerium-142 = 5% → 0.05",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.95 × 140.0) + (0.05 × 142.0)",
 "average atomic mass = 133.0 + 7.10",
 "average atomic mass = 140.1 amu"
]

[
 {
  "value": 141.0,
  "misconception": "you averaged the two masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Cerium-140 makes up 95% of the atoms, so the average sits close to 140.0, not at the halfway point: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
 },
 {
  "value": 14010,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write cerium-140's 95% as 0.95 and cerium-142's 5% as 0.05 first: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
 },
 {
  "value": 141.9,
  "misconception": "you swapped the two abundances between the isotopes",
  "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Cerium-140 carries the 95%, not cerium-142: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
 },
 {
  "value": 140.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Cerium-142's 5% still pulls the average above 140.0: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of cerium-140 = 95% → 0.95\nfraction of cerium-142 = 5% → 0.05\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.95 × 140.0) + (0.05 × 142.0)\naverage atomic mass = 133.0 + 7.10\naverage atomic mass = 140.1 amu\nThe average must land between 140.0 and 142.0, close to 140.0 because cerium-140 dominates — 140.1 passes that check.",
 "anticipatedWrong": [
  {
   "value": 141.0,
   "misconception": "you averaged the two masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Cerium-140 makes up 95% of the atoms, so the average sits close to 140.0, not at the halfway point: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
  },
  {
   "value": 14010,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write cerium-140's 95% as 0.95 and cerium-142's 5% as 0.05 first: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
  },
  {
   "value": 141.9,
   "misconception": "you swapped the two abundances between the isotopes",
   "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Cerium-140 carries the 95%, not cerium-142: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
  },
  {
   "value": 140.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Cerium-142's 5% still pulls the average above 140.0: (0.95 × 140.0) + (0.05 × 142.0) = 140.1 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of iron-54 = 6.00% → 0.0600",
 "fraction of iron-56 = 91.0% → 0.910",
 "fraction of iron-57 = 2.00% → 0.0200",
 "fraction of iron-58 = 1.00% → 0.0100",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0)",
 "average atomic mass = 3.24 + 50.96 + 1.14 + 0.58",
 "average atomic mass = 55.92 amu",
 "Rounded to 3 significant figures: 55.9 amu"
]

[
 {
  "value": 56.25,
  "misconception": "you averaged the four masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the four masses as if the isotopes were equally abundant. Iron-56 carries 91.0% of the weight: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92, which rounds to 55.9 amu."
 },
 {
  "value": 56.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all four isotopes, so it lands just below 56.0: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92 → 55.9 amu."
 },
 {
  "value": 5592,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92 → 55.9 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of iron-54 = 6.00% → 0.0600\nfraction of iron-56 = 91.0% → 0.910\nfraction of iron-57 = 2.00% → 0.0200\nfraction of iron-58 = 1.00% → 0.0100\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0)\naverage atomic mass = 3.24 + 50.96 + 1.14 + 0.58\naverage atomic mass = 55.92 amu\nRounded to 3 significant figures: 55.9 amu\nIron-56 dominates, so the average sits just below 56.0, pulled down mainly by iron-54 — not at the plain four-way average of 56.25.",
 "anticipatedWrong": [
  {
   "value": 56.25,
   "misconception": "you averaged the four masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the four masses as if the isotopes were equally abundant. Iron-56 carries 91.0% of the weight: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92, which rounds to 55.9 amu."
  },
  {
   "value": 56.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all four isotopes, so it lands just below 56.0: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92 → 55.9 amu."
  },
  {
   "value": 5592,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.0600 × 54.0) + (0.910 × 56.0) + (0.0200 × 57.0) + (0.0100 × 58.0) = 55.92 → 55.9 amu."
  }
 ]
}

[
 "Write the percent abundance as a decimal fraction:",
 "fraction of samarium-152 = 26.5% → 0.265",
 "Write down the equation:",
 "contribution of samarium-152 = fraction × mass",
 "Substitute in the values, and calculate:",
 "contribution of samarium-152 = 0.265 × 152.0",
 "contribution of samarium-152 = 40.28 amu"
]

[
 {
  "value": 4028,
  "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
  "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 26.5% → 0.265, and the samarium-152 term is 0.265 × 152.0 = 40.28 amu."
 },
 {
  "value": 152.0,
  "misconception": "you reported samarium-152's whole mass instead of its fraction × mass share",
  "feedback": "This answer is wrong — you reported samarium-152's whole mass. Its term in the average is only its share: the fraction 0.265 times the mass 152.0 amu, which is 40.28 amu."
 },
 {
  "value": 4.028,
  "misconception": "you shifted the decimal one place too far and turned 26.5% into 0.0265",
  "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 26.5% into 0.0265. Dividing the percent by 100 gives 0.265, and 0.265 × 152.0 = 40.28 amu."
 }
]

{
 "keyExplanation": "Write the percent abundance as a decimal fraction:\nfraction of samarium-152 = 26.5% → 0.265\nWrite down the equation:\ncontribution of samarium-152 = fraction × mass\nSubstitute in the values, and calculate:\ncontribution of samarium-152 = 0.265 × 152.0\ncontribution of samarium-152 = 40.28 amu\nAn isotope's fraction is less than 1, so its term must be smaller than its own mass — 40.28 amu sits below 152.0 amu and passes that check; 4028 does not.",
 "anticipatedWrong": [
  {
   "value": 4028,
   "misconception": "you multiplied by the percent without first writing it as a decimal fraction",
   "feedback": "This answer is wrong — you multiplied by the percent without first writing it as a decimal fraction. Divide the percent by 100 first: 26.5% → 0.265, and the samarium-152 term is 0.265 × 152.0 = 40.28 amu."
  },
  {
   "value": 152.0,
   "misconception": "you reported samarium-152's whole mass instead of its fraction × mass share",
   "feedback": "This answer is wrong — you reported samarium-152's whole mass. Its term in the average is only its share: the fraction 0.265 times the mass 152.0 amu, which is 40.28 amu."
  },
  {
   "value": 4.028,
   "misconception": "you shifted the decimal one place too far and turned 26.5% into 0.0265",
   "feedback": "This answer is wrong — you shifted the decimal one place too far and turned 26.5% into 0.0265. Dividing the percent by 100 gives 0.265, and 0.265 × 152.0 = 40.28 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of rhenium-185 = 45% → 0.45",
 "fraction of rhenium-187 = 55% → 0.55",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.45 × 185.0) + (0.55 × 187.0)",
 "average atomic mass = 83.25 + 102.85",
 "average atomic mass = 186.1 amu"
]

[
 {
  "value": 186.0,
  "misconception": "you averaged the two masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Rhenium-187 makes up 55% of the sample, so its mass counts for more: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
 },
 {
  "value": 18610,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write rhenium-185's 45% as 0.45 and rhenium-187's 55% as 0.55 first: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
 },
 {
  "value": 185.9,
  "misconception": "you swapped the two abundances between the isotopes",
  "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Rhenium-187 carries the 55% in this sample, not rhenium-185: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
 },
 {
  "value": 187.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Rhenium-185's 45% pulls the average well below 187.0: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of rhenium-185 = 45% → 0.45\nfraction of rhenium-187 = 55% → 0.55\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.45 × 185.0) + (0.55 × 187.0)\naverage atomic mass = 83.25 + 102.85\naverage atomic mass = 186.1 amu\nThe same routine works for any stated mixture: each isotope's fraction times its mass, added. The average must land between 185.0 and 187.0, on rhenium-187's side because rhenium-187 dominates the sample — 186.1 passes that check.",
 "anticipatedWrong": [
  {
   "value": 186.0,
   "misconception": "you averaged the two masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the two masses as if the isotopes were equally abundant. Rhenium-187 makes up 55% of the sample, so its mass counts for more: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
  },
  {
   "value": 18610,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Write rhenium-185's 45% as 0.45 and rhenium-187's 55% as 0.55 first: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
  },
  {
   "value": 185.9,
   "misconception": "you swapped the two abundances between the isotopes",
   "feedback": "This answer is wrong — you swapped the two abundances between the isotopes. Rhenium-187 carries the 55% in this sample, not rhenium-185: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
  },
  {
   "value": 187.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. Rhenium-185's 45% pulls the average well below 187.0: (0.45 × 185.0) + (0.55 × 187.0) = 186.1 amu."
  }
 ]
}

[
 "Write each percent abundance as a decimal fraction:",
 "fraction of barium-138 = 70.5% → 0.705",
 "fraction of barium-137 = 12.0% → 0.120",
 "fraction of barium-136 = 8.00% → 0.0800",
 "fraction of barium-135 = 6.00% → 0.0600",
 "fraction of barium-134 = 3.50% → 0.0350",
 "Write down the equation:",
 "average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄) + (fraction₅ × mass₅)",
 "Substitute in the values, and calculate:",
 "average atomic mass = (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0)",
 "average atomic mass = 97.29 + 16.44 + 10.88 + 8.10 + 4.69",
 "average atomic mass = 137.40 amu",
 "Reported to 4 significant figures: 137.4 amu"
]

[
 {
  "value": 136.0,
  "misconception": "you averaged the five masses as if the isotopes were equally abundant",
  "feedback": "This answer is wrong — you averaged the five masses as if the isotopes were equally abundant. Barium-138 carries 70.5% of the weight: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
 },
 {
  "value": 138.0,
  "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
  "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all five isotopes, so it lands below 138.0: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
 },
 {
  "value": 13740,
  "misconception": "you multiplied by the percents without first writing them as decimal fractions",
  "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
 }
]

{
 "keyExplanation": "Write each percent abundance as a decimal fraction:\nfraction of barium-138 = 70.5% → 0.705\nfraction of barium-137 = 12.0% → 0.120\nfraction of barium-136 = 8.00% → 0.0800\nfraction of barium-135 = 6.00% → 0.0600\nfraction of barium-134 = 3.50% → 0.0350\nWrite down the equation:\naverage atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃) + (fraction₄ × mass₄) + (fraction₅ × mass₅)\nSubstitute in the values, and calculate:\naverage atomic mass = (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0)\naverage atomic mass = 97.29 + 16.44 + 10.88 + 8.10 + 4.69\naverage atomic mass = 137.40 amu\nReported to 4 significant figures: 137.4 amu\nBarium-138 dominates, so the average sits below 138.0, pulled down by the lighter isotopes — not at the plain five-way average of 136.0.",
 "anticipatedWrong": [
  {
   "value": 136.0,
   "misconception": "you averaged the five masses as if the isotopes were equally abundant",
   "feedback": "This answer is wrong — you averaged the five masses as if the isotopes were equally abundant. Barium-138 carries 70.5% of the weight: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
  },
  {
   "value": 138.0,
   "misconception": "you reported the most abundant isotope's mass instead of calculating the weighted average",
   "feedback": "This answer is wrong — you reported the most abundant isotope's mass instead of calculating the weighted average. The average blends all five isotopes, so it lands below 138.0: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
  },
  {
   "value": 13740,
   "misconception": "you multiplied by the percents without first writing them as decimal fractions",
   "feedback": "This answer is wrong — you multiplied by the percents without first writing them as decimal fractions. Divide each percent by 100 first: (0.705 × 138.0) + (0.120 × 137.0) + (0.0800 × 136.0) + (0.0600 × 135.0) + (0.0350 × 134.0) = 137.4 amu."
  }
 ]
}

[
 {
  "value": 8,
  "misconception": "you stopped at the s and p sublevels — level 3 also has a d sublevel, so it holds 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — 8 stops at level 3's s and p sublevels; level 3 also has a d sublevel, so it holds 2 + 6 + 10 = 18 electrons."
 },
 {
  "value": 10,
  "misconception": "you counted only the d sublevel — add the s and p as well: 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — 10 counts only level 3's d sublevel; add the s and p sublevels as well: 2 + 6 + 10 = 18 electrons."
 }
]

{
 "keyExplanation": "Level 3 contains an s, a p, and a d sublevel. Their capacities are 2, 6, and 10 electrons, so the level holds at most 2 + 6 + 10 = 18 electrons."
}

[
 {
  "value": 16,
  "misconception": "you grouped by position in the string — the 3d¹⁰ block sits between 4s² and 4p⁴, but its number says level 3; only the blocks whose number is 4 count",
  "feedback": "This answer is wrong — you grouped selenium's blocks by their position in the string and pulled the 3d¹⁰ block into level 4. The 3d¹⁰ block sits between 4s² and 4p⁴, but its number says level 3. Only the blocks whose number is 4 count: 4s² and 4p⁴, giving 2 + 4 = 6."
 },
 {
  "value": 2,
  "misconception": "you stopped at the 4s² block — the 4p⁴ block further along the string also belongs to level 4",
  "feedback": "This answer is wrong — you stopped at selenium's 4s² block. The 4p⁴ block further along the string, past the 3d¹⁰ interruption, also belongs to level 4: 2 + 4 = 6."
 },
 {
  "value": 18,
  "misconception": "you totaled level 3's electrons — the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3, not level 4",
  "feedback": "This answer is wrong — you totaled level 3's electrons. In selenium's string the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3; level 4 holds only 4s² and 4p⁴, giving 2 + 4 = 6."
 }
]

{
 "keyExplanation": "Collect every block whose number is 4, wherever it sits in selenium's string: 4s² and 4p⁴ — the 3d¹⁰ block sits between them, but its number says level 3, so it does not count. Adding the superscripts: 2 + 4 = 6 electrons in main energy level 4."
}

[
 {
  "value": "1s²2s²2p⁶",
  "misconception": "you filled 2p to its capacity instead of stopping at the electron count — your superscripts total 10, but boron has 5 electrons",
  "feedback": "This answer is wrong — you filled 2p to its capacity instead of stopping at the electron count. Your superscripts total 10, but a neutral boron atom has exactly 5 electrons: 1s takes 2, 2s takes 2, and 2p takes only the last 1 — 1s²2s²2p¹."
 },
 {
  "value": "1s²2p³",
  "misconception": "your superscripts total 5, but you skipped the 2s sublevel — 2s fills before 2p in the filling order",
  "feedback": "This answer is wrong — your superscripts total 5, but you skipped the 2s sublevel. The filling order is 1s, 2s, 2p: after 1s takes 2, the next 2 electrons fill 2s, and the last 1 goes to 2p — 1s²2s²2p¹."
 }
]

{
 "keyExplanation": "Write down the electron count: a neutral boron atom has 5 electrons.\nFill in order: 1s takes 2 (3 left), 2s takes 2 (1 left), 2p takes the last 1.\nWrite the blocks: 1s²2s²2p¹.\nCheck: 2 + 2 + 1 = 5.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶",
   "misconception": "you filled 2p to its capacity instead of stopping at the electron count — your superscripts total 10, but boron has 5 electrons",
   "feedback": "This answer is wrong — you filled 2p to its capacity instead of stopping at the electron count. Your superscripts total 10, but a neutral boron atom has exactly 5 electrons: 1s takes 2, 2s takes 2, and 2p takes only the last 1 — 1s²2s²2p¹."
  },
  {
   "value": "1s²2p³",
   "misconception": "your superscripts total 5, but you skipped the 2s sublevel — 2s fills before 2p in the filling order",
   "feedback": "This answer is wrong — your superscripts total 5, but you skipped the 2s sublevel. The filling order is 1s, 2s, 2p: after 1s takes 2, the next 2 electrons fill 2s, and the last 1 goes to 2p — 1s²2s²2p¹."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s¹",
  "misconception": "your superscripts total 11, one short — after 2p⁶, 2 electrons remain for 3s",
  "feedback": "This answer is wrong — your superscripts total 11, one short. The atom holds exactly 12 electrons: after 1s², 2s² and 2p⁶ use 10, both remaining electrons fill 3s — 1s²2s²2p⁶3s²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶",
  "misconception": "you filled past the electron count — your superscripts total 18, but the atom has exactly 12 electrons",
  "feedback": "This answer is wrong — you filled past the electron count. Your superscripts total 18, but the atom holds exactly 12 electrons: 3s takes the last 2 and the configuration stops there — 1s²2s²2p⁶3s²."
 }
]

{
 "keyExplanation": "Write down the electron count: 12 electrons.\nFill in order: 1s takes 2 (10 left), 2s takes 2 (8 left), 2p takes 6 (2 left), and 2 electrons remain for 3s.\nWrite the blocks: 1s²2s²2p⁶3s².\nCheck: 2 + 2 + 6 + 2 = 12.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s¹",
   "misconception": "your superscripts total 11, one short — after 2p⁶, 2 electrons remain for 3s",
   "feedback": "This answer is wrong — your superscripts total 11, one short. The atom holds exactly 12 electrons: after 1s², 2s² and 2p⁶ use 10, both remaining electrons fill 3s — 1s²2s²2p⁶3s²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶",
   "misconception": "you filled past the electron count — your superscripts total 18, but the atom has exactly 12 electrons",
   "feedback": "This answer is wrong — you filled past the electron count. Your superscripts total 18, but the atom holds exactly 12 electrons: 3s takes the last 2 and the configuration stops there — 1s²2s²2p⁶3s²."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁶",
  "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block fills before 4p",
  "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵",
  "misconception": "your superscripts total 35, one short — the noble gas that ends period 4 has 36 electrons, so 4p fills completely",
  "feedback": "This answer is wrong — your superscripts total 35, one short. The noble gas that ends period 4 sits at atomic number 36, so 4p fills completely: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
 }
]

