Snip a gold ring in half and each piece is still gold. Snip a piece in half again, and again — every speck is still gold. Could the cutting go on forever?
Chemistry needs to know whether an element has a smallest piece — a point where the cutting has to stop.
The idea
Cutting a piece of gold in half leaves two smaller pieces of gold, and cutting those leaves smaller pieces of gold still.
The cutting cannot go on forever — eventually one last particle of gold is left.
That single particle is still gold, but cutting it in half leaves pieces that are not gold at all.
Every cut leaves gold — until the last particle is cut.
The smallest particle of an element that is still that element is called an 'atom'.
Every element works the same way: one gold atom is the smallest possible piece of gold, and one iron atom is the smallest possible piece of iron.
Worked examples
Worked example 1. What is the smallest particle of copper that is still copper?
Step 1
The smallest particle of an element that is still that element is one atom of it.
Step 2
One copper atom — any smaller piece is no longer copper.
Worked example 2. A silver atom is somehow cut in half. Is either half silver?
Step 1
A silver atom is the smallest particle that is still silver.
Step 2
No — anything smaller than one silver atom is not silver.
You can now state that an atom is the smallest particle of an element that is still that element.
Check your understanding
What is the smallest particle of zinc that is still zinc?
AOne zinc atom.correct
BHalf of a zinc atom.
This option is wrong — you kept the element through a cut below one atom — cutting a zinc atom leaves pieces that are not zinc.
CThe smallest speck of zinc that an eye can see.
This option is wrong — you used visibility as the limit — the limit is one atom, which is far smaller than anything an eye can see.
DThere is none — zinc can be cut into ever-smaller pieces of zinc forever.
This option is wrong — you let the cutting go on forever — the cutting stops being zinc at one zinc atom.
The smallest particle of an element that is still that element is one atom of it. So the smallest particle of zinc that is still zinc is one zinc atom. Anything smaller than one zinc atom is no longer zinc.
Check your understanding
If a single helium atom could be split into pieces, what would the pieces be?
APieces of matter that are not helium.correct
BTwo smaller helium atoms.
This option is wrong — you cut the atom like a lump of the element — one helium atom is already the smallest particle that is still helium.
CA tiny amount of helium, smaller than one atom.
This option is wrong — you allowed helium smaller than one atom — one atom is the smallest amount of helium there is.
DThe same helium atom, only lighter than before.
This option is wrong — you kept the atom whole while removing matter from it — splitting an atom leaves separate pieces, and none of them is helium.
One helium atom is the smallest particle that is still helium. Anything smaller than that one atom is no longer helium. So the pieces would be matter that is not helium.
Check your understanding
A jar holds exactly 1000 neon atoms. What is the smallest amount of neon that could be taken out of the jar while still taking out neon?
AOne neon atom.correct
BHalf of a neon atom.
This option is wrong — you went below one atom — half of a neon atom is not neon, so it would not count as taking out neon.
CTen neon atoms — a single atom does not count as neon on its own.
This option is wrong — you required a crowd of atoms — one neon atom is already neon, and it is the smallest amount that is.
DAny amount, however small — neon has no smallest piece.
This option is wrong — you let neon shrink forever — every element has a smallest particle that is still that element, its atom.
The smallest particle of neon that is still neon is one neon atom. Taking out anything smaller would not be taking out neon. So the smallest amount of neon that can leave the jar is one atom.
Lesson 2 of 65 · ATM-002
Dalton's atomic theory
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Wonder this:
By the early 1800s, chemists kept meeting the same pattern: water made anywhere on Earth always contains hydrogen and oxygen in the same proportion. In 1803, John Dalton proposed a set of claims about atoms that explained why.
You've already seen that every element has a smallest particle — its atom. Dalton built his whole theory on that idea.
The idea
Dalton's atomic theory makes four claims.
First: every element is made of its own kind of atom.
Second: atoms of the same element are identical, while atoms of different elements differ.
Third: atoms combine in fixed whole-number ratios to form compounds.
Fourth: chemical changes rearrange atoms — no atom is created or destroyed.
The third claim explains the water pattern: water always forms from hydrogen and oxygen atoms combined in the same 2 to 1 ratio.
The fourth claim is the law of conservation of mass in atomic form — if no atom is created or destroyed, the total mass cannot change.
Worked examples
Worked example 1. Under Dalton's theory, how does one aluminum atom compare with another aluminum atom?
Step 1
They are identical — atoms of the same element are identical.
Worked example 2. When iron rusts, iron atoms combine with oxygen atoms. Under Dalton's theory, what happens to the total number of atoms during the change?
Step 1
It stays the same — the change only rearranges atoms; none are created or destroyed.
You can now state the four points of Dalton's atomic theory: every element is made of its own kind of atom, atoms of the same element are identical while atoms of different elements differ, atoms combine in fixed whole-number ratios to form compounds, and chemical changes rearrange atoms without creating or destroying them.