{
 "keyExplanation": "Period 4 ends at the noble gas krypton — the periodic table puts it at atomic number 36, so a neutral atom has 36 electrons.\nFill in order: 1s², 2s², 2p⁶, 3s², 3p⁶ use 18; then 4s² (20 placed), all of 3d¹⁰ (30 placed), and the last 6 fill 4p.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶.\nCheck: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 = 36.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁶",
   "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block fills before 4p",
   "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵",
   "misconception": "your superscripts total 35, one short — the noble gas that ends period 4 has 36 electrons, so 4p fills completely",
   "feedback": "This answer is wrong — your superscripts total 35, one short. The noble gas that ends period 4 sits at atomic number 36, so 4p fills completely: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d¹",
  "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
  "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁷",
  "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
  "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
 }
]

{
 "keyExplanation": "The first element of period 4 sits at atomic number 19 — a neutral atom has 19 electrons.\nFill in order: 1s through 3p take 18 (1 left), and 4s — not 3d — takes the last electron.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s¹.\nCheck: 2 + 2 + 6 + 2 + 6 + 1 = 19.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d¹",
   "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
   "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁷",
   "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
   "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
  }
 ]
}

[
 {
  "value": "1s²2s¹",
  "misconception": "you wrote the full configuration — the shorthand replaces lithium's inner 1s² with the bracketed symbol of helium, the noble gas before it",
  "feedback": "This answer is wrong — you wrote lithium's full configuration. The shorthand replaces the inner 1s² with the bracketed symbol of helium, the noble gas before lithium: [He]2s¹."
 },
 {
  "value": "[He]1s²2s¹",
  "misconception": "you kept the replaced blocks as well as the bracket — [He] already stands for the 1s² electrons, so they are not written again",
  "feedback": "This answer is wrong — you kept the replaced 1s² as well as the bracket. [He] already stands for those 2 electrons, so they are not written again: the shorthand is [He]2s¹."
 }
]

{
 "keyExplanation": "Write the full configuration: 1s²2s¹.\nThe nearest noble gas before lithium is helium, with 2 electrons.\nReplace helium's stretch 1s² with [He].\nThe shorthand is [He]2s¹ — 2 inside the bracket plus 1 shown makes 3.",
 "anticipatedWrong": [
  {
   "value": "1s²2s¹",
   "misconception": "you wrote the full configuration — the shorthand replaces lithium's inner 1s² with the bracketed symbol of helium, the noble gas before it",
   "feedback": "This answer is wrong — you wrote lithium's full configuration. The shorthand replaces the inner 1s² with the bracketed symbol of helium, the noble gas before lithium: [He]2s¹."
  },
  {
   "value": "[He]1s²2s¹",
   "misconception": "you kept the replaced blocks as well as the bracket — [He] already stands for the 1s² electrons, so they are not written again",
   "feedback": "This answer is wrong — you kept the replaced 1s² as well as the bracket. [He] already stands for those 2 electrons, so they are not written again: the shorthand is [He]2s¹."
  }
 ]
}

[
 {
  "value": "[Ar]4s²4p³",
  "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
  "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p³."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets argon's 18 electrons as [Ar]",
  "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the first 18 electrons with [Ar]: [Ar]4s²3d¹⁰4p³."
 }
]

{
 "keyExplanation": "Germanium sits at 32 and selenium at 34, so the element between them is at atomic number 33 — 33 electrons.\nThe nearest noble gas before it is argon (18): bracket it as [Ar].\nFill the remaining 15 in order: 4s², all of 3d¹⁰, then 4p³.\nWrite: [Ar]4s²3d¹⁰4p³. Check: 18 + 2 + 10 + 3 = 33.",
 "anticipatedWrong": [
  {
   "value": "[Ar]4s²4p³",
   "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
   "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p³."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets argon's 18 electrons as [Ar]",
   "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the first 18 electrons with [Ar]: [Ar]4s²3d¹⁰4p³."
  }
 ]
}

[
 {
  "value": 8,
  "misconception": "you used level 2's total — level 1 contains only an s sublevel",
  "feedback": "This answer is wrong — 8 is level 2's total (its s and p sublevels together). Level 1 contains only an s sublevel, so at most 2 electrons can fit in it."
 },
 {
  "value": 18,
  "misconception": "you used level 3's total — level 1 contains only an s sublevel",
  "feedback": "This answer is wrong — 18 is level 3's total (s + p + d). Level 1 contains only an s sublevel, so at most 2 electrons can fit in it."
 },
 {
  "value": 6,
  "misconception": "you gave level 1 a p sublevel's worth of electrons — the p sublevels start at level 2",
  "feedback": "This answer is wrong — 6 is a p sublevel's capacity, and level 1 has no p sublevel; the p sublevels start at level 2. Level 1's single s sublevel caps it at 2 electrons."
 }
]

{
 "keyExplanation": "Level 1 contains only an s sublevel, and an s sublevel holds at most 2 electrons — so at most 2 electrons can fit in main energy level 1."
}

[
 {
  "value": 8,
  "misconception": "you missed the 3d¹⁰ block sitting after 4s² — every block whose number is 3 counts, giving 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — you missed the 3d¹⁰ block sitting after 4s² in germanium's string; every block whose number is 3 counts, giving 2 + 6 + 10 = 18."
 },
 {
  "value": 10,
  "misconception": "you counted only the 3d block — the 3s² and 3p⁶ blocks belong to level 3 too, giving 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — you counted only germanium's 3d block; the 3s² and 3p⁶ blocks belong to level 3 too, giving 2 + 6 + 10 = 18."
 },
 {
  "value": 4,
  "misconception": "you counted level 4's electrons — the blocks 4s² and 4p² belong to level 4, not level 3",
  "feedback": "This answer is wrong — you counted level 4's electrons; the blocks 4s² and 4p² belong to level 4, not level 3. Every block whose number is 3 counts: 2 + 6 + 10 = 18."
 }
]

{
 "keyExplanation": "Collect every block whose number is 3, wherever it sits in the string: 3s², 3p⁶, and 3d¹⁰ — the 3d block appears after 4s² but still belongs to level 3. Adding the superscripts: 2 + 6 + 10 = 18 electrons in main energy level 3."
}

[
 {
  "value": "1s²2s¹2p¹",
  "misconception": "you moved to 2p before 2s was full — a sublevel fills to its capacity before the next one starts",
  "feedback": "This answer is wrong — you moved to 2p before 2s was full. A sublevel fills to its capacity before the next one starts: 2s takes both of beryllium's remaining electrons, so the configuration is 1s²2s², and 2p never opens."
 },
 {
  "value": "1s²2s²2p⁶",
  "misconception": "you kept filling past beryllium's 4 electrons — stop the moment the electron count is used up",
  "feedback": "This answer is wrong — you kept filling past beryllium's 4 electrons. Stop the moment the electron count is used up: 1s takes 2 and 2s takes the last 2, so the configuration ends at 1s²2s²."
 }
]

{
 "keyExplanation": "Write down the electron count: a neutral beryllium atom has 4 electrons.\nFill in order: 1s takes 2 (2 left), 2s takes the last 2.\nWrite the blocks: 1s²2s².\nCheck: 2 + 2 = 4 — every sublevel ends exactly full.",
 "anticipatedWrong": [
  {
   "value": "1s²2s¹2p¹",
   "misconception": "you moved to 2p before 2s was full — a sublevel fills to its capacity before the next one starts",
   "feedback": "This answer is wrong — you moved to 2p before 2s was full. A sublevel fills to its capacity before the next one starts: 2s takes both of beryllium's remaining electrons, so the configuration is 1s²2s², and 2p never opens."
  },
  {
   "value": "1s²2s²2p⁶",
   "misconception": "you kept filling past beryllium's 4 electrons — stop the moment the electron count is used up",
   "feedback": "This answer is wrong — you kept filling past beryllium's 4 electrons. Stop the moment the electron count is used up: 1s takes 2 and 2s takes the last 2, so the configuration ends at 1s²2s²."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²",
  "misconception": "you filled 3s to its capacity instead of stopping at the electron count — the atomic number is 11, so only 1 electron remains for 3s",
  "feedback": "This answer is wrong — you filled 3s to its capacity instead of stopping at the electron count. The atomic number is 11, so a neutral atom has exactly 11 electrons: after 1s², 2s² and 2p⁶, only 1 electron remains for 3s — 1s²2s²2p⁶3s¹."
 },
 {
  "value": "1s²2s²2p⁷",
  "misconception": "you overfilled the 2p sublevel — a p sublevel holds at most 6 electrons, so the 11th electron opens 3s",
  "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel holds at most 6 electrons, so after 2p⁶ the 11th electron opens 3s — 1s²2s²2p⁶3s¹."
 }
]

{
 "keyExplanation": "Write down the electron count: 11 electrons.\nFill in order: 1s takes 2 (9 left), 2s takes 2 (7 left), 2p takes 6 (1 left), and 1 electron remains for 3s.\nWrite the blocks: 1s²2s²2p⁶3s¹.\nCheck: 2 + 2 + 6 + 1 = 11.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²",
   "misconception": "you filled 3s to its capacity instead of stopping at the electron count — the atomic number is 11, so only 1 electron remains for 3s",
   "feedback": "This answer is wrong — you filled 3s to its capacity instead of stopping at the electron count. The atomic number is 11, so a neutral atom has exactly 11 electrons: after 1s², 2s² and 2p⁶, only 1 electron remains for 3s — 1s²2s²2p⁶3s¹."
  },
  {
   "value": "1s²2s²2p⁷",
   "misconception": "you overfilled the 2p sublevel — a p sublevel holds at most 6 electrons, so the 11th electron opens 3s",
   "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel holds at most 6 electrons, so after 2p⁶ the 11th electron opens 3s — 1s²2s²2p⁶3s¹."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁴",
  "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block sits between 4s and 4p",
  "feedback": "This answer is wrong — you skipped the 3d sublevel: these superscripts total only 24, not 34. After 4s takes 2 there are 14 electrons left, so 3d fills completely (10) before 4p takes the last 4: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵",
  "misconception": "your superscripts total 35, one too many — the atom has exactly 34 electrons, so 4p stops at 4",
  "feedback": "This answer is wrong — its superscripts total 35, one too many. The atom has exactly 34 electrons, so after the full 3d¹⁰ only 4 remain for 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴."
 }
]

{
 "keyExplanation": "Germanium sits at atomic number 32, so two places to the right in period 4 is atomic number 34 — a neutral atom with 34 electrons.\nFill in order: 1s through 3p take 18 (16 left), 4s takes 2 (14 left), 3d takes 10 (4 left), 4p takes the last 4.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴.\nCheck: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 4 = 34.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁴",
   "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block sits between 4s and 4p",
   "feedback": "This answer is wrong — you skipped the 3d sublevel: these superscripts total only 24, not 34. After 4s takes 2 there are 14 electrons left, so 3d fills completely (10) before 4p takes the last 4: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵",
   "misconception": "your superscripts total 35, one too many — the atom has exactly 34 electrons, so 4p stops at 4",
   "feedback": "This answer is wrong — its superscripts total 35, one too many. The atom has exactly 34 electrons, so after the full 3d¹⁰ only 4 remain for 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d²",
  "misconception": "you sent the last two electrons into 3d — 4s fills before 3d, so the final block is 4s²",
  "feedback": "This answer is wrong — you sent the last two of the 20 electrons into 3d. 4s fills before 3d, so after 1s through 3p take 18 electrons, the last 2 enter 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁸",
  "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the last two electrons belong in 4s",
  "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the last 2 of the 20 electrons enter 4s: 1s²2s²2p⁶3s²3p⁶4s²."
 }
]

{
 "keyExplanation": "The second element of period 4 sits at atomic number 20 — a neutral atom has 20 electrons.\nFill in order: 1s through 3p take 18 (2 left), and 4s — not 3d — takes the last 2.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s².\nCheck: 2 + 2 + 6 + 2 + 6 + 2 = 20.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d²",
   "misconception": "you sent the last two electrons into 3d — 4s fills before 3d, so the final block is 4s²",
   "feedback": "This answer is wrong — you sent the last two of the 20 electrons into 3d. 4s fills before 3d, so after 1s through 3p take 18 electrons, the last 2 enter 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁸",
   "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the last two electrons belong in 4s",
   "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the last 2 of the 20 electrons enter 4s: 1s²2s²2p⁶3s²3p⁶4s²."
  }
 ]
}

[
 {
  "value": "[Ne]2s²2p⁴",
  "misconception": "you bracketed neon, which comes after oxygen — a noble gas later in the table cannot stand in for electrons the atom does not have; helium is the nearest noble gas before it",
  "feedback": "This answer is wrong — you bracketed neon, which comes after oxygen. The bracket must name the nearest noble gas BEFORE the element: helium. [He]2s²2p⁴."
 },
 {
  "value": "1s²2s²2p⁴",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
  "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²2p⁴."
 }
]

{
 "keyExplanation": "Oxygen's atomic number is 8 — a neutral atom has 8 electrons.\nThe nearest noble gas before oxygen is helium (2 electrons): bracket it as [He].\nFill the remaining 6 in order: 2s², then 2p⁴.\nWrite: [He]2s²2p⁴. Check: 2 + 2 + 4 = 8.",
 "anticipatedWrong": [
  {
   "value": "[Ne]2s²2p⁴",
   "misconception": "you bracketed neon, which comes after oxygen — a noble gas later in the table cannot stand in for electrons the atom does not have; helium is the nearest noble gas before it",
   "feedback": "This answer is wrong — you bracketed neon, which comes after oxygen. The bracket must name the nearest noble gas BEFORE the element: helium. [He]2s²2p⁴."
  },
  {
   "value": "1s²2s²2p⁴",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
   "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²2p⁴."
  }
 ]
}

[
 {
  "value": "[Ar]4s²4p⁵",
  "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
  "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p⁵."
 },
 {
  "value": "[Ne]3s²3p⁵",
  "misconception": "you wrote the shorthand of chlorine itself — the question asks about the element one period BELOW chlorine, whose configuration runs through period 4",
  "feedback": "This answer is wrong — [Ne]3s²3p⁵ is chlorine's own shorthand. The element directly below chlorine sits one period down, at atomic number 35: [Ar]4s²3d¹⁰4p⁵."
 }
]

{
 "keyExplanation": "Directly below chlorine sits the element at atomic number 35 — 35 electrons.\nThe nearest noble gas before it is argon (18): bracket it as [Ar].\nFill the remaining 17 in order: 4s², all of 3d¹⁰, then 4p⁵.\nWrite: [Ar]4s²3d¹⁰4p⁵. Check: 18 + 2 + 10 + 5 = 35.",
 "anticipatedWrong": [
  {
   "value": "[Ar]4s²4p⁵",
   "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
   "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p⁵."
  },
  {
   "value": "[Ne]3s²3p⁵",
   "misconception": "you wrote the shorthand of chlorine itself — the question asks about the element one period BELOW chlorine, whose configuration runs through period 4",
   "feedback": "This answer is wrong — [Ne]3s²3p⁵ is chlorine's own shorthand. The element directly below chlorine sits one period down, at atomic number 35: [Ar]4s²3d¹⁰4p⁵."
  }
 ]
}

[
 {
  "value": 2,
  "misconception": "you gave the s sublevel's capacity — a p sublevel is full at 6 electrons",
  "feedback": "This answer is wrong — 2 is an s sublevel's capacity; a p sublevel is only completely full at 6 electrons."
 },
 {
  "value": 10,
  "misconception": "you gave the d sublevel's capacity — a p sublevel is full at 6 electrons",
  "feedback": "This answer is wrong — 10 is a d sublevel's capacity; a completely full p sublevel holds 6 electrons."
 },
 {
  "value": 8,
  "misconception": "you gave a whole level's total — the question asks about one p sublevel on its own",
  "feedback": "This answer is wrong — 8 is the total for all of level 2 (its s and p sublevels together); the question asks about one p sublevel on its own, which is full at 6 electrons."
 }
]

{
 "keyExplanation": "Full means at capacity. The capacities are fixed by letter: s holds 2, p holds 6, d holds 10 — so a completely full p sublevel holds exactly 6 electrons."
}

[
 {
  "value": 17,
  "misconception": "you grouped by position in the string — the 3d¹⁰ block sits between 4s² and 4p⁵, but its number says level 3; only the blocks whose number is 4 count",
  "feedback": "This answer is wrong — you grouped bromine's blocks by their position in the string and pulled the 3d¹⁰ block into level 4. The 3d¹⁰ block sits between 4s² and 4p⁵, but its number says level 3. Only the blocks whose number is 4 count: 4s² and 4p⁵, giving 2 + 5 = 7."
 },
 {
  "value": 2,
  "misconception": "you stopped at the 4s² block — the 4p⁵ block further along the string also belongs to level 4",
  "feedback": "This answer is wrong — you stopped at bromine's 4s² block. The 4p⁵ block further along the string, past the 3d¹⁰ interruption, also belongs to level 4: 2 + 5 = 7."
 },
 {
  "value": 18,
  "misconception": "you totaled level 3's electrons — the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3, not level 4",
  "feedback": "This answer is wrong — you totaled level 3's electrons. In bromine's string the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3; level 4 holds only 4s² and 4p⁵, giving 2 + 5 = 7."
 }
]

{
 "keyExplanation": "Collect every block whose number is 4, wherever it sits in bromine's string: 4s² and 4p⁵ — the 3d¹⁰ block sits between them, but its number says level 3, so it does not count. Adding the superscripts: 2 + 5 = 7 electrons in main energy level 4."
}

[
 {
  "value": "1s³",
  "misconception": "you overfilled the 1s sublevel — an s sublevel holds at most 2 electrons, so the third electron moves on to 2s",
  "feedback": "This answer is wrong — you overfilled the 1s sublevel. An s sublevel holds at most 2 electrons in any level, so lithium's third electron moves on to 2s: 1s²2s¹."
 },
 {
  "value": "1s²2s²",
  "misconception": "you filled 2s to its capacity instead of stopping at the electron count — your superscripts total 4, but lithium has 3 electrons",
  "feedback": "This answer is wrong — you filled 2s to its capacity instead of stopping at the electron count. Your superscripts total 4, but a neutral lithium atom has exactly 3 electrons: after 1s takes 2, only 1 electron is left for 2s — 1s²2s¹."
 }
]

{
 "keyExplanation": "Write down the electron count: a neutral lithium atom has 3 electrons.\nFill in order: 1s takes 2 (1 left), 2s takes the last 1.\nWrite the blocks: 1s²2s¹.\nCheck: 2 + 1 = 3.",
 "anticipatedWrong": [
  {
   "value": "1s³",
   "misconception": "you overfilled the 1s sublevel — an s sublevel holds at most 2 electrons, so the third electron moves on to 2s",
   "feedback": "This answer is wrong — you overfilled the 1s sublevel. An s sublevel holds at most 2 electrons in any level, so lithium's third electron moves on to 2s: 1s²2s¹."
  },
  {
   "value": "1s²2s²",
   "misconception": "you filled 2s to its capacity instead of stopping at the electron count — your superscripts total 4, but lithium has 3 electrons",
   "feedback": "This answer is wrong — you filled 2s to its capacity instead of stopping at the electron count. Your superscripts total 4, but a neutral lithium atom has exactly 3 electrons: after 1s takes 2, only 1 electron is left for 2s — 1s²2s¹."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s¹",
  "misconception": "your superscripts total 11, one short — after 1s², 2s² and 2p⁶, exactly 2 electrons remain for 3s",
  "feedback": "This answer is wrong — your superscripts total 11, one short. The atom contains exactly 12 electrons: after 1s², 2s² and 2p⁶ use 10, exactly 2 remain for 3s — 1s²2s²2p⁶3s²."
 },
 {
  "value": "1s²2s²2p⁸",
  "misconception": "you overfilled the 2p sublevel — it is full at 6 electrons, so the last 2 belong in 3s",
  "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel is full at 6 electrons, so the last 2 of the atom's 12 belong in 3s — 1s²2s²2p⁶3s²."
 }
]

{
 "keyExplanation": "Write down the electron count: 12 electrons.\nFill in order: 1s takes 2 (10 left), 2s takes 2 (8 left), 2p takes 6 (2 left), and 2 electrons remain for 3s.\nWrite the blocks: 1s²2s²2p⁶3s².\nCheck: 2 + 2 + 6 + 2 = 12.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s¹",
   "misconception": "your superscripts total 11, one short — after 1s², 2s² and 2p⁶, exactly 2 electrons remain for 3s",
   "feedback": "This answer is wrong — your superscripts total 11, one short. The atom contains exactly 12 electrons: after 1s², 2s² and 2p⁶ use 10, exactly 2 remain for 3s — 1s²2s²2p⁶3s²."
  },
  {
   "value": "1s²2s²2p⁸",
   "misconception": "you overfilled the 2p sublevel — it is full at 6 electrons, so the last 2 belong in 3s",
   "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel is full at 6 electrons, so the last 2 of the atom's 12 belong in 3s — 1s²2s²2p⁶3s²."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²4p²",
  "misconception": "you skipped the 3d sublevel — from gallium onward the full 3d¹⁰ block sits between 4s and 4p",
  "feedback": "This answer is wrong — you skipped the 3d sublevel: from gallium onward the full 3d¹⁰ block sits between 4s and 4p. Germanium's 32 electrons fill 1s through 3p (18), then 4s², then the full 3d¹⁰, then 4p²: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d¹²4s²",
  "misconception": "you put 4s after 3d in the fill and gave 3d the last electrons — 4s fills first, and germanium's 3d is completely full at 10",
  "feedback": "This answer is wrong — you put 4s after 3d in the fill and gave 3d the last electrons. 4s fills first, and a d sublevel holds at most 10, so germanium's 3d is completely full at 3d¹⁰ — never 3d¹². The fill gives 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²."
 }
]

{
 "keyExplanation": "The periodic table puts germanium at atomic number 32 — a neutral atom has 32 electrons.\nFill in order: 1s through 3p take 18 (14 left), 4s takes 2 (12 left), 3d takes 10 (2 left), 4p takes the last 2.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p².\nCheck: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 2 = 32.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²4p²",
   "misconception": "you skipped the 3d sublevel — from gallium onward the full 3d¹⁰ block sits between 4s and 4p",
   "feedback": "This answer is wrong — you skipped the 3d sublevel: from gallium onward the full 3d¹⁰ block sits between 4s and 4p. Germanium's 32 electrons fill 1s through 3p (18), then 4s², then the full 3d¹⁰, then 4p²: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d¹²4s²",
   "misconception": "you put 4s after 3d in the fill and gave 3d the last electrons — 4s fills first, and germanium's 3d is completely full at 10",
   "feedback": "This answer is wrong — you put 4s after 3d in the fill and gave 3d the last electrons. 4s fills first, and a d sublevel holds at most 10, so germanium's 3d is completely full at 3d¹⁰ — never 3d¹². The fill gives 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d¹",
  "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
  "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁷",
  "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
  "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
 }
]

{
 "keyExplanation": "The element that starts period 4 sits at atomic number 19 — a neutral atom has 19 electrons.\nFill in order: 1s through 3p take 18 (1 left), and 4s — not 3d — takes the last electron.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s¹.\nCheck: 2 + 2 + 6 + 2 + 6 + 1 = 19.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d¹",
   "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
   "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁷",
   "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
   "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
  }
 ]
}

[
 {
  "value": "1s²2s²",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
  "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²."
 },
 {
  "value": "[He]2s¹2p¹",
  "misconception": "you moved to 2p before 2s was full — a sublevel fills to its capacity before the next one starts, so both remaining electrons sit in 2s",
  "feedback": "This answer is wrong — you moved to 2p before 2s was full. A sublevel fills to capacity before the next opens: both of beryllium's remaining electrons sit in 2s — [He]2s²."
 }
]

{
 "keyExplanation": "Beryllium's atomic number is 4 — a neutral atom has 4 electrons.\nThe nearest noble gas before beryllium is helium (2 electrons): bracket it as [He].\nFill the remaining 2 in order: both go to 2s.\nWrite: [He]2s². Check: 2 + 2 = 4.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
   "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²."
  },
  {
   "value": "[He]2s¹2p¹",
   "misconception": "you moved to 2p before 2s was full — a sublevel fills to its capacity before the next one starts, so both remaining electrons sit in 2s",
   "feedback": "This answer is wrong — you moved to 2p before 2s was full. A sublevel fills to capacity before the next opens: both of beryllium's remaining electrons sit in 2s — [He]2s²."
  }
 ]
}

[
 {
  "value": "[Kr]",
  "misconception": "you bracketed the atom itself — the shorthand always brackets the noble gas that comes BEFORE the element, then writes the remaining electrons",
  "feedback": "This answer is wrong — you bracketed the atom itself. The shorthand brackets the noble gas BEFORE the element — argon here — and writes the rest: [Ar]4s²3d¹⁰4p⁶."
 },
 {
  "value": "[Ar]4s²4p⁶",
  "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
  "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p⁶."
 }
]

{
 "keyExplanation": "The noble gas that ends period 4 sits at atomic number 36 — 36 electrons.\nAn atom never brackets itself: the nearest noble gas BEFORE it is argon (18), so the bracket is [Ar].\nFill the remaining 18 in order: 4s², all of 3d¹⁰, then 4p⁶.\nWrite: [Ar]4s²3d¹⁰4p⁶. Check: 18 + 2 + 10 + 6 = 36.",
 "anticipatedWrong": [
  {
   "value": "[Kr]",
   "misconception": "you bracketed the atom itself — the shorthand always brackets the noble gas that comes BEFORE the element, then writes the remaining electrons",
   "feedback": "This answer is wrong — you bracketed the atom itself. The shorthand brackets the noble gas BEFORE the element — argon here — and writes the rest: [Ar]4s²3d¹⁰4p⁶."
  },
  {
   "value": "[Ar]4s²4p⁶",
   "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
   "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: [Ar]4s²3d¹⁰4p⁶."
  }
 ]
}

[
 {
  "value": 8,
  "misconception": "you stopped at the s and p sublevels — level 3 also has a d sublevel, so it holds 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — 8 stops at level 3's s and p sublevels; a completely full level 3 also has its d sublevel full, so it holds 2 + 6 + 10 = 18 electrons."
 },
 {
  "value": 10,
  "misconception": "you counted only the d sublevel — add the s and p as well: 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — 10 counts only level 3's d sublevel; a completely full level 3 also has its s and p sublevels full: 2 + 6 + 10 = 18 electrons."
 }
]

{
 "keyExplanation": "Level 3 contains an s, a p, and a d sublevel. Their capacities are 2, 6, and 10 electrons, so a completely full level 3 holds 2 + 6 + 10 = 18 electrons."
}

[
 {
  "value": 8,
  "misconception": "you left the 3d block out of level 3 — a block belongs to the level named by its leading number, so 3d¹⁰ counts toward level 3 alongside 3s² and 3p⁶: 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — you left the 3d block out of level 3 — a block belongs to the level named by its leading number, so 3d¹⁰ counts toward level 3 alongside 3s² and 3p⁶: 2 + 6 + 10 = 18."
 },
 {
  "value": 10,
  "misconception": "you counted only the 3d block — the 3s² and 3p⁶ blocks belong to level 3 too, giving 2 + 6 + 10 = 18",
  "feedback": "This answer is wrong — you counted only krypton's 3d block; the 3s² and 3p⁶ blocks belong to level 3 too, giving 2 + 6 + 10 = 18."
 },
 {
  "value": 36,
  "misconception": "you totaled the whole configuration — only the blocks whose number is 3 belong to level 3",
  "feedback": "This answer is wrong — you totaled krypton's whole configuration. Only the blocks whose number is 3 belong to level 3: 3s², 3p⁶, and 3d¹⁰, giving 2 + 6 + 10 = 18."
 }
]

{
 "keyExplanation": "Collect every block whose number is 3, wherever it sits in krypton's string: 3s², 3p⁶, and 3d¹⁰ — the 3d block appears after 4s² but still belongs to level 3. Adding the superscripts: 2 + 6 + 10 = 18 electrons in main energy level 3."
}

[
 {
  "value": "1s²2p⁵",
  "misconception": "your superscripts total 7, but you skipped the 2s sublevel — 2s fills before 2p in the filling order",
  "feedback": "This answer is wrong — your superscripts total 7, but you skipped the 2s sublevel. The filling order is 1s, 2s, 2p: after 1s takes 2, 2s takes 2, and 2p takes the last 3 — 1s²2s²2p³."
 },
 {
  "value": "1s²2s²2p²",
  "misconception": "your superscripts total 6, one short — recount the fill: after 2s, this atom still has 3 electrons for 2p",
  "feedback": "This answer is wrong — your superscripts total 6, one short. The atomic number is 7, so a neutral atom of this element has exactly 7 electrons: after 1s² and 2s², 3 electrons remain for 2p — 1s²2s²2p³."
 }
]

{
 "keyExplanation": "Write down the electron count: the atomic number is 7, so a neutral atom of this element has 7 electrons.\nFill in order: 1s takes 2 (5 left), 2s takes 2 (3 left), 2p takes the last 3.\nWrite the blocks: 1s²2s²2p³.\nCheck: 2 + 2 + 3 = 7.",
 "anticipatedWrong": [
  {
   "value": "1s²2p⁵",
   "misconception": "your superscripts total 7, but you skipped the 2s sublevel — 2s fills before 2p in the filling order",
   "feedback": "This answer is wrong — your superscripts total 7, but you skipped the 2s sublevel. The filling order is 1s, 2s, 2p: after 1s takes 2, 2s takes 2, and 2p takes the last 3 — 1s²2s²2p³."
  },
  {
   "value": "1s²2s²2p²",
   "misconception": "your superscripts total 6, one short — recount the fill: after 2s, this atom still has 3 electrons for 2p",
   "feedback": "This answer is wrong — your superscripts total 6, one short. The atomic number is 7, so a neutral atom of this element has exactly 7 electrons: after 1s² and 2s², 3 electrons remain for 2p — 1s²2s²2p³."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3p¹",
  "misconception": "your superscripts total 11, but you skipped the 3s sublevel — 3s fills before 3p in the filling order",
  "feedback": "This answer is wrong — you skipped the 3s sublevel. Its superscripts do total 11, but 3s fills before 3p in the filling order: after 2p takes 6, the one electron left opens 3s, not 3p: 1s²2s²2p⁶3s¹."
 },
 {
  "value": "1s²2s²2p⁷",
  "misconception": "you overfilled the 2p sublevel — a p sublevel holds at most 6 electrons, so the last electron moves on to 3s",
  "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel holds at most 6 electrons, so the superscripts may total 11 but 2p can never carry 7: after 2p takes its 6, the last electron opens 3s: 1s²2s²2p⁶3s¹."
 }
]

{
 "keyExplanation": "Write down the electron count: 11 electrons are given directly.\nFill in order: 1s takes 2 (9 left), 2s takes 2 (7 left), 2p takes 6 (1 left), 3s takes the last electron.\nWrite the blocks: 1s²2s²2p⁶3s¹.\nCheck: 2 + 2 + 6 + 1 = 11.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3p¹",
   "misconception": "your superscripts total 11, but you skipped the 3s sublevel — 3s fills before 3p in the filling order",
   "feedback": "This answer is wrong — you skipped the 3s sublevel. Its superscripts do total 11, but 3s fills before 3p in the filling order: after 2p takes 6, the one electron left opens 3s, not 3p: 1s²2s²2p⁶3s¹."
  },
  {
   "value": "1s²2s²2p⁷",
   "misconception": "you overfilled the 2p sublevel — a p sublevel holds at most 6 electrons, so the last electron moves on to 3s",
   "feedback": "This answer is wrong — you overfilled the 2p sublevel. A p sublevel holds at most 6 electrons, so the superscripts may total 11 but 2p can never carry 7: after 2p takes its 6, the last electron opens 3s: 1s²2s²2p⁶3s¹."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁵",
  "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block sits between 4s and 4p",
  "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶",
  "misconception": "your superscripts total 36 — that is krypton itself; the element one place to its left has one electron fewer, so 4p stops at 5",
  "feedback": "This answer is wrong — your superscripts total 36, which is krypton itself. The element one place to krypton's left has one electron fewer, so 4p stops at 5: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵."
 }
]

{
 "keyExplanation": "Krypton, the noble gas that ends period 4, sits at atomic number 36 — one place to its left is atomic number 35, so a neutral atom has 35 electrons.\nFill in order: 1s², 2s², 2p⁶, 3s², 3p⁶ use 18; then 4s² (20 placed), all of 3d¹⁰ (30 placed), and the last 5 enter 4p.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵.\nCheck: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 5 = 35.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²4p⁵",
   "misconception": "you skipped the 3d sublevel — once 4s is full, the whole 3d¹⁰ block sits between 4s and 4p",
   "feedback": "This answer is wrong — you skipped the 3d sublevel. Once 4s is full, the whole 3d¹⁰ block fills before 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶",
   "misconception": "your superscripts total 36 — that is krypton itself; the element one place to its left has one electron fewer, so 4p stops at 5",
   "feedback": "This answer is wrong — your superscripts total 36, which is krypton itself. The element one place to krypton's left has one electron fewer, so 4p stops at 5: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d²",
  "misconception": "you sent the last two electrons into 3d — 4s fills before 3d, so the final block is 4s²",
  "feedback": "This answer is wrong — you sent the last two of the 20 electrons into 3d. 4s fills before 3d, so after 1s through 3p take 18 electrons, the last 2 enter 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁸",
  "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the last two electrons belong in 4s",
  "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the last 2 of the 20 electrons enter 4s: 1s²2s²2p⁶3s²3p⁶4s²."
 }
]

{
 "keyExplanation": "Second from the left in period 4 means atomic number 20 — a neutral atom has 20 electrons.\nFill in order: 1s through 3p take 18 (2 left), and 4s — not 3d — takes the last 2.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s².\nCheck: 2 + 2 + 6 + 2 + 6 + 2 = 20.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d²",
   "misconception": "you sent the last two electrons into 3d — 4s fills before 3d, so the final block is 4s²",
   "feedback": "This answer is wrong — you sent the last two of the 20 electrons into 3d. 4s fills before 3d, so after 1s through 3p take 18 electrons, the last 2 enter 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁸",
   "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the last two electrons belong in 4s",
   "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the last 2 of the 20 electrons enter 4s: 1s²2s²2p⁶3s²3p⁶4s²."
  }
 ]
}