Check your understanding
Under Dalton's atomic theory, what happens to atoms during a chemical change?
AThey are rearranged into new combinations — none are created or destroyed.correct
BSome atoms are destroyed, which is why substances seem to disappear.
This option is wrong — you let atoms vanish — Dalton's fourth claim says chemical changes destroy no atoms.
CNew atoms are created to build the new substances.
This option is wrong — you created atoms from nothing — new substances are built by rearranging the atoms already there.
DEach atom changes into an atom of a different element.
This option is wrong — you let atoms switch elements — in Dalton's theory an atom keeps its kind; only the combinations change.
Dalton's fourth claim covers chemical changes. Chemical changes rearrange atoms — no atom is created or destroyed. The same atoms end up in new combinations.
Check your understanding
Table salt always contains sodium and chlorine atoms combined in the same 1 to 1 ratio. Which of Dalton's claims does this show?
AAtoms combine in fixed whole-number ratios to form compounds.correct
BEvery element is made of its own kind of atom.
This option is wrong — you picked the own-kind claim — that claim is about what an element is made of, not about how atoms combine.
CAtoms of the same element are identical.
This option is wrong — you picked the identical-atoms claim — that claim compares atoms of one element, not the recipe of a compound.
DChemical changes rearrange atoms without creating or destroying them.
This option is wrong — you picked the rearrangement claim — that claim tracks atoms through a change, not the fixed recipe of a compound.
The observation is about a compound's recipe: 1 sodium to 1 chlorine, every time. Dalton's third claim says atoms combine in fixed whole-number ratios to form compounds. A fixed 1 to 1 ratio is exactly such a ratio.
Check your understanding
A chemist weighs a sealed flask before and after a chemical change happens inside it, and finds exactly the same mass. Which of Dalton's claims explains the result?
AChemical changes rearrange atoms without creating or destroying them.correct
BAtoms combine in fixed whole-number ratios to form compounds.
This option is wrong — you picked the fixed-ratio claim — that claim sets a compound's recipe, not what happens to total mass.
CEvery element is made of its own kind of atom.
This option is wrong — you picked the own-kind claim — that claim says nothing about mass staying the same through a change.
DAtoms of the same element are identical, while atoms of different elements differ.
This option is wrong — you picked the identical-atoms claim — comparing atoms does not explain why the flask's mass is unchanged.
The observation is about total mass through a change. Dalton's fourth claim says chemical changes rearrange atoms — none created, none destroyed. If every atom survives, the total mass cannot change.
Lesson 3 of 65 · ATM-003
Thomson finds the electron
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Wonder this:
In 1897, J. J. Thomson sealed a metal plate inside a glass tube, pumped out the air, and switched on a high voltage. A glowing beam streamed off the metal.
The question was what the beam was made of.
The idea
The beam bent toward a positively charged plate, so the beam's particles must carry negative charge — opposite charges attract.
The particles weighed far less than any whole atom — even hydrogen, the lightest atom, is far heavier.
The beam curves toward the positive plate, so its particles carry negative charge.
Swapping the metal changed nothing: an iron plate and an aluminum plate released exactly the same particles.
So atoms of every element contain identical, tiny, negatively charged particles that they can release.
These particles were later named 'electrons'.
Worked examples
Worked example 1. A tube's metal plate is swapped from zinc to lead. How do the particles released from the lead compare with those from the zinc?
Step 1
They are identical — atoms of every element release the same negatively charged particles.
Worked example 2. How does the mass of one electron compare with the mass of a whole atom?
Step 1
An electron is far lighter than any whole atom.
You can now describe Thomson's discovery of the electron: atoms of every element can release identical, negatively charged particles far lighter than any whole atom, later named electrons.
Check your understanding
In Thomson's experiment, the glowing beam bent toward a positively charged plate. What does the bend show about the beam's particles?
BThey carry positive charge — like charges pull together.
This option is wrong — you attracted like charges — like charges push apart; it is OPPOSITE charges that attract.
CThey carry no charge — any beam bends toward a charged plate.
This option is wrong — you let uncharged particles feel the pull — a charged plate only bends particles that carry charge themselves.
DThey carry negative charge — the positive plate pushed the beam away.
This option is wrong — you turned the bend into a push — the beam moved TOWARD the positive plate, which is a pull, not a push.
The beam moved toward the positive plate. Opposite charges attract, so particles pulled toward positive charge must be negative. The beam's particles carry negative charge.
Check your understanding
The same particles stream out of the tube whether its plate is made of copper or of tin. What does this show?
AAtoms of every element contain the same kind of negatively charged particle.correct
BCopper and tin must really be the same element.
This option is wrong — you merged the two metals into one element — the metals differ; it is the released particles that are identical.