[
 {
  "value": "[Ne]2s²2p⁵",
  "misconception": "you used neon because it sits nearest to fluorine — but neon comes AFTER fluorine in the table, and a later noble gas cannot stand in for electrons fluorine does not have; use helium",
  "feedback": "This answer is wrong — you used neon because it sits nearest to fluorine. But neon comes AFTER fluorine in the table, and a later noble gas cannot stand in for electrons fluorine does not have. The nearest noble gas BEFORE fluorine is helium: [He]2s²2p⁵."
 },
 {
  "value": "[He]2p⁵",
  "misconception": "you dropped the 2s block — only helium's own block is replaced by [He]; the 2s² must stay written out",
  "feedback": "This answer is wrong — you dropped the 2s block. Only helium's own block 1s² is replaced by [He]; fluorine's 2s² must stay written out: [He]2s²2p⁵."
 }
]

{
 "keyExplanation": "Write the full configuration: 1s²2s²2p⁵.\nThe nearest noble gas BEFORE fluorine is helium — neon sits nearer but comes after fluorine, so it cannot be used.\nReplace helium's stretch 1s² with [He].\nThe shorthand is [He]2s²2p⁵ — 2 inside the bracket plus 7 shown makes 9.",
 "anticipatedWrong": [
  {
   "value": "[Ne]2s²2p⁵",
   "misconception": "you used neon because it sits nearest to fluorine — but neon comes AFTER fluorine in the table, and a later noble gas cannot stand in for electrons fluorine does not have; use helium",
   "feedback": "This answer is wrong — you used neon because it sits nearest to fluorine. But neon comes AFTER fluorine in the table, and a later noble gas cannot stand in for electrons fluorine does not have. The nearest noble gas BEFORE fluorine is helium: [He]2s²2p⁵."
  },
  {
   "value": "[He]2p⁵",
   "misconception": "you dropped the 2s block — only helium's own block is replaced by [He]; the 2s² must stay written out",
   "feedback": "This answer is wrong — you dropped the 2s block. Only helium's own block 1s² is replaced by [He]; fluorine's 2s² must stay written out: [He]2s²2p⁵."
  }
 ]
}

[
 {
  "value": "[Ar]4s²4p²",
  "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
  "feedback": "This answer is wrong — [Ar] holds 18 and 4s²4p² shows only 4 more, so this string accounts for just 22 of germanium's 32 electrons. After 4s² the full 3d¹⁰ block fills before 4p: the shorthand is [Ar]4s²3d¹⁰4p²."
 },
 {
  "value": "[Ne]3s²3p⁶4s²3d¹⁰4p²",
  "misconception": "you stopped the replacement at neon — argon also comes before germanium and is nearer, so the shorthand starts from [Ar]",
  "feedback": "This answer is wrong — all 32 electrons are there, but the replacement stopped at neon. Argon also comes before germanium and is the nearest noble gas, so its whole stretch 1s²2s²2p⁶3s²3p⁶ is replaced: [Ar]4s²3d¹⁰4p²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand",
  "feedback": "This answer is wrong as written — the full configuration is correct, but the question asks for the noble-gas shorthand: replace the opening stretch 1s²2s²2p⁶3s²3p⁶ (argon's 18 electrons) with [Ar], leaving [Ar]4s²3d¹⁰4p²."
 }
]

{
 "keyExplanation": "The periodic table puts germanium at atomic number 32 — 32 electrons.\nThe nearest noble gas before germanium is argon, with 18 electrons.\nReplace argon's stretch 1s²2s²2p⁶3s²3p⁶ with [Ar].\nThe shorthand is [Ar]4s²3d¹⁰4p² — 18 inside the bracket plus 14 shown makes 32.",
 "anticipatedWrong": [
  {
   "value": "[Ar]4s²4p²",
   "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
   "feedback": "This answer is wrong — [Ar] holds 18 and 4s²4p² shows only 4 more, so this string accounts for just 22 of germanium's 32 electrons. After 4s² the full 3d¹⁰ block fills before 4p: the shorthand is [Ar]4s²3d¹⁰4p²."
  },
  {
   "value": "[Ne]3s²3p⁶4s²3d¹⁰4p²",
   "misconception": "you stopped the replacement at neon — argon also comes before germanium and is nearer, so the shorthand starts from [Ar]",
   "feedback": "This answer is wrong — all 32 electrons are there, but the replacement stopped at neon. Argon also comes before germanium and is the nearest noble gas, so its whole stretch 1s²2s²2p⁶3s²3p⁶ is replaced: [Ar]4s²3d¹⁰4p²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand",
   "feedback": "This answer is wrong as written — the full configuration is correct, but the question asks for the noble-gas shorthand: replace the opening stretch 1s²2s²2p⁶3s²3p⁶ (argon's 18 electrons) with [Ar], leaving [Ar]4s²3d¹⁰4p²."
  }
 ]
}

[
 {
  "value": 6,
  "misconception": "you counted only the p sublevel — level 2 also has an s sublevel, so it holds 2 + 6 = 8",
  "feedback": "This answer is wrong — 6 counts only level 2's p sublevel; a completely full level 2 also has its s sublevel full, so it holds 2 + 6 = 8 electrons."
 },
 {
  "value": 2,
  "misconception": "you counted only the s sublevel — level 2 also has a p sublevel, so it holds 2 + 6 = 8",
  "feedback": "This answer is wrong — 2 counts only level 2's s sublevel; a completely full level 2 also has its p sublevel full, so it holds 2 + 6 = 8 electrons."
 },
 {
  "value": 18,
  "misconception": "you used level 3's total — level 2 has no d sublevel, so it holds 2 + 6 = 8",
  "feedback": "This answer is wrong — 18 is level 3's total. Level 2 has no d sublevel, so even completely full it holds 2 + 6 = 8 electrons."
 }
]

{
 "keyExplanation": "Level 2 contains an s and a p sublevel. The s holds at most 2 and the p holds at most 6. Completely full means both are at capacity: 2 + 6 = 8 electrons."
}

[
 {
  "value": 15,
  "misconception": "you grouped by position in the string — the 3d¹⁰ block sits between 4s² and 4p³, but its number says level 3; only the blocks whose number is 4 count",
  "feedback": "This answer is wrong — you grouped arsenic's blocks by their position in the string and pulled the 3d¹⁰ block into level 4. The 3d¹⁰ block sits between 4s² and 4p³, but its number says level 3. Only the blocks whose number is 4 count: 4s² and 4p³, giving 2 + 3 = 5."
 },
 {
  "value": 2,
  "misconception": "you stopped at the 4s² block — the 4p³ block further along the string also belongs to level 4",
  "feedback": "This answer is wrong — you stopped at arsenic's 4s² block. The 4p³ block further along the string, past the 3d¹⁰ interruption, also belongs to level 4: 2 + 3 = 5."
 },
 {
  "value": 18,
  "misconception": "you totaled level 3's electrons — the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3, not level 4",
  "feedback": "This answer is wrong — you totaled level 3's electrons. In arsenic's string the blocks 3s², 3p⁶, and 3d¹⁰ belong to level 3; level 4 holds only 4s² and 4p³, giving 2 + 3 = 5."
 }
]

{
 "keyExplanation": "Collect every block whose number is 4, wherever it sits in arsenic's string: 4s² and 4p³ — the 3d¹⁰ block sits between them, but its number says level 3, so it does not count. Adding the superscripts: 2 + 3 = 5 electrons in main energy level 4."
}

[
 {
  "value": "1s²2s²2p⁶",
  "misconception": "your superscripts total 10, one too many — a neutral atom of this element has exactly 9 electrons, so 2p stops at 5",
  "feedback": "This answer is wrong — your superscripts total 10, one too many. The atomic number is 9, so a neutral atom of this element has exactly 9 electrons: after 1s² and 2s², only 5 electrons remain for 2p — 1s²2s²2p⁵."
 },
 {
  "value": "1s²2s²2p⁴",
  "misconception": "your superscripts total 8, one short — recount the fill: after 2s, 5 electrons remain for 2p",
  "feedback": "This answer is wrong — your superscripts total 8, one short. A neutral atom of this element has 9 electrons: 1s takes 2, 2s takes 2, and 2p takes the last 5 — 1s²2s²2p⁵."
 }
]

{
 "keyExplanation": "Write down the electron count: the atomic number is 9, so a neutral atom of this element has 9 electrons.\nFill in order: 1s takes 2 (7 left), 2s takes 2 (5 left), 2p takes the last 5.\nWrite the blocks: 1s²2s²2p⁵.\nCheck: 2 + 2 + 5 = 9.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶",
   "misconception": "your superscripts total 10, one too many — a neutral atom of this element has exactly 9 electrons, so 2p stops at 5",
   "feedback": "This answer is wrong — your superscripts total 10, one too many. The atomic number is 9, so a neutral atom of this element has exactly 9 electrons: after 1s² and 2s², only 5 electrons remain for 2p — 1s²2s²2p⁵."
  },
  {
   "value": "1s²2s²2p⁴",
   "misconception": "your superscripts total 8, one short — recount the fill: after 2s, 5 electrons remain for 2p",
   "feedback": "This answer is wrong — your superscripts total 8, one short. A neutral atom of this element has 9 electrons: 1s takes 2, 2s takes 2, and 2p takes the last 5 — 1s²2s²2p⁵."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p¹",
  "misconception": "you filled past the count — your superscripts total 13, but the atom holds exactly 12 electrons, so the configuration ends at 3s²",
  "feedback": "This answer is wrong — you filled past the count. Your superscripts total 13, but the atom holds exactly 12 electrons: 3s takes the last 2 and the configuration ends at 1s²2s²2p⁶3s² — 3p never opens."
 },
 {
  "value": "1s²2s²2p⁶3s¹",
  "misconception": "your superscripts total 11, one short — recount the fill: 2 electrons remain for 3s",
  "feedback": "This answer is wrong — your superscripts total 11, one short. The electron count is 12: after 1s², 2s² and 2p⁶, both remaining electrons fill 3s — 1s²2s²2p⁶3s²."
 }
]

{
 "keyExplanation": "Write down the electron count: 12 electrons.\nFill in order: 1s takes 2 (10 left), 2s takes 2 (8 left), 2p takes 6 (2 left), and 2 electrons remain for 3s.\nWrite the blocks: 1s²2s²2p⁶3s².\nCheck: 2 + 2 + 6 + 2 = 12.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p¹",
   "misconception": "you filled past the count — your superscripts total 13, but the atom holds exactly 12 electrons, so the configuration ends at 3s²",
   "feedback": "This answer is wrong — you filled past the count. Your superscripts total 13, but the atom holds exactly 12 electrons: 3s takes the last 2 and the configuration ends at 1s²2s²2p⁶3s² — 3p never opens."
  },
  {
   "value": "1s²2s²2p⁶3s¹",
   "misconception": "your superscripts total 11, one short — recount the fill: 2 electrons remain for 3s",
   "feedback": "This answer is wrong — your superscripts total 11, one short. The electron count is 12: after 1s², 2s² and 2p⁶, both remaining electrons fill 3s — 1s²2s²2p⁶3s²."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d¹⁰4p⁶4s²",
  "misconception": "you wrote 4s after 4p — in filling order 4s comes first, then 3d, then 4p",
  "feedback": "This answer is wrong — you wrote 4s after 4p. The filling order runs 4s, then 3d, then 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰",
  "misconception": "your superscripts total 30 — you stopped before 4p; the noble gas closing period 4 carries a full 4p⁶",
  "feedback": "This answer is wrong — your superscripts total 30, six short. After 3d¹⁰, the remaining 6 electrons fill 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
 }
]

{
 "keyExplanation": "The noble gas that closes period 4 is krypton, atomic number 36 on the periodic table — a neutral atom has 36 electrons.\nFill in order: 1s², 2s², 2p⁶, 3s², 3p⁶ use 18; then 4s² (20 placed), all of 3d¹⁰ (30 placed), and the last 6 fill 4p.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶.\nCheck: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 = 36.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d¹⁰4p⁶4s²",
   "misconception": "you wrote 4s after 4p — in filling order 4s comes first, then 3d, then 4p",
   "feedback": "This answer is wrong — you wrote 4s after 4p. The filling order runs 4s, then 3d, then 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰",
   "misconception": "your superscripts total 30 — you stopped before 4p; the noble gas closing period 4 carries a full 4p⁶",
   "feedback": "This answer is wrong — your superscripts total 30, six short. After 3d¹⁰, the remaining 6 electrons fill 4p: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶."
  }
 ]
}

[
 {
  "value": "1s²2s²2p⁶3s²3p⁶3d¹",
  "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
  "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁷",
  "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
  "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
 }
]

{
 "keyExplanation": "The leftmost element of period 4 sits at atomic number 19 — a neutral atom has 19 electrons.\nFill in order: 1s through 3p take 18 (1 left), and 4s — not 3d — takes the last electron.\nWrite the blocks: 1s²2s²2p⁶3s²3p⁶4s¹.\nCheck: 2 + 2 + 6 + 2 + 6 + 1 = 19.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p⁶3s²3p⁶3d¹",
   "misconception": "you put the 19th electron in 3d — the filling order's surprise is exactly here: 4s fills before 3d",
   "feedback": "This answer is wrong — you put the 19th electron in 3d. The filling order's surprise sits exactly here: 4s fills before 3d, so after 1s through 3p take 18 electrons, the 19th enters 4s. The configuration is 1s²2s²2p⁶3s²3p⁶4s¹."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁷",
   "misconception": "you overfilled the 3p sublevel — a p sublevel holds at most 6 electrons, so the 19th electron belongs in 4s",
   "feedback": "This answer is wrong — you overfilled the 3p sublevel. A p sublevel holds at most 6 electrons, so 3p stops at 3p⁶ and the 19th electron belongs in 4s: 1s²2s²2p⁶3s²3p⁶4s¹."
  }
 ]
}

[
 {
  "value": "1s²2s²2p¹",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
  "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²2p¹."
 },
 {
  "value": "[He]2s³",
  "misconception": "you overfilled 2s — an s sublevel holds at most 2 electrons, so boron's fifth electron opens 2p",
  "feedback": "This answer is wrong — you overfilled 2s. An s sublevel holds at most 2 electrons, so boron's fifth electron opens 2p: [He]2s²2p¹."
 }
]

{
 "keyExplanation": "Boron's atomic number is 5 — a neutral atom has 5 electrons.\nThe nearest noble gas before boron is helium (2 electrons): bracket it as [He].\nFill the remaining 3 in order: 2s², then 2p¹.\nWrite: [He]2s²2p¹. Check: 2 + 2 + 1 = 5.",
 "anticipatedWrong": [
  {
   "value": "1s²2s²2p¹",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand, which brackets helium's 1s² as [He]",
   "feedback": "This answer is wrong — you wrote the full configuration. The noble-gas shorthand replaces the 1s² stretch with the bracketed noble gas: [He]2s²2p¹."
  },
  {
   "value": "[He]2s³",
   "misconception": "you overfilled 2s — an s sublevel holds at most 2 electrons, so boron's fifth electron opens 2p",
   "feedback": "This answer is wrong — you overfilled 2s. An s sublevel holds at most 2 electrons, so boron's fifth electron opens 2p: [He]2s²2p¹."
  }
 ]
}

[
 {
  "value": "[Ar]4s²4p²",
  "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
  "feedback": "This answer is wrong — [Ar] holds 18 and 4s²4p² shows only 4 more, so this string accounts for just 22 of the atom's 32 electrons. After 4s² the full 3d¹⁰ block fills before 4p: the shorthand is [Ar]4s²3d¹⁰4p²."
 },
 {
  "value": "[Ne]3s²3p⁶4s²3d¹⁰4p²",
  "misconception": "you stopped the replacement at neon — argon's 18 also fits inside 32 and is nearer, so the shorthand starts from [Ar]",
  "feedback": "This answer is wrong — all 32 electrons are there, but the replacement stopped at neon's 10. Argon's 18 electrons also fit inside 32, and the shorthand always uses the nearest noble gas below the count, so argon's whole stretch is replaced: [Ar]4s²3d¹⁰4p²."
 },
 {
  "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²",
  "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand",
  "feedback": "This answer is wrong as written — the configuration itself is correct for 32 electrons, but the question asks for the noble-gas shorthand: replace the opening stretch 1s²2s²2p⁶3s²3p⁶ (argon's 18 electrons) with [Ar], leaving [Ar]4s²3d¹⁰4p²."
 }
]

{
 "keyExplanation": "Directly below silicon sits the element at atomic number 32 — 32 electrons.\nWrite those 18 electrons as the bracketed symbol [Ar], then place the remaining 32 − 18 = 14 electrons in the filling order: 4s², then the full 3d¹⁰ block, then 4p².\nThe shorthand is [Ar]4s²3d¹⁰4p² — 18 inside the bracket plus 14 shown makes 32.",
 "anticipatedWrong": [
  {
   "value": "[Ar]4s²4p²",
   "misconception": "you skipped the 3d sublevel — the full 3d¹⁰ block sits between 4s and 4p, inside or outside a shorthand alike",
   "feedback": "This answer is wrong — [Ar] holds 18 and 4s²4p² shows only 4 more, so this string accounts for just 22 of the atom's 32 electrons. After 4s² the full 3d¹⁰ block fills before 4p: the shorthand is [Ar]4s²3d¹⁰4p²."
  },
  {
   "value": "[Ne]3s²3p⁶4s²3d¹⁰4p²",
   "misconception": "you stopped the replacement at neon — argon's 18 also fits inside 32 and is nearer, so the shorthand starts from [Ar]",
   "feedback": "This answer is wrong — all 32 electrons are there, but the replacement stopped at neon's 10. Argon's 18 electrons also fit inside 32, and the shorthand always uses the nearest noble gas below the count, so argon's whole stretch is replaced: [Ar]4s²3d¹⁰4p²."
  },
  {
   "value": "1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²",
   "misconception": "you wrote the full configuration — the question asks for the noble-gas shorthand",
   "feedback": "This answer is wrong as written — the configuration itself is correct for 32 electrons, but the question asks for the noble-gas shorthand: replace the opening stretch 1s²2s²2p⁶3s²3p⁶ (argon's 18 electrons) with [Ar], leaving [Ar]4s²3d¹⁰4p²."
  }
 ]
}

[
 {
  "value": 4,
  "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
  "feedback": "This answer is wrong — you added the two elements' counts together. Sharing a column means sharing the SAME count: barium has 2 valence electrons, so strontium also has 2."
 }
]

{
 "keyExplanation": "Every element in a column of the periodic table has the same number of valence electrons. Barium has 2 valence electrons, and strontium sits in barium's column, so a strontium atom also has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
   "check": {
    "expr": "2+2",
    "expected": 4
   },
   "feedback": "This answer is wrong — you added the two elements' counts together. Sharing a column means sharing the SAME count: barium has 2 valence electrons, so strontium also has 2."
  }
 ]
}

[
 "Count every dot around the symbol, pairs included:",
 "two pairs and two single dots give 2 + 2 + 1 + 1 = 6",
 "Selenium has 6 valence electrons."
]

[
 {
  "value": 4,
  "misconception": "you counted each pair as one dot — a pair is two valence electrons",
  "feedback": "This answer is wrong — you counted each pair as one dot. A pair is two valence electrons: selenium's two pairs and two single dots give 2 + 2 + 1 + 1 = 6."
 },
 {
  "value": 2,
  "misconception": "you counted only the single dots — the paired dots are valence electrons too",
  "feedback": "This answer is wrong — you counted only selenium's two single dots. The paired dots are valence electrons too: 2 + 2 + 1 + 1 = 6."
 }
]

{
 "keyExplanation": "Count every dot, pairs included: two pairs and two single dots give 2 + 2 + 1 + 1 = 6. Selenium has 6 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you counted each pair as one dot — a pair is two valence electrons",
   "feedback": "This answer is wrong — you counted each pair as one dot. A pair is two valence electrons: selenium's two pairs and two single dots give 2 + 2 + 1 + 1 = 6."
  },
  {
   "value": 2,
   "misconception": "you counted only the single dots — the paired dots are valence electrons too",
   "feedback": "This answer is wrong — you counted only selenium's two single dots. The paired dots are valence electrons too: 2 + 2 + 1 + 1 = 6."
  }
 ]
}

[
 "The highest level number in the configuration is 4.",
 "The only level-4 sublevel is 4s² — the 3d¹⁰ electrons belong to level 3, so they are inner electrons.",
 "Zinc has 2 valence electrons."
]

[
 {
  "value": 12,
  "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
  "feedback": "This answer is wrong — you included the 3d¹⁰ electrons. 3d belongs to level 3, and level 4 is the highest level here: only 4s² counts, so zinc has 2 valence electrons."
 },
 {
  "value": 30,
  "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 4, and only 4s² sits there, so zinc has 2 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number in the configuration is 4, and the only level-4 sublevel is 4s². The 3d¹⁰ electrons belong to level 3, so they are inner electrons. Zinc has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 12,
   "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
   "check": {
    "expr": "2+10",
    "expected": 12
   },
   "feedback": "This answer is wrong — you included the 3d¹⁰ electrons. 3d belongs to level 3, and level 4 is the highest level here: only 4s² counts, so zinc has 2 valence electrons."
  },
  {
   "value": 30,
   "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "2+2+6+2+6+2+10",
    "expected": 30
   },
   "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 4, and only 4s² sits there, so zinc has 2 valence electrons."
  }
 ]
}

[
 "The bracketed [Ar] holds inner electrons, so it never counts.",
 "The highest level number in the configuration is 4.",
 "The level-4 sublevels are 4s² and 4p⁶ — the 3d¹⁰ electrons are inner electrons of level 3.",
 "Add the level-4 superscripts: 2 + 6 = 8 valence electrons."
]

[
 {
  "value": 18,
  "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
  "feedback": "This answer is wrong — you included the 3d¹⁰ electrons. 3d belongs to level 3, and level 4 is the highest level here — the level-4 sublevels are 4s² and 4p⁶, so krypton has 2 + 6 = 8 valence electrons."
 },
 {
  "value": 6,
  "misconception": "you counted only the 4p electrons — the 4s electrons sit in level 4 too",
  "feedback": "This answer is wrong — you counted only the 4p electrons. The 4s electrons sit in level 4 too — add both level-4 superscripts: 2 + 6 = 8 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number is 4, with sublevels 4s² and 4p⁶ — the 3d¹⁰ electrons belong to level 3, so they are inner electrons. Krypton has 2 + 6 = 8 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 18,
   "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
   "check": {
    "expr": "2+10+6",
    "expected": 18
   },
   "feedback": "This answer is wrong — you included the 3d¹⁰ electrons. 3d belongs to level 3, and level 4 is the highest level here — the level-4 sublevels are 4s² and 4p⁶, so krypton has 2 + 6 = 8 valence electrons."
  },
  {
   "value": 6,
   "misconception": "you counted only the 4p electrons — the 4s electrons sit in level 4 too",
   "check": {
    "expr": "6",
    "expected": 6
   },
   "feedback": "This answer is wrong — you counted only the 4p electrons. The 4s electrons sit in level 4 too — add both level-4 superscripts: 2 + 6 = 8 valence electrons."
  }
 ]
}

[
 {
  "value": 7,
  "misconception": "you used the period number — the column, not the row, gives the valence count",
  "feedback": "This answer is wrong — 7 is radium's period, its row in the table. The column, not the row, gives the valence count: radium sits in column 2, and columns 1 and 2 give the column number directly. Radium has 2 valence electrons."
 },
 {
  "value": -8,
  "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
  "feedback": "This answer is wrong — you subtracted 10 from radium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Radium has 2 valence electrons."
 }
]

{
 "keyExplanation": "Radium is a main-group element in column 2, and columns 1 and 2 give the column number directly. Radium has 2 valence electrons, whatever its row — the rule works in every period, so sitting in period 7 changes nothing.",
 "anticipatedWrong": [
  {
   "value": 7,
   "misconception": "you used the period number — the column, not the row, gives the valence count",
   "check": {
    "expr": "7",
    "expected": 7
   },
   "feedback": "This answer is wrong — 7 is radium's period, its row in the table. The column, not the row, gives the valence count: radium sits in column 2, and columns 1 and 2 give the column number directly. Radium has 2 valence electrons."
  },
  {
   "value": -8,
   "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
   "check": {
    "expr": "2-10",
    "expected": -8
   },
   "feedback": "This answer is wrong — you subtracted 10 from radium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Radium has 2 valence electrons."
  }
 ]
}

[
 {
  "value": -2,
  "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
  "feedback": "This answer is wrong — you subtracted the wrong way. Charge is protons minus electrons: 29 − 27 = +2, written 2+. With more protons than electrons the ion is positive."
 },
 {
  "value": 56,
  "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
  "feedback": "This answer is wrong — you added the counts. Charge is the difference: 29 − 27 = +2, written 2+."
 }
]

{
 "keyExplanation": "protons = 29\nelectrons = 27\ncharge = number of protons − number of electrons\ncharge = 29 − 27\ncharge = +2, written 2+\nTwo protons are left uncanceled, so the ion is positive.",
 "anticipatedWrong": [
  {
   "value": -2,
   "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
   "feedback": "This answer is wrong — you subtracted the wrong way. Charge is protons minus electrons: 29 − 27 = +2, written 2+. With more protons than electrons the ion is positive.",
   "check": {
    "expr": "27-29",
    "expected": -2
   }
  },
  {
   "value": 56,
   "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
   "feedback": "This answer is wrong — you added the counts. Charge is the difference: 29 − 27 = +2, written 2+.",
   "check": {
    "expr": "29+27",
    "expected": 56
   }
  }
 ]
}

[
 {
  "value": 1,
  "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
  "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 9 − 10 = −1, written 1−."
 },
 {
  "value": 1,
  "misconception": "you flipped the sign — protons minus electrons comes out negative here",
  "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 9 − 10 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
 },
 {
  "value": 19,
  "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
  "feedback": "This answer is wrong — you added the counts. Charge is the difference: 9 − 10 = −1, written 1−."
 }
]

{
 "keyExplanation": "protons = 9\nelectrons = 10\ncharge = number of protons − number of electrons\ncharge = 9 − 10\ncharge = −1, written 1−\nOne electron is left uncanceled, so the ion is negative.",
 "anticipatedWrong": [
  {
   "value": 1,
   "typedVariants": [
    "1"
   ],
   "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
   "check": {
    "expr": "abs(9-10)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 9 − 10 = −1, written 1−."
  },
  {
   "value": 1,
   "typedVariants": [
    "+1",
    "1+"
   ],
   "misconception": "you flipped the sign — protons minus electrons comes out negative here",
   "check": {
    "expr": "-(9-10)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 9 − 10 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
  },
  {
   "value": 19,
   "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
   "check": {
    "expr": "9+10",
    "expected": 19
   },
   "feedback": "This answer is wrong — you added the counts. Charge is the difference: 9 − 10 = −1, written 1−."
  }
 ]
}

[
 {
  "value": 48,
  "misconception": "you added the charge instead of subtracting — a 1+ charge means one electron LOST",
  "feedback": "This answer is wrong — you added the charge instead of subtracting; a 1+ charge means one electron LOST. number of electrons = 47 − 1 = 46: a cation has lost electrons, so 46 below 47 is right."
 },
 {
  "value": 47,
  "misconception": "you ignored the charge — Ag⁺ is an ion, so its electron count differs from its proton count",
  "feedback": "This answer is wrong — you ignored the charge; Ag⁺ is an ion, so its electron count differs from its proton count. number of electrons = 47 − 1 = 46: a cation has lost electrons, so 46 below 47 is right."
 }
]

{
 "keyExplanation": "protons = 47, charge = +1\nnumber of electrons = number of protons − charge\nnumber of electrons = 47 − 1\nnumber of electrons = 46\nA cation has lost electrons, so the count sits below the proton count — 46 below 47 checks out.",
 "anticipatedWrong": [
  {
   "value": 48,
   "misconception": "you added the charge instead of subtracting — a 1+ charge means one electron LOST",
   "check": {
    "expr": "47+1",
    "expected": 48
   },
   "feedback": "This answer is wrong — you added the charge instead of subtracting; a 1+ charge means one electron LOST. number of electrons = 47 − 1 = 46: a cation has lost electrons, so 46 below 47 is right."
  },
  {
   "value": 47,
   "misconception": "you ignored the charge — Ag⁺ is an ion, so its electron count differs from its proton count",
   "check": {
    "expr": "47",
    "expected": 47
   },
   "feedback": "This answer is wrong — you ignored the charge; Ag⁺ is an ion, so its electron count differs from its proton count. number of electrons = 47 − 1 = 46: a cation has lost electrons, so 46 below 47 is right."
  }
 ]
}

[
 {
  "value": 40,
  "misconception": "you added the charge instead of subtracting — a 2+ charge means two electrons LOST",
  "feedback": "This answer is wrong — you added the charge instead of subtracting; a 2+ charge means two electrons LOST. Electrons = protons − charge = 38 − 2 = 36."
 },
 {
  "value": 86,
  "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
  "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 38 − 2 = 36; the mass number 88 matters only for neutrons."
 },
 {
  "value": 38,
  "misconception": "you ignored the charge — the ion has lost two electrons from its 38 protons",
  "feedback": "This answer is wrong — you ignored the charge; the ion has lost two electrons from its 38 protons. Electrons = 38 − 2 = 36."
 }
]

{
 "keyExplanation": "Protons: the atomic number is 38.\nElectrons: protons − charge = 38 − 2 = 36.\nA cation has lost electrons, so 36 below 38 checks out — the mass number 88 matters only for neutrons.",
 "anticipatedWrong": [
  {
   "value": 40,
   "misconception": "you added the charge instead of subtracting — a 2+ charge means two electrons LOST",
   "check": {
    "expr": "38+2",
    "expected": 40
   },
   "feedback": "This answer is wrong — you added the charge instead of subtracting; a 2+ charge means two electrons LOST. Electrons = protons − charge = 38 − 2 = 36."
  },
  {
   "value": 86,
   "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
   "check": {
    "expr": "88-2",
    "expected": 86
   },
   "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 38 − 2 = 36; the mass number 88 matters only for neutrons."
  },
  {
   "value": 38,
   "misconception": "you ignored the charge — the ion has lost two electrons from its 38 protons",
   "check": {
    "expr": "38",
    "expected": 38
   },
   "feedback": "This answer is wrong — you ignored the charge; the ion has lost two electrons from its 38 protons. Electrons = 38 − 2 = 36."
  }
 ]
}

[
 {
  "value": 59,
  "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
  "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 61 + 2 = 63. Check the sign: an ion with 59 protons and 61 electrons would carry a 2− charge, not 2+."
 },
 {
  "value": 61,
  "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 2+ charge",
  "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 2+ charge means the proton count sits two above the electron count: protons = electrons + charge = 61 + 2 = 63."
 }
]

{
 "keyExplanation": "Start from the taught equation: charge = number of protons − number of electrons. This time the proton count is the unknown, so make the number of protons the subject: number of protons = number of electrons + charge. A 2+ charge counts as +2, so protons = 61 + 2 = 63. Check with the plain-words rule: a cation has lost electrons, so its electron count sits below its proton count — 61 sits below 63 by exactly the two charges.",
 "anticipatedWrong": [
  {
   "value": 59,
   "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
   "check": {
    "expr": "61-2",
    "expected": 59
   },
   "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 61 + 2 = 63. Check the sign: an ion with 59 protons and 61 electrons would carry a 2− charge, not 2+."
  },
  {
   "value": 61,
   "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 2+ charge",
   "check": {
    "expr": "61",
    "expected": 61
   },
   "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 2+ charge means the proton count sits two above the electron count: protons = electrons + charge = 61 + 2 = 63."
  }
 ]
}

[
 {
  "value": 4,
  "misconception": "you gave beryllium's atomic number — the column, not the proton count, gives the valence count",
  "feedback": "This answer is wrong — you gave beryllium's atomic number. The column, not the proton count, gives the valence count: column 2 means 2 valence electrons."
 }
]

{
 "keyExplanation": "Beryllium is a main-group element in column 2, and columns 1 and 2 give the valence-electron count directly: beryllium has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you gave beryllium's atomic number — the column, not the proton count, gives the valence count",
   "check": {
    "expr": "4",
    "expected": 4
   },
   "feedback": "This answer is wrong — you gave beryllium's atomic number. The column, not the proton count, gives the valence count: column 2 means 2 valence electrons."
  }
 ]
}

[
 "Count the dots around the symbol:",
 "three single dots give 1 + 1 + 1 = 3",
 "Boron has 3 valence electrons; its 2 inner electrons hide inside the letter B."
]

[
 {
  "value": 5,
  "misconception": "you gave boron's total electron count — the dots show only the valence electrons",
  "feedback": "This answer is wrong — 5 is boron's total electron count. The dots show only the valence electrons: three single dots give 3; boron's 2 inner electrons hide inside the letter B."
 }
]

{
 "keyExplanation": "Count the dots around the symbol: three single dots. Boron has 3 valence electrons; its 2 inner electrons hide inside the letter B.",
 "anticipatedWrong": [
  {
   "value": 5,
   "misconception": "you gave boron's total electron count — the dots show only the valence electrons",
   "feedback": "This answer is wrong — 5 is boron's total electron count. The dots show only the valence electrons: three single dots give 3; boron's 2 inner electrons hide inside the letter B."
  }
 ]
}

[
 {
  "value": 6,
  "misconception": "you counted only the 3p electrons — the 3s electrons sit in level 3 too",
  "feedback": "This answer is wrong — you counted only the 3p electrons; the 3s electrons sit in level 3 too. Add every level-3 superscript: 2 + 6 = 8 valence electrons."
 },
 {
  "value": 18,
  "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom; only the highest level's electrons are valence electrons. Level 3 is the highest level here, with 3s² and 3p⁶: 2 + 6 = 8 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number in the configuration is 3, with sublevels 3s² and 3p⁶. Argon has 2 + 6 = 8 valence electrons; the 10 electrons in levels 1 and 2 are all inner electrons.",
 "anticipatedWrong": [
  {
   "value": 6,
   "misconception": "you counted only the 3p electrons — the 3s electrons sit in level 3 too",
   "check": {
    "expr": "6",
    "expected": 6
   },
   "feedback": "This answer is wrong — you counted only the 3p electrons; the 3s electrons sit in level 3 too. Add every level-3 superscript: 2 + 6 = 8 valence electrons."
  },
  {
   "value": 18,
   "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "2+2+6+2+6",
    "expected": 18
   },
   "feedback": "This answer is wrong — you counted every electron in the atom; only the highest level's electrons are valence electrons. Level 3 is the highest level here, with 3s² and 3p⁶: 2 + 6 = 8 valence electrons."
  }
 ]
}