CEach metal releases its own kind of particle, and the kinds just happen to look alike.
This option is wrong — you kept one particle kind per element — every test shows the particles are identical, not merely similar.
DThe particles come from leftover air in the tube, not from the metal.
This option is wrong — you sourced the particles from the air — the tube's air was pumped out, and the beam still streams off the metal.
Swapping the metal changes nothing about the particles. If the particles came from the particular metal's kind of atom alone, different metals should give different particles. Identical particles from every metal show that atoms of every element contain the same particle.
Check your understanding
One of the particles Thomson discovered is compared with a whole helium atom — one of the lightest atoms there is. Which statement is correct?
AThe particle is far lighter than the helium atom.correct
BThe particle and the helium atom have about the same mass.
This option is wrong — you matched the particle to a very light atom — the electron is far lighter than any whole atom.
CThe particle is far heavier than the helium atom.
This option is wrong — you flipped the comparison — the electron is far lighter than any whole atom, not heavier.
DThe particle is lighter than a gold atom but heavier than a helium atom.
This option is wrong — you slotted the electron between atoms — it is lighter than EVERY whole atom, helium included.
Thomson's particles weighed far less than any whole atom. Even hydrogen, the lightest atom of all, is far heavier than an electron — and helium is heavier still. So the particle is far lighter than the helium atom.
Lesson 4 of 65 · ATM-004
Why Dalton's atom had to change
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Thomson's electrons created a problem for Dalton's theory.
The idea
Dalton pictured the atom as the smallest piece of matter, with no smaller parts inside.
Thomson showed that atoms of every element release electrons — particles far smaller than any atom.
An atom with no parts could not release anything.
Because atoms can release smaller charged particles, atoms must be built from smaller parts.
This is how scientific models change: when an observation contradicts a model, the model must be revised.
Worked examples
Worked example 1. A student says, 'Atoms are solid balls with nothing inside them.' Which discovery shows this cannot be right, and why?
Step 1
Atoms of every element release electrons.
Step 2
A solid ball with nothing inside would have nothing to release.
Step 3
Thomson's electron — a released particle must have been a part of the atom, so atoms have parts.
Worked example 2. The electrons released by different elements are identical. Does that fit an atom with no smaller parts?
Step 1
If atoms had no parts, there would be nothing inside any atom to come out.
Step 2
The same piece coming out of atoms of different elements means those atoms all contain that inner part.
Step 3
No — identical pieces coming out of different atoms means atoms are built from smaller parts.
You can now explain why the discovery of the electron forced a change to Dalton's model: because atoms can release smaller charged particles, atoms must be built from smaller parts rather than being indivisible.
Check your understanding
Which part of Dalton's picture of the atom did the discovery of the electron disprove?
AThe atom is the smallest piece of matter, with no smaller parts inside.correct
BEvery element is made of its own kind of atom.
This option is wrong — you picked the own-kind claim — identical electrons from every element say nothing against elements having their own atoms.
CAtoms combine in fixed whole-number ratios to form compounds.
This option is wrong — you picked the fixed-ratio claim — the electron is about the atom's insides, not about combining recipes.
DChemical changes rearrange atoms without creating or destroying them.
This option is wrong — you picked the rearrangement claim — releasing an electron is not a chemical change being tracked; the finding is that atoms have parts.
Atoms release electrons, which are far smaller than any atom. An atom with no parts could not release anything. So the no-smaller-parts picture is the part that fell.
Check your understanding
Why does the release of electrons force the conclusion that atoms are built from smaller parts?
AA particle that comes out of an atom must have been part of the atom.correct
BAtoms create each electron from nothing at the moment of release.
This option is wrong — you let the atom make matter from nothing — what comes out must have been inside all along.
CThe electrons drift in from the surrounding air and bounce off the atoms.
This option is wrong — you sourced the electrons from outside — the tube's air was pumped out, and the particles still streamed off the metal's atoms.
DEach atom shrinks down and becomes the electron it releases.
This option is wrong — you turned the whole atom into the electron — the atom remains after the release, minus one small part.
Electrons come out of atoms. Whatever comes out of an atom must have been a part of it. So atoms are built from smaller parts.
Check your understanding
After Thomson's discovery, which statement gives the correct revised picture of the atom?
AAn atom contains smaller parts, including the electrons it can release.correct
BAn atom is the smallest piece of matter, so nothing smaller than an atom exists.
This option is wrong — you kept Dalton's old picture — the electron is smaller than any atom and comes from inside atoms.
CAn electron is simply the smallest kind of whole atom.
This option is wrong — you made the electron an atom — it is a PART of atoms, present in the atoms of every element.
DAtoms have smaller parts, but only the atoms of metals do.
This option is wrong — you limited the revision to metals — every element's atoms release the same electrons, so every atom has parts.