[
 "The bracketed [Kr] holds inner electrons, so it never counts.",
 "The highest level number in the configuration is 5.",
 "The level-5 sublevels are 5s² and 5p⁴ — the 4d¹⁰ electrons are inner electrons of level 4.",
 "Add the level-5 superscripts: 2 + 4 = 6 valence electrons."
]

[
 {
  "value": 16,
  "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
  "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p⁴, so tellurium has 2 + 4 = 6 valence electrons."
 },
 {
  "value": 4,
  "misconception": "you counted only the 5p electrons — the 5s electrons sit in level 5 too",
  "feedback": "This answer is wrong — you counted only the 5p electrons. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 4 = 6 valence electrons."
 },
 {
  "value": 52,
  "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
  "feedback": "This answer is wrong — you included the bracketed krypton's electrons. The bracketed part is all inner electrons — only the level-5 superscripts count: 2 + 4 = 6 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number is 5, with sublevels 5s² and 5p⁴ — the 4d¹⁰ electrons belong to level 4, so they are inner electrons. Tellurium has 2 + 4 = 6 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 16,
   "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
   "check": {
    "expr": "2+10+4",
    "expected": 16
   },
   "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p⁴, so tellurium has 2 + 4 = 6 valence electrons."
  },
  {
   "value": 4,
   "misconception": "you counted only the 5p electrons — the 5s electrons sit in level 5 too",
   "check": {
    "expr": "4",
    "expected": 4
   },
   "feedback": "This answer is wrong — you counted only the 5p electrons. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 4 = 6 valence electrons."
  },
  {
   "value": 52,
   "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
   "check": {
    "expr": "36+2+10+4",
    "expected": 52
   },
   "feedback": "This answer is wrong — you included the bracketed krypton's electrons. The bracketed part is all inner electrons — only the level-5 superscripts count: 2 + 4 = 6 valence electrons."
  }
 ]
}

[
 {
  "value": 6,
  "misconception": "you used the period number — the column, not the row, gives the valence count",
  "feedback": "This answer is wrong — 6 is barium's period, its row in the table. The column, not the row, gives the valence count: barium sits in column 2, and columns 1 and 2 give the column number directly. Barium has 2 valence electrons."
 },
 {
  "value": -8,
  "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
  "feedback": "This answer is wrong — you subtracted 10 from barium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Barium has 2 valence electrons."
 }
]

{
 "keyExplanation": "Barium is a main-group element in column 2, and columns 1 and 2 give the column number directly. Barium has 2 valence electrons, whatever its row.",
 "anticipatedWrong": [
  {
   "value": 6,
   "misconception": "you used the period number — the column, not the row, gives the valence count",
   "check": {
    "expr": "6",
    "expected": 6
   },
   "feedback": "This answer is wrong — 6 is barium's period, its row in the table. The column, not the row, gives the valence count: barium sits in column 2, and columns 1 and 2 give the column number directly. Barium has 2 valence electrons."
  },
  {
   "value": -8,
   "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
   "check": {
    "expr": "2-10",
    "expected": -8
   },
   "feedback": "This answer is wrong — you subtracted 10 from barium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Barium has 2 valence electrons."
  }
 ]
}

[
 {
  "value": -1,
  "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
  "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 3 − 2 = +1. This ion has more protons than electrons, so its charge is positive, written 1+."
 },
 {
  "value": 5,
  "misconception": "you added the counts instead of subtracting",
  "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 3 − 2 = +1, written 1+."
 }
]

{
 "keyExplanation": "protons = 3\nelectrons = 2\ncharge = number of protons − number of electrons\ncharge = 3 − 2\ncharge = +1, written 1+\nOne proton is left uncanceled, so the ion is positive.",
 "anticipatedWrong": [
  {
   "value": -1,
   "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
   "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 3 − 2 = +1. This ion has more protons than electrons, so its charge is positive, written 1+."
  },
  {
   "value": 5,
   "misconception": "you added the counts instead of subtracting",
   "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 3 − 2 = +1, written 1+."
  }
 ]
}

[
 {
  "value": 2,
  "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
  "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 8 − 10 = −2, written 2−."
 },
 {
  "value": 2,
  "misconception": "you flipped the sign — protons minus electrons comes out negative here",
  "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 8 − 10 = −2, written 2−. More electrons than protons makes the ion negative, never positive."
 },
 {
  "value": 18,
  "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
  "feedback": "This answer is wrong — you added the counts. Charge is the difference: 8 − 10 = −2, written 2−."
 }
]

{
 "keyExplanation": "protons = 8\nelectrons = 10\ncharge = number of protons − number of electrons\ncharge = 8 − 10\ncharge = −2, written 2−\nTwo electrons are left uncanceled, so the ion is negative.",
 "anticipatedWrong": [
  {
   "value": 2,
   "typedVariants": [
    "2"
   ],
   "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
   "check": {
    "expr": "abs(8-10)",
    "expected": 2
   },
   "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 8 − 10 = −2, written 2−."
  },
  {
   "value": 2,
   "typedVariants": [
    "+2",
    "2+"
   ],
   "misconception": "you flipped the sign — protons minus electrons comes out negative here",
   "check": {
    "expr": "-(8-10)",
    "expected": 2
   },
   "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 8 − 10 = −2, written 2−. More electrons than protons makes the ion negative, never positive."
  },
  {
   "value": 18,
   "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
   "check": {
    "expr": "8+10",
    "expected": 18
   },
   "feedback": "This answer is wrong — you added the counts. Charge is the difference: 8 − 10 = −2, written 2−."
  }
 ]
}

[
 {
  "value": 48,
  "misconception": "you subtracted the charge — a negative charge means electrons were gained, so you add",
  "feedback": "This answer is wrong — you subtracted the charge. A negative charge means electrons were GAINED: 51 + 3 = 54 electrons."
 },
 {
  "value": 51,
  "misconception": "you ignored the charge — the ion is not neutral, and the 3− means three extra electrons",
  "feedback": "This answer is wrong — you ignored the charge. The 3− means three extra electrons: 51 + 3 = 54 electrons."
 }
]

{
 "keyExplanation": "The atomic number 51 gives the protons, and a neutral antimony atom would have 51 electrons. The 3− charge means the ion has gained 3 electrons: 51 + 3 = 54 electrons.",
 "anticipatedWrong": [
  {
   "value": 48,
   "misconception": "you subtracted the charge — a negative charge means electrons were gained, so you add",
   "check": {
    "expr": "51-3",
    "expected": 48
   },
   "feedback": "This answer is wrong — you subtracted the charge. A negative charge means electrons were GAINED: 51 + 3 = 54 electrons."
  },
  {
   "value": 51,
   "misconception": "you ignored the charge — the ion is not neutral, and the 3− means three extra electrons",
   "check": {
    "expr": "51",
    "expected": 51
   },
   "feedback": "This answer is wrong — you ignored the charge. The 3− means three extra electrons: 51 + 3 = 54 electrons."
  }
 ]
}

[
 {
  "value": 64,
  "misconception": "you brought the charge into the neutron count — the charge changes only the electrons",
  "feedback": "This answer is wrong — you brought the charge into the neutron count; the charge changes only the electrons. Neutrons = mass number − atomic number = 114 − 48 = 66."
 },
 {
  "value": 114,
  "misconception": "you gave the mass number — subtract the atomic number to get the neutrons",
  "feedback": "This answer is wrong — you gave the mass number; subtract the atomic number to get the neutrons: 114 − 48 = 66."
 },
 {
  "value": 46,
  "misconception": "you gave the electron count — the question asks for neutrons, which come from mass number minus atomic number",
  "feedback": "This answer is wrong — you gave the electron count (48 − 2 = 46); the question asks for neutrons, which come from mass number minus atomic number: 114 − 48 = 66."
 }
]

{
 "keyExplanation": "Neutrons: mass number − atomic number = 114 − 48 = 66.\nThe ²⁺ charge changes only the electron count; the isotope part alone fixes the 48 protons and 66 neutrons.",
 "anticipatedWrong": [
  {
   "value": 64,
   "misconception": "you brought the charge into the neutron count — the charge changes only the electrons",
   "check": {
    "expr": "114-48-2",
    "expected": 64
   },
   "feedback": "This answer is wrong — you brought the charge into the neutron count; the charge changes only the electrons. Neutrons = mass number − atomic number = 114 − 48 = 66."
  },
  {
   "value": 114,
   "misconception": "you gave the mass number — subtract the atomic number to get the neutrons",
   "check": {
    "expr": "114",
    "expected": 114
   },
   "feedback": "This answer is wrong — you gave the mass number; subtract the atomic number to get the neutrons: 114 − 48 = 66."
  },
  {
   "value": 46,
   "misconception": "you gave the electron count — the question asks for neutrons, which come from mass number minus atomic number",
   "check": {
    "expr": "48-2",
    "expected": 46
   },
   "feedback": "This answer is wrong — you gave the electron count (48 − 2 = 46); the question asks for neutrons, which come from mass number minus atomic number: 114 − 48 = 66."
  }
 ]
}

[
 {
  "value": 42,
  "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
  "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 44 + 2 = 46. Check the sign: an ion with 42 protons and 44 electrons would carry a 2− charge, not 2+."
 },
 {
  "value": 44,
  "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 2+ charge",
  "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 2+ charge means the proton count sits two above the electron count: protons = electrons + charge = 44 + 2 = 46."
 }
]

{
 "keyExplanation": "Start from the taught equation: charge = number of protons − number of electrons. This time the proton count is the unknown, so make the number of protons the subject: number of protons = number of electrons + charge. A 2+ charge counts as +2, so protons = 44 + 2 = 46. Check with the plain-words rule: a cation has lost electrons, so its electron count sits below its proton count — 44 sits below 46 by exactly the two charges.",
 "anticipatedWrong": [
  {
   "value": 42,
   "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
   "check": {
    "expr": "44-2",
    "expected": 42
   },
   "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 44 + 2 = 46. Check the sign: an ion with 42 protons and 44 electrons would carry a 2− charge, not 2+."
  },
  {
   "value": 44,
   "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 2+ charge",
   "check": {
    "expr": "44",
    "expected": 44
   },
   "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 2+ charge means the proton count sits two above the electron count: protons = electrons + charge = 44 + 2 = 46."
  }
 ]
}

[
 {
  "value": 12,
  "misconception": "you added 10 to the column number — the subtract-10 step belongs to columns 13 through 18, and it runs the other way",
  "feedback": "This answer is wrong — you added 10 to the column number. The subtract-10 step belongs to columns 13 through 18, and it runs the other way: columns 1 and 2 give the count directly, so column 2 means 2 valence electrons."
 }
]

{
 "keyExplanation": "Barium is a main-group element in column 2, and columns 1 and 2 give the valence-electron count directly: a barium atom has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 12,
   "misconception": "you added 10 to the column number — the subtract-10 step belongs to columns 13 through 18, and it runs the other way",
   "check": {
    "expr": "2+10",
    "expected": 12
   },
   "feedback": "This answer is wrong — you added 10 to the column number. The subtract-10 step belongs to columns 13 through 18, and it runs the other way: columns 1 and 2 give the count directly, so column 2 means 2 valence electrons."
  }
 ]
}

[
 "Count every dot around the symbol, pairs included:",
 "three pairs and one single dot give 2 + 2 + 2 + 1 = 7",
 "Astatine has 7 valence electrons."
]

[
 {
  "value": 4,
  "misconception": "you counted each pair as one dot — a pair is two valence electrons",
  "feedback": "This answer is wrong — you counted each pair as one dot. A pair is two valence electrons: 2 + 2 + 2 + 1 = 7."
 },
 {
  "value": 1,
  "misconception": "you counted only the single dots — every dot is a valence electron, paired or not",
  "feedback": "This answer is wrong — you counted only the single dots. Every dot is a valence electron, paired or not: 2 + 2 + 2 + 1 = 7."
 }
]

{
 "keyExplanation": "Count every dot, pairs included: three pairs and one single give 2 + 2 + 2 + 1 = 7. Astatine has 7 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you counted each pair as one dot — a pair is two valence electrons",
   "feedback": "This answer is wrong — you counted each pair as one dot. A pair is two valence electrons: 2 + 2 + 2 + 1 = 7."
  },
  {
   "value": 1,
   "misconception": "you counted only the single dots — every dot is a valence electron, paired or not",
   "feedback": "This answer is wrong — you counted only the single dots. Every dot is a valence electron, paired or not: 2 + 2 + 2 + 1 = 7."
  }
 ]
}

[
 {
  "value": 13,
  "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
  "feedback": "This answer is wrong — you included the 3d¹⁰ electrons; 3d belongs to level 3, and level 4 is the highest level here. Add only the level-4 superscripts: 2 + 1 = 3 valence electrons."
 },
 {
  "value": 1,
  "misconception": "you counted only the 4p electron — the 4s electrons sit in level 4 too",
  "feedback": "This answer is wrong — you counted only the 4p electron; the 4s electrons sit in level 4 too. Add every level-4 superscript: 2 + 1 = 3 valence electrons."
 },
 {
  "value": 31,
  "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom; only the highest level's electrons are valence electrons. The highest level is 4, with 4s² and 4p¹: 2 + 1 = 3 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number in the configuration is 4, with sublevels 4s² and 4p¹ — the 3d¹⁰ electrons belong to level 3, so they are inner electrons. Gallium has 2 + 1 = 3 valence electrons; the 28 electrons in levels 1 through 3 are all inner electrons.",
 "anticipatedWrong": [
  {
   "value": 13,
   "misconception": "you included the 3d¹⁰ electrons — 3d belongs to level 3, and level 4 is the highest level here",
   "check": {
    "expr": "2+10+1",
    "expected": 13
   },
   "feedback": "This answer is wrong — you included the 3d¹⁰ electrons; 3d belongs to level 3, and level 4 is the highest level here. Add only the level-4 superscripts: 2 + 1 = 3 valence electrons."
  },
  {
   "value": 1,
   "misconception": "you counted only the 4p electron — the 4s electrons sit in level 4 too",
   "check": {
    "expr": "1",
    "expected": 1
   },
   "feedback": "This answer is wrong — you counted only the 4p electron; the 4s electrons sit in level 4 too. Add every level-4 superscript: 2 + 1 = 3 valence electrons."
  },
  {
   "value": 31,
   "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "2+2+6+2+6+2+10+1",
    "expected": 31
   },
   "feedback": "This answer is wrong — you counted every electron in the atom; only the highest level's electrons are valence electrons. The highest level is 4, with 4s² and 4p¹: 2 + 1 = 3 valence electrons."
  }
 ]
}

[
 "The bracketed [Kr] holds inner electrons, so it never counts.",
 "The highest level number in the configuration is 5.",
 "The only level-5 sublevel is 5s² — the 4d¹⁰ electrons are inner electrons of level 4.",
 "Cadmium has 2 valence electrons."
]

[
 {
  "value": 12,
  "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
  "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here: only 5s² counts, so cadmium has 2 valence electrons."
 },
 {
  "value": 48,
  "misconception": "you counted every electron in the atom, bracket included — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom, bracket included. Only the highest level's electrons are valence electrons: the highest level is 5, and only 5s² sits there, so cadmium has 2 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number is 5, and the only level-5 sublevel is 5s² — the 4d¹⁰ electrons belong to level 4, so they are inner electrons, and the bracketed [Kr] never counts. Cadmium has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 12,
   "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
   "check": {
    "expr": "2+10",
    "expected": 12
   },
   "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here: only 5s² counts, so cadmium has 2 valence electrons."
  },
  {
   "value": 48,
   "misconception": "you counted every electron in the atom, bracket included — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "36+2+10",
    "expected": 48
   },
   "feedback": "This answer is wrong — you counted every electron in the atom, bracket included. Only the highest level's electrons are valence electrons: the highest level is 5, and only 5s² sits there, so cadmium has 2 valence electrons."
  }
 ]
}

[
 {
  "value": 6,
  "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
  "feedback": "This answer is wrong — you added the two elements' counts together — sharing a column means sharing the same count, not combining counts"
 }
]

{
 "keyExplanation": "Every element in a column of the periodic table has the same number of valence electrons. Thallium has 3, and boron sits in thallium's column, so a boron atom also has 3 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 6,
   "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
   "check": {
    "expr": "3+3",
    "expected": 6
   },
   "feedback": "This answer is wrong — you added the two elements' counts together — sharing a column means sharing the same count, not combining counts"
  }
 ]
}

[
 {
  "value": -2,
  "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
  "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 50 − 48 = +2. This ion has more protons than electrons, so its charge is positive, written 2+."
 },
 {
  "value": 98,
  "misconception": "you added the counts instead of subtracting",
  "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 50 − 48 = +2, written 2+."
 }
]

{
 "keyExplanation": "protons = 50\nelectrons = 48\ncharge = number of protons − number of electrons\ncharge = 50 − 48\ncharge = +2, written 2+\nTwo protons are left uncanceled, so the ion is positive.",
 "anticipatedWrong": [
  {
   "value": -2,
   "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
   "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 50 − 48 = +2. This ion has more protons than electrons, so its charge is positive, written 2+."
  },
  {
   "value": 98,
   "misconception": "you added the counts instead of subtracting",
   "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 50 − 48 = +2, written 2+."
  }
 ]
}

[
 {
  "value": 1,
  "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
  "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 1 − 2 = −1, written 1−."
 },
 {
  "value": 1,
  "misconception": "you flipped the sign — protons minus electrons comes out negative here",
  "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 1 − 2 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
 },
 {
  "value": 3,
  "misconception": "you added the counts instead of subtracting",
  "feedback": "This answer is wrong — you added the counts instead of subtracting. The equation is charge = number of protons − number of electrons: 1 − 2 = −1, written 1−."
 }
]

{
 "keyExplanation": "protons = 1\nelectrons = 2\ncharge = number of protons − number of electrons\ncharge = 1 − 2\ncharge = −1, written 1−\nOne electron is left uncanceled, so the ion is negative.",
 "anticipatedWrong": [
  {
   "value": 1,
   "typedVariants": [
    "1"
   ],
   "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
   "check": {
    "expr": "abs(1-2)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 1 − 2 = −1, written 1−."
  },
  {
   "value": 1,
   "typedVariants": [
    "+1",
    "1+"
   ],
   "misconception": "you flipped the sign — protons minus electrons comes out negative here",
   "check": {
    "expr": "-(1-2)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 1 − 2 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
  },
  {
   "value": 3,
   "typedVariants": [
    "3"
   ],
   "misconception": "you added the counts instead of subtracting",
   "feedback": "This answer is wrong — you added the counts instead of subtracting. The equation is charge = number of protons − number of electrons: 1 − 2 = −1, written 1−.",
   "check": {
    "expr": "1+2",
    "expected": 3
   }
  }
 ]
}

[
 {
  "value": 52,
  "misconception": "you subtracted the charge's size — a 1− charge means one electron GAINED, so the count goes up",
  "feedback": "This answer is wrong — you subtracted the charge's size; a 1− charge means one electron GAINED, so the count goes up. number of electrons = 53 − (−1) = 54: an anion has gained electrons, so 54 above 53 is right."
 },
 {
  "value": 53,
  "misconception": "you ignored the charge — I⁻ is an ion, so its electron count differs from its proton count",
  "feedback": "This answer is wrong — you ignored the charge; I⁻ is an ion, so its electron count differs from its proton count. number of electrons = 53 − (−1) = 54: an anion has gained electrons, so 54 above 53 is right."
 }
]

{
 "keyExplanation": "protons = 53, charge = −1\nnumber of electrons = number of protons − charge\nnumber of electrons = 53 − (−1)\nnumber of electrons = 54\nAn anion has gained electrons, so the count sits above the proton count — 54 above 53 checks out.",
 "anticipatedWrong": [
  {
   "value": 52,
   "misconception": "you subtracted the charge's size — a 1− charge means one electron GAINED, so the count goes up",
   "check": {
    "expr": "53-1",
    "expected": 52
   },
   "feedback": "This answer is wrong — you subtracted the charge's size; a 1− charge means one electron GAINED, so the count goes up. number of electrons = 53 − (−1) = 54: an anion has gained electrons, so 54 above 53 is right."
  },
  {
   "value": 53,
   "misconception": "you ignored the charge — I⁻ is an ion, so its electron count differs from its proton count",
   "check": {
    "expr": "53",
    "expected": 53
   },
   "feedback": "This answer is wrong — you ignored the charge; I⁻ is an ion, so its electron count differs from its proton count. number of electrons = 53 − (−1) = 54: an anion has gained electrons, so 54 above 53 is right."
  }
 ]
}

[
 {
  "value": 19,
  "misconception": "you brought the charge into the neutron count — the charge changes only the electrons",
  "feedback": "This answer is wrong — you brought the charge into the neutron count; the charge changes only the electrons. Neutrons = mass number − atomic number = 31 − 15 = 16."
 },
 {
  "value": 18,
  "misconception": "you gave the electron count — the question asks for neutrons, which come from mass number minus atomic number",
  "feedback": "This answer is wrong — you gave the electron count (15 − (−3) = 18); the question asks for neutrons, which come from mass number minus atomic number: 31 − 15 = 16."
 }
]

{
 "keyExplanation": "Neutrons: mass number − atomic number = 31 − 15 = 16.\nThe ³⁻ charge changes only the electron count; the isotope part alone fixes the 15 protons and 16 neutrons.",
 "anticipatedWrong": [
  {
   "value": 19,
   "misconception": "you brought the charge into the neutron count — the charge changes only the electrons",
   "check": {
    "expr": "31-15+3",
    "expected": 19
   },
   "feedback": "This answer is wrong — you brought the charge into the neutron count; the charge changes only the electrons. Neutrons = mass number − atomic number = 31 − 15 = 16."
  },
  {
   "value": 18,
   "misconception": "you gave the electron count — the question asks for neutrons, which come from mass number minus atomic number",
   "check": {
    "expr": "15-(-3)",
    "expected": 18
   },
   "feedback": "This answer is wrong — you gave the electron count (15 − (−3) = 18); the question asks for neutrons, which come from mass number minus atomic number: 31 − 15 = 16."
  }
 ]
}

[
 {
  "value": 39,
  "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
  "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 42 + 3 = 45. Check the sign: an ion with 39 protons and 42 electrons would carry a 3− charge, not 3+."
 },
 {
  "value": 42,
  "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
  "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 42 + 3 = 45."
 }
]

{
 "keyExplanation": "Start from the taught equation: charge = number of protons − number of electrons. This time the proton count is the unknown, so make the number of protons the subject: number of protons = number of electrons + charge. A 3+ charge counts as +3, so protons = 42 + 3 = 45. Check with the plain-words rule: a cation has lost electrons, so its electron count sits below its proton count — 42 sits below 45 by exactly the three charges.",
 "anticipatedWrong": [
  {
   "value": 39,
   "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
   "check": {
    "expr": "42-3",
    "expected": 39
   },
   "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 42 + 3 = 45. Check the sign: an ion with 39 protons and 42 electrons would carry a 3− charge, not 3+."
  },
  {
   "value": 42,
   "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
   "check": {
    "expr": "42",
    "expected": 42
   },
   "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 42 + 3 = 45."
  }
 ]
}

[
 {
  "value": 4,
  "misconception": "you gave beryllium's atomic number — the column, not the proton count, gives the valence count",
  "feedback": "This answer is wrong — you gave beryllium's atomic number. The column, not the proton count, gives the valence count: column 2 means 2 valence electrons."
 }
]

{
 "keyExplanation": "Beryllium is a main-group element in column 2, and columns 1 and 2 give the valence-electron count directly: a beryllium atom has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you gave beryllium's atomic number — the column, not the proton count, gives the valence count",
   "check": {
    "expr": "4",
    "expected": 4
   },
   "feedback": "This answer is wrong — you gave beryllium's atomic number. The column, not the proton count, gives the valence count: column 2 means 2 valence electrons."
  }
 ]
}

[
 "Count every dot around the symbol, pairs included:",
 "four pairs give 2 + 2 + 2 + 2 = 8",
 "Radon has 8 valence electrons — every one of them sits in a pair."
]

[
 {
  "value": 4,
  "misconception": "you counted each pair as one dot — a pair is two valence electrons",
  "feedback": "This answer is wrong — you counted each of radon's four pairs as one dot. A pair is two valence electrons: 2 + 2 + 2 + 2 = 8."
 }
]

{
 "keyExplanation": "Count every dot, pairs included: four pairs give 2 + 2 + 2 + 2 = 8. Radon has 8 valence electrons — every one of them sits in a pair.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you counted each pair as one dot — a pair is two valence electrons",
   "feedback": "This answer is wrong — you counted each of radon's four pairs as one dot. A pair is two valence electrons: 2 + 2 + 2 + 2 = 8."
  }
 ]
}

[
 "The highest level number in the configuration is 6.",
 "The only level-6 sublevel is 6s² — everything in levels 1 through 5 is inner.",
 "Barium has 2 valence electrons."
]

[
 {
  "value": 8,
  "misconception": "you counted the level-5 electrons — level 6 is the highest level, and only 6s² sits there",
  "feedback": "This answer is wrong — you counted the level-5 electrons (5s² and 5p⁶). Level 6 is the highest level, and only 6s² sits there: barium has 2 valence electrons."
 },
 {
  "value": 56,
  "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 6, and only 6s² sits there, so barium has 2 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number in the configuration is 6, and the only level-6 sublevel is 6s². Everything in levels 1 through 5 is inner. Barium has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 8,
   "misconception": "you counted the level-5 electrons — level 6 is the highest level, and only 6s² sits there",
   "check": {
    "expr": "2+6",
    "expected": 8
   },
   "feedback": "This answer is wrong — you counted the level-5 electrons (5s² and 5p⁶). Level 6 is the highest level, and only 6s² sits there: barium has 2 valence electrons."
  },
  {
   "value": 56,
   "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "2+2+6+2+6+2+10+6+2+10+6+2",
    "expected": 56
   },
   "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 6, and only 6s² sits there, so barium has 2 valence electrons."
  }
 ]
}

[
 "The bracketed [Kr] holds inner electrons, so it never counts.",
 "The highest level number in the configuration is 5.",
 "The level-5 sublevels are 5s² and 5p² — the 4d¹⁰ electrons are inner electrons of level 4.",
 "Add the level-5 superscripts: 2 + 2 = 4 valence electrons."
]

[
 {
  "value": 14,
  "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
  "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p², so tin has 2 + 2 = 4 valence electrons."
 },
 {
  "value": 2,
  "misconception": "you counted only the 5p electrons — the 5s electrons sit in level 5 too",
  "feedback": "This answer is wrong — you counted only the 5p electrons. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 2 = 4 valence electrons."
 },
 {
  "value": 50,
  "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
  "feedback": "This answer is wrong — you included the bracketed krypton's electrons. In a noble-gas shorthand the bracketed part is all inner electrons, so [Kr] never counts — only the level-5 sublevels 5s² and 5p² count, and tin has 2 + 2 = 4 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number is 5, with sublevels 5s² and 5p² — the 4d¹⁰ electrons belong to level 4, so they are inner electrons. Tin has 2 + 2 = 4 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 14,
   "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
   "check": {
    "expr": "2+10+2",
    "expected": 14
   },
   "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p², so tin has 2 + 2 = 4 valence electrons."
  },
  {
   "value": 2,
   "misconception": "you counted only the 5p electrons — the 5s electrons sit in level 5 too",
   "check": {
    "expr": "2",
    "expected": 2
   },
   "feedback": "This answer is wrong — you counted only the 5p electrons. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 2 = 4 valence electrons."
  },
  {
   "value": 50,
   "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
   "check": {
    "expr": "36+2+10+2",
    "expected": 50
   },
   "feedback": "This answer is wrong — you included the bracketed krypton's electrons. In a noble-gas shorthand the bracketed part is all inner electrons, so [Kr] never counts — only the level-5 sublevels 5s² and 5p² count, and tin has 2 + 2 = 4 valence electrons."
  }
 ]
}

[
 {
  "value": 5,
  "misconception": "you used the period number — the column, not the row, gives the valence count",
  "feedback": "This answer is wrong — 5 is strontium's period, its row in the table. The column, not the row, gives the valence count: strontium sits in column 2, and columns 1 and 2 give the column number directly. Strontium has 2 valence electrons."
 },
 {
  "value": -8,
  "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
  "feedback": "This answer is wrong — you subtracted 10 from strontium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Strontium has 2 valence electrons."
 }
]

{
 "keyExplanation": "Strontium is a main-group element in column 2, and columns 1 and 2 give the column number directly. Strontium has 2 valence electrons, whatever its row — the rule works in every period, so sitting in period 5 changes nothing.",
 "anticipatedWrong": [
  {
   "value": 5,
   "misconception": "you used the period number — the column, not the row, gives the valence count",
   "check": {
    "expr": "5",
    "expected": 5
   },
   "feedback": "This answer is wrong — 5 is strontium's period, its row in the table. The column, not the row, gives the valence count: strontium sits in column 2, and columns 1 and 2 give the column number directly. Strontium has 2 valence electrons."
  },
  {
   "value": -8,
   "misconception": "you subtracted 10 from the column — the subtraction applies only to columns 13 through 18",
   "check": {
    "expr": "2-10",
    "expected": -8
   },
   "feedback": "This answer is wrong — you subtracted 10 from strontium's column number. The subtraction applies only to columns 13 through 18; columns 1 and 2 give the column number directly. Strontium has 2 valence electrons."
  }
 ]
}

[
 {
  "value": -3,
  "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
  "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 49 − 46 = +3. This ion has more protons than electrons, so its charge is positive, written 3+."
 },
 {
  "value": 95,
  "misconception": "you added the counts instead of subtracting",
  "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 49 − 46 = +3, written 3+."
 }
]

{
 "keyExplanation": "protons = 49\nelectrons = 46\ncharge = number of protons − number of electrons\ncharge = 49 − 46\ncharge = +3, written 3+\nThree protons are left uncanceled, so the ion is positive.",
 "anticipatedWrong": [
  {
   "value": -3,
   "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
   "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 49 − 46 = +3. This ion has more protons than electrons, so its charge is positive, written 3+."
  },
  {
   "value": 95,
   "misconception": "you added the counts instead of subtracting",
   "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 49 − 46 = +3, written 3+."
  }
 ]
}

[
 {
  "value": 4,
  "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
  "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 6 − 10 = −4, written 4−."
 },
 {
  "value": 4,
  "misconception": "you flipped the sign — protons minus electrons comes out negative here",
  "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 6 − 10 = −4, written 4−. More electrons than protons makes the ion negative, never positive."
 },
 {
  "value": 16,
  "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
  "feedback": "This answer is wrong — you added the counts. Charge is the difference: 6 − 10 = −4, written 4−."
 }
]

{
 "keyExplanation": "protons = 6\nelectrons = 10\ncharge = number of protons − number of electrons\ncharge = 6 − 10\ncharge = −4, written 4−\nFour electrons are left uncanceled, so the ion is negative.",
 "anticipatedWrong": [
  {
   "value": 4,
   "typedVariants": [
    "4"
   ],
   "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
   "check": {
    "expr": "abs(6-10)",
    "expected": 4
   },
   "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 6 − 10 = −4, written 4−."
  },
  {
   "value": 4,
   "typedVariants": [
    "+4",
    "4+"
   ],
   "misconception": "you flipped the sign — protons minus electrons comes out negative here",
   "check": {
    "expr": "-(6-10)",
    "expected": 4
   },
   "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 6 − 10 = −4, written 4−. More electrons than protons makes the ion negative, never positive."
  },
  {
   "value": 16,
   "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
   "check": {
    "expr": "6+10",
    "expected": 16
   },
   "feedback": "This answer is wrong — you added the counts. Charge is the difference: 6 − 10 = −4, written 4−."
  }
 ]
}

[
 {
  "value": 28,
  "misconception": "you added the charge instead of subtracting — a 2+ charge means two electrons LOST",
  "feedback": "This answer is wrong — you added the charge instead of subtracting; a 2+ charge means two electrons LOST. number of electrons = 26 − 2 = 24: a cation has lost electrons, so 24 below 26 is right."
 },
 {
  "value": 26,
  "misconception": "you ignored the charge — Fe²⁺ is an ion, so its electron count differs from its proton count",
  "feedback": "This answer is wrong — you ignored the charge; Fe²⁺ is an ion, so its electron count differs from its proton count. number of electrons = 26 − 2 = 24: a cation has lost electrons, so 24 below 26 is right."
 }
]

{
 "keyExplanation": "protons = 26, charge = +2\nnumber of electrons = number of protons − charge\nnumber of electrons = 26 − 2\nnumber of electrons = 24\nA cation has lost electrons, so the count sits below the proton count — 24 below 26 checks out.",
 "anticipatedWrong": [
  {
   "value": 28,
   "misconception": "you added the charge instead of subtracting — a 2+ charge means two electrons LOST",
   "check": {
    "expr": "26+2",
    "expected": 28
   },
   "feedback": "This answer is wrong — you added the charge instead of subtracting; a 2+ charge means two electrons LOST. number of electrons = 26 − 2 = 24: a cation has lost electrons, so 24 below 26 is right."
  },
  {
   "value": 26,
   "misconception": "you ignored the charge — Fe²⁺ is an ion, so its electron count differs from its proton count",
   "check": {
    "expr": "26",
    "expected": 26
   },
   "feedback": "This answer is wrong — you ignored the charge; Fe²⁺ is an ion, so its electron count differs from its proton count. number of electrons = 26 − 2 = 24: a cation has lost electrons, so 24 below 26 is right."
  }
 ]
}

[
 {
  "value": 14,
  "misconception": "you subtracted the charge's size — a 2− charge means two electrons GAINED, so the count goes up",
  "feedback": "This answer is wrong — you subtracted the charge's size; a 2− charge means two electrons GAINED, so the count goes up. Electrons = protons − charge = 16 − (−2) = 18."
 },
 {
  "value": 34,
  "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
  "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 16 − (−2) = 18; the mass number 32 matters only for neutrons."
 },
 {
  "value": 16,
  "misconception": "you ignored the charge (16 is the proton count — and for this nuclide, 32 − 16 makes the neutron count 16 as well); the ion has gained two electrons beyond its 16 protons",
  "feedback": "This answer is wrong — 16 is the proton count (and, for this particular nuclide, 32 − 16 also makes the neutron count 16); you ignored the charge. The ion has GAINED two electrons beyond its 16 protons: electrons = 16 − (−2) = 18."
 }
]