Atoms of every element release electrons. A released particle was a part of the atom. So every atom is built from smaller parts, electrons among them.
Lesson 5 of 65 · ATM-005
Thomson's plum-pudding model
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Ordinary matter shows no overall electric charge, yet its atoms contain negative electrons. So an atom must also hold positive charge somewhere — and Thomson proposed a picture of how the atom's insides are arranged.
The idea
Thomson pictured the atom as a ball of positive charge spread thinly through its whole volume.
The tiny negative electrons sit embedded throughout the ball, like fruit pieces in a pudding.
A helium atom in the plum-pudding model: 2 electrons embedded in a ball of thinly spread positive charge.
The spread-out positive charge balances the electrons' negative charge, so the whole atom shows no overall charge.
This picture is called the 'plum-pudding model' of the atom.
In this model, a helium atom is a positive sphere holding 2 embedded electrons.
Worked examples
Worked example 1. In the plum-pudding model, where are a beryllium atom's 4 electrons?
Step 1
Embedded throughout a ball of thinly spread positive charge.
Worked example 2. In the plum-pudding model, where is an atom's positive charge?
Step 1
Spread thinly through the whole ball of the atom — not gathered in any one spot.
You can now describe Thomson's plum-pudding model of the atom: a ball of thinly spread positive charge with the tiny negative electrons embedded throughout it.
Check your understanding
In Thomson's plum-pudding model, how is the positive charge arranged in an atom?
ASpread thinly through the whole atom.correct
BPacked into one small spot at the atom's center.
This option is wrong — you packed the positive charge into one spot — in the plum-pudding model it fills the whole ball thinly and evenly.
CCarried by the electrons themselves.
This option is wrong — you gave the positive charge to the electrons — electrons are negative; the positive charge is the ball they sit in.
DFormed into a thin skin around the atom's outside, with the electrons inside.
This option is wrong — you pushed the positive charge to the surface — the model spreads it through the atom's whole volume.
Picture the pudding itself. The positive charge is the ball — spread thinly through the atom's whole volume. The electrons are the fruit pieces embedded in it.
Check your understanding
A carbon atom is drawn using the plum-pudding model. Where do its 6 electrons belong in the drawing?
AEmbedded throughout the ball of positive charge.correct
BCircling around the outside of the ball.
This option is wrong — you moved the electrons outside — in this model they sit INSIDE the positive ball, like fruit in a pudding.
CGathered into one clump at the exact center of the ball.
This option is wrong — you clumped the electrons at the center — they are embedded throughout the ball, not gathered in one spot.
DIn the empty space between one atom and the next.
This option is wrong — you placed the electrons outside the atom entirely — the model puts them inside the atom's positive ball.
In the plum-pudding model the atom is a ball of thinly spread positive charge. The electrons sit embedded throughout that ball. So the 6 electrons are drawn at scattered spots inside the ball.
Check your understanding
Which picture shows the plum-pudding model of an atom?
Acorrect
B
This option is wrong — you swapped the charges — the ball is the POSITIVE charge and the small embedded particles are the negative electrons.
C
This option is wrong — you gathered the positive charge into a tiny center — in the plum-pudding model it is spread thinly through the whole ball.
D
This option is wrong — you put the electrons on the atom's rim — the model embeds them THROUGH the ball of positive charge.
Look for the ball first: the positive charge fills the whole atom, evenly and thinly. Then look for the electrons: small dark circles embedded at scattered spots inside the ball. A tiny center, a rim of electrons, or swapped shading all break the model.
Lesson 6 of 65 · ATM-006
The gold-foil experiment
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Wonder this:
Ernest Rutherford's team aimed a beam of fast, positively charged particles at a sheet of gold foil so thin that light shines through it. They expected every particle to punch straight through the soft, thinly spread atom of Thomson's model.
Detectors around the foil recorded where every particle went.
The idea
Nearly all of the particles passed straight through the foil, exactly as expected.
A few particles were knocked slightly off course.
Nearly all particles passed straight through the foil — a rare few bounced back.
But about 1 particle in every few thousand bounced back sharply toward the source.
The bounces were completely unexpected — and they happened for every sheet of gold foil the team tried.
Worked examples
Worked example 1. Out of several thousand particles fired at the foil, about how many bounced back sharply?
Step 1
Only one or a few — nearly all of the particles passed straight through.
Worked example 2. The experiment is repeated with a fresh sheet of gold foil. What result appears?
Step 1
The same one — nearly all particles pass straight through, and a rare few bounce back sharply.
You can now describe the result of Rutherford's gold-foil experiment: nearly all the fast, positively charged particles fired at a thin gold foil passed straight through, while a very small number bounced back sharply.
Check your understanding
In the gold-foil experiment, what happened to nearly all of the fast, positively charged particles fired at the foil?
AThey passed straight through the foil.correct
BThey bounced back sharply toward the source.
This option is wrong — you made the rare result the common one — only about 1 in a few thousand bounced back.
CThey were absorbed and stayed inside the foil.
This option is wrong — you stopped the particles in the foil — the detectors caught them on the far side, straight through.
DThey slowed down and stopped just short of the foil.
This option is wrong — you stopped the particles before the foil — nearly all of them went straight through it.
Recall the counts. Nearly all of the particles passed straight through the foil. Only a rare few were deflected or bounced back.
Check your understanding
Which result of the gold-foil experiment was the unexpected one?
AA very small number of particles bounced back sharply.correct
BNearly all of the particles passed straight through.
This option is wrong — you flagged the expected result — straight-through was exactly what the team predicted; the bounces were the shock.
CMost of the particles bounced back, and only a few passed through.
This option is wrong — you reversed the counts — nearly all passed through; the bounces were rare.
DThe particles passed through some sheets of foil but not through others.
This option is wrong — you made the result depend on the sheet — every sheet gave the same result, including the rare bounces.
The team expected every particle to punch straight through. Nearly all did — that part matched the prediction. The shock was the rare few that bounced back sharply.
Check your understanding
About what share of the particles fired at the gold foil bounced back sharply?
AAbout 1 in every few thousand.correct
BAbout half of them.
This option is wrong — you inflated the bounces — they were far rarer, about 1 in a few thousand.
CNearly all of them.
This option is wrong — you swapped the two results — nearly all PASSED THROUGH; the bounces were the rare few.
DNone at all — every particle passed through or was only nudged.
This option is wrong — you erased the bounces — a rare few really did bounce back, and that was the experiment's great surprise.
Nearly all particles passed straight through. A few were knocked slightly off course. About 1 in every few thousand bounced back sharply.
Lesson 7 of 65 · ATM-007
Why plum pudding failed
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Did You Know?
A rare hard bounce was exactly what the plum-pudding model could not allow.
The idea
In the plum-pudding model, the atom's positive charge is spread thinly through the whole atom.
Thinly spread charge pushes a passing positive particle only gently — enough to nudge it slightly off course, never to turn it around.
Yet a few particles bounced straight back, and two positive charges push apart strongly when they come very close.
Thin, spread-out charge cannot turn a fast particle around
Only a tiny, dense, positive center can explain a particle bouncing straight back.
So a particle that bounces straight back must have hit something small, heavy, and positive.
Because the bounces were rare, that dense center must be tiny — nearly every particle missed it.
The gold-foil result therefore rules out the plum-pudding model: the atom's positive charge is packed into one tiny, dense center.
Worked examples
Worked example 1. Why could a plum-pudding atom never bounce a fast positive particle straight back?
Step 1
Its positive charge is spread thinly through the whole atom.
Step 2
Thinly spread charge gives only gentle pushes — enough to nudge a fast particle, never to reverse it.
Step 3
Nothing in the model is concentrated enough to turn a fast particle around.
Worked example 2. Only about 1 particle in every few thousand bounced back. Why so few?
Step 1
A particle only bounces when it comes very close to the dense positive center.
Step 2
The center is tiny compared with the whole atom, so nearly every particle misses it.
Step 3
The rareness of the bounces shows the dense center is tiny.
You can now explain why the gold-foil result rules out the plum-pudding model: because thinly spread positive charge could not turn a fast positive particle around, the rare hard bounces mean the atom's positive charge is packed into one tiny, dense center.
Check your understanding
Why must a particle that bounced straight back off the foil have hit something dense and positive?
AOnly a concentrated positive charge pushes a fast positive particle hard enough to turn it around.correct
BThe foil's surface is hard, like a stone wall, so any particle that hits it rebounds straight back.
This option is wrong — you made the bounce mechanical — the turn-around comes from the strong push between two positive charges, not from a hard surface.
CThe particle ran out of speed inside the foil and drifted back out.
This option is wrong — you slowed the particle to a stop — a drifting particle would not fly back sharply; only a strong push does that.
DThe atom's electrons pushed the particle back.
This option is wrong — you used the electrons — they are far too light to turn a fast particle, and their negative charge would pull it, not push it.
The bounced particle is positive and fast. Two positive charges push apart strongly when they come very close. Only a small, heavy, concentrated positive charge can push hard enough to reverse it.
Check your understanding
Why did the gold-foil result rule out the plum-pudding model?
AThinly spread positive charge could never turn a fast positive particle around, yet a few particles bounced straight back.correct
BBecause nearly all of the particles passed straight through, and the plum-pudding model said the atom would block them.
This option is wrong — you made pass-through the contradiction — the plum-pudding atom is soft and thin, so pass-through fit the model; the bounces did not.
CBecause the particles came out negatively charged after crossing the foil.