{
 "keyExplanation": "Protons: the atomic number is 16.\nElectrons: protons − charge = 16 − (−2) = 18.\nAn anion has gained electrons, so 18 above 16 checks out — the mass number 32 matters only for neutrons.",
 "anticipatedWrong": [
  {
   "value": 14,
   "misconception": "you subtracted the charge's size — a 2− charge means two electrons GAINED, so the count goes up",
   "check": {
    "expr": "16-2",
    "expected": 14
   },
   "feedback": "This answer is wrong — you subtracted the charge's size; a 2− charge means two electrons GAINED, so the count goes up. Electrons = protons − charge = 16 − (−2) = 18."
  },
  {
   "value": 34,
   "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
   "check": {
    "expr": "32-(-2)",
    "expected": 34
   },
   "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 16 − (−2) = 18; the mass number 32 matters only for neutrons."
  },
  {
   "value": 16,
   "misconception": "you ignored the charge (16 is the proton count — and for this nuclide, 32 − 16 makes the neutron count 16 as well); the ion has gained two electrons beyond its 16 protons",
   "check": {
    "expr": "16",
    "expected": 16
   },
   "feedback": "This answer is wrong — 16 is the proton count (and, for this particular nuclide, 32 − 16 also makes the neutron count 16); you ignored the charge. The ion has GAINED two electrons beyond its 16 protons: electrons = 16 − (−2) = 18."
  }
 ]
}

[
 {
  "value": 52,
  "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
  "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 55 + 3 = 58. Check the sign: an ion with 52 protons and 55 electrons would carry a 3− charge, not 3+."
 },
 {
  "value": 55,
  "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
  "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 55 + 3 = 58."
 }
]

{
 "keyExplanation": "Start from the taught equation: charge = number of protons − number of electrons. This time the proton count is the unknown, so make the number of protons the subject: number of protons = number of electrons + charge. A 3+ charge counts as +3, so protons = 55 + 3 = 58. Check with the plain-words rule: a cation has lost electrons, so its electron count sits below its proton count — 55 sits below 58 by exactly the three charges.",
 "anticipatedWrong": [
  {
   "value": 52,
   "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
   "check": {
    "expr": "55-3",
    "expected": 52
   },
   "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 55 + 3 = 58. Check the sign: an ion with 52 protons and 55 electrons would carry a 3− charge, not 3+."
  },
  {
   "value": 55,
   "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
   "check": {
    "expr": "55",
    "expected": 55
   },
   "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 55 + 3 = 58."
  }
 ]
}

[
 {
  "value": 4,
  "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
  "feedback": "This answer is wrong — you added the two elements' counts together. Sharing a column means sharing the SAME count: beryllium has 2 valence electrons, so barium also has 2."
 }
]

{
 "keyExplanation": "Every element in a column of the periodic table has the same number of valence electrons. Beryllium has 2 valence electrons, and barium sits in beryllium's column, so a barium atom also has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
   "check": {
    "expr": "2+2",
    "expected": 4
   },
   "feedback": "This answer is wrong — you added the two elements' counts together. Sharing a column means sharing the SAME count: beryllium has 2 valence electrons, so barium also has 2."
  }
 ]
}

[
 "Count every dot around the symbol, pairs included:",
 "four pairs give 2 + 2 + 2 + 2 = 8",
 "Krypton has 8 valence electrons, all of them in pairs."
]

[
 {
  "value": 4,
  "misconception": "you counted each pair as one dot — a pair is two valence electrons",
  "feedback": "This answer is wrong — you counted each of the four pairs as one dot. A pair is two valence electrons: 2 + 2 + 2 + 2 = 8."
 }
]

{
 "keyExplanation": "Count every dot, pairs included: four pairs give 2 + 2 + 2 + 2 = 8. Krypton has 8 valence electrons, all of them in pairs.",
 "anticipatedWrong": [
  {
   "value": 4,
   "misconception": "you counted each pair as one dot — a pair is two valence electrons",
   "feedback": "This answer is wrong — you counted each of the four pairs as one dot. A pair is two valence electrons: 2 + 2 + 2 + 2 = 8."
  }
 ]
}

[
 "The highest level number in the configuration is 5.",
 "The only level-5 sublevel is 5s² — the 4s², 3d¹⁰, and 4p⁶ electrons are all inner.",
 "Strontium has 2 valence electrons."
]

[
 {
  "value": 8,
  "misconception": "you counted the level-4 electrons — level 5 is the highest level, and only 5s² sits there",
  "feedback": "This answer is wrong — you counted the level-4 electrons (4s² and 4p⁶). Level 5 is the highest level, and only 5s² sits there: strontium has 2 valence electrons."
 },
 {
  "value": 38,
  "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
  "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 5, and only 5s² sits there, so strontium has 2 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number in the configuration is 5, and the only level-5 sublevel is 5s². Everything in levels 1 through 4 is inner. Strontium has 2 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 8,
   "misconception": "you counted the level-4 electrons — level 5 is the highest level, and only 5s² sits there",
   "check": {
    "expr": "2+6",
    "expected": 8
   },
   "feedback": "This answer is wrong — you counted the level-4 electrons (4s² and 4p⁶). Level 5 is the highest level, and only 5s² sits there: strontium has 2 valence electrons."
  },
  {
   "value": 38,
   "misconception": "you counted every electron in the atom — only the highest level's electrons are valence electrons",
   "check": {
    "expr": "2+2+6+2+6+2+10+6+2",
    "expected": 38
   },
   "feedback": "This answer is wrong — you counted every electron in the atom. Only the highest level's electrons are valence electrons: the highest level is 5, and only 5s² sits there, so strontium has 2 valence electrons."
  }
 ]
}

[
 "The bracketed [Kr] holds inner electrons, so it never counts.",
 "The highest level number in the configuration is 5.",
 "The level-5 sublevels are 5s² and 5p¹ — the 4d¹⁰ electrons are inner electrons of level 4.",
 "Add the level-5 superscripts: 2 + 1 = 3 valence electrons."
]

[
 {
  "value": 13,
  "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
  "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p¹, so indium has 2 + 1 = 3 valence electrons."
 },
 {
  "value": 1,
  "misconception": "you counted only the 5p electron — the 5s electrons sit in level 5 too",
  "feedback": "This answer is wrong — you counted only the 5p electron. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 1 = 3 valence electrons."
 },
 {
  "value": 49,
  "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
  "feedback": "This answer is wrong — you included the bracketed krypton's electrons. In a noble-gas shorthand the bracketed part is all inner electrons, so [Kr] never counts — only the level-5 sublevels 5s² and 5p¹ count, and indium has 2 + 1 = 3 valence electrons."
 }
]

{
 "keyExplanation": "The highest level number is 5, with sublevels 5s² and 5p¹ — the 4d¹⁰ electrons belong to level 4, so they are inner electrons. Indium has 2 + 1 = 3 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 13,
   "misconception": "you included the 4d¹⁰ electrons — 4d belongs to level 4, and level 5 is the highest level here",
   "check": {
    "expr": "2+10+1",
    "expected": 13
   },
   "feedback": "This answer is wrong — you included the 4d¹⁰ electrons. 4d belongs to level 4, and level 5 is the highest level here — the level-5 sublevels are 5s² and 5p¹, so indium has 2 + 1 = 3 valence electrons."
  },
  {
   "value": 1,
   "misconception": "you counted only the 5p electron — the 5s electrons sit in level 5 too",
   "check": {
    "expr": "1",
    "expected": 1
   },
   "feedback": "This answer is wrong — you counted only the 5p electron. The 5s electrons sit in level 5 too — add both level-5 superscripts: 2 + 1 = 3 valence electrons."
  },
  {
   "value": 49,
   "misconception": "you included the bracketed krypton's electrons — the bracketed part is all inner electrons",
   "check": {
    "expr": "36+2+10+1",
    "expected": 49
   },
   "feedback": "This answer is wrong — you included the bracketed krypton's electrons. In a noble-gas shorthand the bracketed part is all inner electrons, so [Kr] never counts — only the level-5 sublevels 5s² and 5p¹ count, and indium has 2 + 1 = 3 valence electrons."
  }
 ]
}

[
 {
  "value": 6,
  "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
  "feedback": "This answer is wrong — you added the two elements' counts together — sharing a column means sharing the same count, not combining counts"
 }
]

{
 "keyExplanation": "Every element in a column of the periodic table has the same number of valence electrons. Boron has 3, and thallium sits in boron's column, so thallium also has 3 valence electrons.",
 "anticipatedWrong": [
  {
   "value": 6,
   "misconception": "you added the two elements' counts together — sharing a column means sharing the same count, not combining counts",
   "check": {
    "expr": "3+3",
    "expected": 6
   },
   "feedback": "This answer is wrong — you added the two elements' counts together — sharing a column means sharing the same count, not combining counts"
  }
 ]
}

[
 {
  "value": -2,
  "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
  "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 78 − 76 = +2. This ion has more protons than electrons, so its charge is positive, written 2+."
 },
 {
  "value": 154,
  "misconception": "you added the counts instead of subtracting",
  "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 78 − 76 = +2, written 2+."
 }
]

{
 "keyExplanation": "protons = 78\nelectrons = 76\ncharge = number of protons − number of electrons\ncharge = 78 − 76\ncharge = +2, written 2+\nTwo protons are left uncanceled, so the ion is positive.",
 "anticipatedWrong": [
  {
   "value": -2,
   "misconception": "you subtracted the wrong way — protons minus electrons, and this ion has more protons, so the charge is positive",
   "feedback": "This answer is wrong — you subtracted the wrong way. The equation is protons minus electrons: 78 − 76 = +2. This ion has more protons than electrons, so its charge is positive, written 2+."
  },
  {
   "value": 154,
   "misconception": "you added the counts instead of subtracting",
   "feedback": "This answer is wrong — you added the two counts instead of subtracting. Charge = number of protons − number of electrons = 78 − 76 = +2, written 2+."
  }
 ]
}

[
 {
  "value": 1,
  "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
  "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 85 − 86 = −1, written 1−."
 },
 {
  "value": 1,
  "misconception": "you flipped the sign — protons minus electrons comes out negative here",
  "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 85 − 86 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
 },
 {
  "value": 171,
  "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
  "feedback": "This answer is wrong — you added the counts. Charge is the difference: 85 − 86 = −1, written 1−."
 }
]

{
 "keyExplanation": "protons = 85\nelectrons = 86\ncharge = number of protons − number of electrons\ncharge = 85 − 86\ncharge = −1, written 1−\nOne electron is left uncanceled, so the ion is negative.",
 "anticipatedWrong": [
  {
   "value": 1,
   "typedVariants": [
    "1"
   ],
   "misconception": "you dropped the sign — with more electrons than protons, the charge is negative",
   "check": {
    "expr": "abs(85-86)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you dropped the sign. This ion has more electrons than protons, so the charge is negative: 85 − 86 = −1, written 1−."
  },
  {
   "value": 1,
   "typedVariants": [
    "+1",
    "1+"
   ],
   "misconception": "you flipped the sign — protons minus electrons comes out negative here",
   "check": {
    "expr": "-(85-86)",
    "expected": 1
   },
   "feedback": "This answer is wrong — you flipped the sign. Charge is protons minus electrons: 85 − 86 = −1, written 1−. More electrons than protons makes the ion negative, never positive."
  },
  {
   "value": 171,
   "misconception": "you added the counts — charge is the difference between protons and electrons, not the total",
   "check": {
    "expr": "85+86",
    "expected": 171
   },
   "feedback": "This answer is wrong — you added the counts. Charge is the difference: 85 − 86 = −1, written 1−."
  }
 ]
}

[
 {
  "value": 60,
  "misconception": "you added the charge instead of subtracting — a 3+ charge means three electrons LOST",
  "feedback": "This answer is wrong — you added the charge instead of subtracting; a 3+ charge means three electrons LOST. number of electrons = 57 − 3 = 54: a cation has lost electrons, so 54 below 57 is right."
 },
 {
  "value": 57,
  "misconception": "you ignored the charge — La³⁺ is an ion, so its electron count differs from its proton count",
  "feedback": "This answer is wrong — you ignored the charge; La³⁺ is an ion, so its electron count differs from its proton count. number of electrons = 57 − 3 = 54: a cation has lost electrons, so 54 below 57 is right."
 }
]

{
 "keyExplanation": "protons = 57, charge = +3\nnumber of electrons = number of protons − charge\nnumber of electrons = 57 − 3\nnumber of electrons = 54\nA cation has lost electrons, so the count sits below the proton count — 54 below 57 checks out.",
 "anticipatedWrong": [
  {
   "value": 60,
   "misconception": "you added the charge instead of subtracting — a 3+ charge means three electrons LOST",
   "check": {
    "expr": "57+3",
    "expected": 60
   },
   "feedback": "This answer is wrong — you added the charge instead of subtracting; a 3+ charge means three electrons LOST. number of electrons = 57 − 3 = 54: a cation has lost electrons, so 54 below 57 is right."
  },
  {
   "value": 57,
   "misconception": "you ignored the charge — La³⁺ is an ion, so its electron count differs from its proton count",
   "check": {
    "expr": "57",
    "expected": 57
   },
   "feedback": "This answer is wrong — you ignored the charge; La³⁺ is an ion, so its electron count differs from its proton count. number of electrons = 57 − 3 = 54: a cation has lost electrons, so 54 below 57 is right."
  }
 ]
}

[
 {
  "value": 27,
  "misconception": "you added the charge instead of subtracting — a 3+ charge means three electrons LOST",
  "feedback": "This answer is wrong — you added the charge instead of subtracting; a 3+ charge means three electrons LOST. Electrons = protons − charge = 24 − 3 = 21."
 },
 {
  "value": 49,
  "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
  "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 24 − 3 = 21; the mass number 52 matters only for neutrons."
 },
 {
  "value": 24,
  "misconception": "you ignored the charge — the ion has lost three electrons from its 24 protons",
  "feedback": "This answer is wrong — you ignored the charge; the ion has lost three electrons from its 24 protons. Electrons = 24 − 3 = 21."
 }
]

{
 "keyExplanation": "Protons: the atomic number is 24.\nElectrons: protons − charge = 24 − 3 = 21.\nA cation has lost electrons, so 21 below 24 checks out — the mass number 52 matters only for neutrons.",
 "anticipatedWrong": [
  {
   "value": 27,
   "misconception": "you added the charge instead of subtracting — a 3+ charge means three electrons LOST",
   "check": {
    "expr": "24+3",
    "expected": 27
   },
   "feedback": "This answer is wrong — you added the charge instead of subtracting; a 3+ charge means three electrons LOST. Electrons = protons − charge = 24 − 3 = 21."
  },
  {
   "value": 49,
   "misconception": "you started from the mass number — electrons come from the ATOMIC number, adjusted by the charge",
   "check": {
    "expr": "52-3",
    "expected": 49
   },
   "feedback": "This answer is wrong — you started from the mass number; electrons come from the ATOMIC number, adjusted by the charge. Electrons = 24 − 3 = 21; the mass number 52 matters only for neutrons."
  },
  {
   "value": 24,
   "misconception": "you ignored the charge — the ion has lost three electrons from its 24 protons",
   "check": {
    "expr": "24",
    "expected": 24
   },
   "feedback": "This answer is wrong — you ignored the charge; the ion has lost three electrons from its 24 protons. Electrons = 24 − 3 = 21."
  }
 ]
}

[
 {
  "value": 36,
  "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
  "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 39 + 3 = 42. Check the sign: an ion with 36 protons and 39 electrons would carry a 3− charge, not 3+."
 },
 {
  "value": 39,
  "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
  "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 39 + 3 = 42."
 }
]

{
 "keyExplanation": "Start from the taught equation: charge = number of protons − number of electrons. This time the proton count is the unknown, so make the number of protons the subject: number of protons = number of electrons + charge. A 3+ charge counts as +3, so protons = 39 + 3 = 42. Check with the plain-words rule: a cation has lost electrons, so its electron count sits below its proton count — 39 sits below 42 by exactly the three charges.",
 "anticipatedWrong": [
  {
   "value": 36,
   "misconception": "you subtracted the charge from the electron count — subtracting finds ELECTRONS from a known proton count; solving for protons means adding the charge back",
   "check": {
    "expr": "39-3",
    "expected": 36
   },
   "feedback": "This answer is wrong — you subtracted the charge from the electron count. Subtracting the charge is the taught move for finding ELECTRONS from a known proton count; here the proton count is the unknown, so rearrange charge = number of protons − number of electrons into protons = electrons + charge = 39 + 3 = 42. Check the sign: an ion with 36 protons and 39 electrons would carry a 3− charge, not 3+."
  },
  {
   "value": 39,
   "misconception": "you gave the electron count as the proton count — equal counts would make the particle a neutral atom, and this ion carries a 3+ charge",
   "check": {
    "expr": "39",
    "expected": 39
   },
   "feedback": "This answer is wrong — you gave the electron count itself. Equal proton and electron counts belong to a neutral atom with a charge of exactly 0; this ion's 3+ charge means the proton count sits three above the electron count: protons = electrons + charge = 39 + 3 = 42."
  }
 ]
}