This option is wrong — you invented a charge change — the particles kept their charge; the problem was the rare sharp bounces.
DBecause the model puts the electrons in the wrong place inside the ball.
This option is wrong — you blamed the electrons' positions — the fatal problem was the spread-out positive charge, which cannot bounce anything back.
The model spreads the positive charge thinly through the whole atom. Thinly spread charge can nudge a fast particle — never reverse it. The rare sharp bounces are impossible in that model, so the model fell.
Check your understanding
The sharp bounces happened to only about 1 particle in every few thousand. What does that rareness show about the dense positive center?
AIt is tiny — nearly every particle crosses the atom without coming near it.correct
BIt is soft — most particles pass through the center without noticing it.
This option is wrong — you softened the center — particles that missed it felt nothing because they MISSED it, not because it is soft.
CThere are many dense centers spread through each atom.
This option is wrong — you multiplied the centers — many centers would bounce many particles, but the bounces were rare.
DIt pushes on only a chosen few of the particles.
This option is wrong — you made the push selective — the push acts on every positive particle that comes close; few ever come close.
A particle only bounces when it comes very close to the dense center. About 1 in a few thousand bounced, so about 1 in a few thousand came that close. The center must be tiny compared with the atom — nearly everything misses it.
Lesson 8 of 65 · ATM-008
Rutherford's nuclear model
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The gold-foil result demanded a new picture of the atom, and Rutherford drew it.
The idea
At the center of the atom sits a tiny, dense, positively charged core.
Rutherford named this core the 'nucleus'.
Rutherford's nuclear model: a tiny positive nucleus, electrons in the mostly empty space around it.
The electrons move through the space around the nucleus.
That space is nearly all of the atom — the atom is mostly empty space.
If an atom were the size of a stadium, its nucleus would be about the size of a marble at the center.
This picture is called the 'nuclear model' of the atom.
Worked examples
Worked example 1. In the nuclear model, where is a silver atom's positive charge?
Step 1
In its nucleus — the tiny, dense core at the atom's center.
Worked example 2. In the nuclear model, what fills nearly all of an atom's volume?
Step 1
Mostly empty space, with the electrons moving through it.
You can now describe Rutherford's nuclear model of the atom: a tiny, dense, positively charged nucleus at the center, with electrons moving through the mostly empty space around it.
Check your understanding
In Rutherford's nuclear model, where is an atom's positive charge?
APacked into the nucleus — the tiny, dense core at the center.correct
BSpread thinly and evenly through the atom's whole volume, as in the earlier model.
This option is wrong — you kept the plum-pudding picture — the gold-foil bounces showed the positive charge is packed into one tiny center.
CCarried by the electrons around the atom.
This option is wrong — you gave the positive charge to the electrons — electrons are negative; the positive charge sits in the nucleus.
DSpread over the atom's outer surface.
This option is wrong — you pushed the charge to the surface — the model packs it into the dense core at the very center.
The nuclear model has one home for positive charge. It is the nucleus — the tiny, dense, positively charged core at the atom's center. Everything around it is mostly empty space with electrons moving through it.
Check your understanding
In the nuclear model, where are an atom's electrons?
AMoving through the mostly empty space around the nucleus.correct
BPacked inside the nucleus along with the positive charge.
This option is wrong — you put the electrons in the nucleus — the nucleus holds the positive charge; the electrons move outside it.
CEmbedded through a ball of positive charge that fills the whole atom.
This option is wrong — you kept the plum-pudding picture — there is no filled ball; the atom is mostly empty space around a tiny nucleus.
DForming a solid shell along the atom's outer edge.
This option is wrong — you froze the electrons into a rim — they move through the space around the nucleus, not along a fixed edge.
The nucleus sits at the center. The electrons move through the space around it. That space is nearly all of the atom — mostly empty.
Check your understanding
How does the size of the nucleus compare with the size of its whole atom?
AThe nucleus is tiny — nearly all of the atom is empty space around it.correct
BThe nucleus takes up about half of the atom.
This option is wrong — you grew the nucleus — it is far smaller; nearly all of the atom is empty space.
CThe nucleus fills nearly the whole atom, with a thin empty rim outside.
This option is wrong — you filled the atom with nucleus — the model is the reverse: a tiny core inside mostly empty space.
DThe nucleus is slightly smaller than the atom, like a pit filling most of a peach.
This option is wrong — you undersized the gap — the nucleus is not slightly smaller but vastly smaller than its atom.
Ask how much of the atom the nucleus takes up. The nucleus is vastly smaller than its atom. Nearly all of the atom is empty space around it.
Lesson 9 of 65 · ATM-009
The three subatomic particles and where they sit
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The nuclear model says where the charges sit. The next question is what particles the atom is actually built from.
The idea
An atom is built from three kinds of particles smaller than any atom, called 'subatomic particles'.
Two of them, 'protons' and 'neutrons', are packed together in the nucleus.
The third, the electron — the particle Thomson discovered — moves in the space outside the nucleus.
A helium atom: 2 protons and 2 neutrons packed in the nucleus, 2 electrons outside it.
A helium atom keeps 2 protons and 2 neutrons in its nucleus, and 2 electrons outside it.
Worked examples
Worked example 1. A boron atom contains 5 protons, 6 neutrons, and 5 electrons. Which of its particles are in its nucleus?
Step 1
Protons and neutrons are packed together in the nucleus; electrons move outside it.
Step 2
The 5 protons and the 6 neutrons — the 5 electrons move outside the nucleus.
Worked example 2. Name the three subatomic particles and where each sits in the atom.
Step 1
Protons and neutrons in the nucleus; electrons in the space outside it.
You can now state the names and locations of the three subatomic particles: protons and neutrons packed together in the nucleus, and electrons moving in the space outside the nucleus.
Check your understanding
Which subatomic particles are found in an atom's nucleus?
AProtons and neutrons.correct
BProtons and electrons.
This option is wrong — you moved the electrons into the nucleus — electrons move in the space outside it; the nucleus holds protons and neutrons.
CNeutrons and electrons.
This option is wrong — you swapped the protons out for electrons — protons and neutrons share the nucleus; electrons stay outside.
DProtons, neutrons, and electrons.
This option is wrong — you packed all three into the nucleus — the electrons move in the space outside it.
Two of the three subatomic particles are packed together in the nucleus. They are the protons and the neutrons. The electrons move in the space outside the nucleus.
Check your understanding
A carbon atom has 6 protons, 6 neutrons, and 6 electrons. Where are its 6 electrons?
AMoving in the space outside the nucleus.correct
BPacked in the nucleus together with the protons.
This option is wrong — you put the electrons in the nucleus — only protons and neutrons are packed there.
CInside the neutrons.
This option is wrong — you nested one particle inside another — electrons are separate particles that move outside the nucleus.
DStuck to the outside surface of the nucleus.
This option is wrong — you parked the electrons on the nucleus — they move through the space outside it, not on its surface.
Protons and neutrons are packed together in the nucleus. Electrons move in the space outside the nucleus. So carbon's 6 electrons are moving outside its nucleus.
Check your understanding
Which subatomic particle moves in the space outside the nucleus?
AThe electron.correct
BThe proton.
This option is wrong — you moved the proton out of the nucleus — protons are packed inside it, with the neutrons.
CThe neutron.
This option is wrong — you moved the neutron out of the nucleus — neutrons are packed inside it, with the protons.
DAll three particles move outside the nucleus.
This option is wrong — you emptied the nucleus — protons and neutrons stay packed inside it; only the electrons move outside.
The nucleus holds the protons and the neutrons. The particle moving in the space outside the nucleus is the electron. That is the same particle Thomson discovered.
Lesson 10 of 65 · ATM-010
Particle charges
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The three subatomic particles differ first in electric charge.
The idea
Every proton carries a charge of 1+.
Every electron carries a charge of 1−.
Every neutron carries no charge at all.
Charges add up: a nucleus with 3 protons carries a total charge of 3+, because its neutrons add nothing.
Charges of the subatomic particles
Particle
Charge
proton
1+
neutron
no charge
electron
1−
One charge per particle: protons 1+, electrons 1−, neutrons none.
Worked examples
Worked example 1. A nucleus contains 5 protons and 6 neutrons. What is its total charge?
Step 1
Each of the 5 protons contributes 1+.
Step 2
The 6 neutrons contribute nothing.
Step 3
The nucleus's total charge is 5+.
Worked example 2. What is the charge of a single neutron?
Step 1
No charge — every neutron is uncharged.
You can now state the electrical charge of each subatomic particle: every proton carries a charge of 1+, every electron a charge of 1−, and every neutron no charge.
Check your understanding
Which line gives the correct charge of each subatomic particle?
AProton 1+, electron 1−, neutron no charge.correct
BProton 1−, electron 1+, neutron no charge.
This option is wrong — you swapped the proton's and electron's charges — the proton is 1+ and the electron is 1−.
CProton 1+, neutron 1−, electron no charge.
This option is wrong — you gave the electron's charge to the neutron — the neutron carries no charge; the electron carries the 1−.
DProton 1+, electron 1−, neutron 1+.
This option is wrong — you charged the neutron — neutrons carry no charge at all.
One charge per particle. Proton: 1+. Electron: 1−. Neutron: no charge at all.
Check your understanding
A nucleus contains 7 protons and 7 neutrons. What is its total charge?
A7+correct
B14+
This option is wrong — you charged the neutrons too — only the 7 protons contribute, at 1+ each.
C0
This option is wrong — you let the neutrons cancel the protons — neutrons have no charge to cancel with, so the 7 proton charges stand.
D7−
This option is wrong — you gave the protons negative charge — each proton carries 1+, so seven of them give 7+.
Each proton contributes 1+; each neutron contributes nothing. 7 protons give 7+ and the 7 neutrons add nothing. The nucleus's total charge is 7+.
Check your understanding
A nucleus is built from 4 protons and 5 neutrons. Which of its particles contribute to its total charge?
AOnly the 4 protons — the total is 4+.correct
BAll 9 particles — the total is 9+.
This option is wrong — you counted every nucleus particle as charged — the 5 neutrons carry no charge, so only the protons count.
COnly the 5 neutrons — the total is 5+.
This option is wrong — you charged the neutrons instead of the protons — neutrons carry nothing; the protons carry the 1+ charges.
DThe protons and neutrons cancel — the total is 0.
This option is wrong — you treated the neutrons as negative — they are uncharged, so nothing cancels the protons' 4+.
Ask what each particle carries. Each proton carries 1+; each neutron carries nothing. So only the 4 protons contribute, and the total charge is 4+.
Lesson 11 of 65 · ATM-011
Particle masses
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Did You Know?
Charge is one difference between the three particles. Mass is the other.
The idea
Atoms and their particles are far too light for grams to be handy, so their masses are measured in 'atomic mass units (amu)'.
A proton has a mass of about 1 amu.
A neutron also has a mass of about 1 amu.
An electron is nearly 2000 times lighter than a proton or a neutron.
Because each proton and each neutron contributes about 1 amu, a nucleus's mass in amu is roughly its count of protons plus neutrons.
Masses of the subatomic particles
Particle
Mass
proton
about 1 amu
neutron
about 1 amu
electron
nearly 2000 times lighter than a proton
Protons and neutrons weigh about 1 amu each; the electron barely registers.
A carbon nucleus of 6 protons and 6 neutrons has a mass of about 12 amu.
Worked examples
Worked example 1. A nitrogen nucleus holds 7 protons and 7 neutrons. About what is its mass in amu?
Step 1
Each proton and each neutron contributes about 1 amu.
Step 2
7 + 7 = 14.
Step 3
About 14 amu.
Worked example 2. Which has more mass — one proton, or three electrons together?
Step 1
An electron is nearly 2000 times lighter than a proton.
Step 2
Even three electrons together are still hundreds of times lighter than one proton.
Step 3
The proton, by far.
You can now state the relative masses of the subatomic particles: a proton and a neutron each have a mass of about 1 atomic mass unit (amu), while an electron is nearly 2000 times lighter.
Check your understanding
Which two subatomic particles have nearly the same mass, about 1 amu each?
AThe proton and the neutron.correct
BThe proton and the electron.
This option is wrong — you paired the electron with a nucleus particle — the electron is nearly 2000 times lighter than either.
CThe neutron and the electron.
This option is wrong — you paired the electron with the neutron — the electron is nearly 2000 times lighter; the neutron's partner in mass is the proton.
DAll three particles have about the same mass.
This option is wrong — you leveled all three masses — the electron is nearly 2000 times lighter than the other two.
Two particles weigh about 1 amu each: the proton and the neutron. The electron is the odd one out. It is nearly 2000 times lighter than either of them.
Check your understanding
An oxygen nucleus holds 8 protons and 8 neutrons. About what is its mass, in amu?
Answer: 16amu
Each proton and each neutron contributes about 1 amu. 8 protons + 8 neutrons = 16 particles of about 1 amu each. The nucleus's mass is about 16 amu.
Check your understanding
How does the mass of an electron compare with the mass of a neutron?
AThe electron is nearly 2000 times lighter.correct
BThe two have about the same mass.
This option is wrong — you leveled the two masses — the neutron weighs about 1 amu and the electron is nearly 2000 times lighter.
CThe electron is about half as heavy.
This option is wrong — you shrank the gap — the difference is a factor of nearly 2000, not 2.
DThe electron is nearly 2000 times heavier.
This option is wrong — you flipped the comparison — it is the electron that is nearly 2000 times LIGHTER.
A neutron weighs about 1 amu. An electron is nearly 2000 times lighter than a proton or a neutron. So the electron is nearly 2000 times lighter than the neutron.
Lesson 12 of 65 · ATM-012
Why the nucleus holds nearly all the mass
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Did You Know?
Put the particle masses together and something striking falls out about where an atom keeps its mass.
The idea
Each proton and each neutron outweighs an electron by a factor of nearly 2000.
So all of an atom's electrons together add almost nothing to its total mass.
Nearly all of an atom's mass therefore sits in its nucleus, where the protons and neutrons are packed.
The 6 electrons of a carbon atom contribute less than 0.1% of its mass.
Worked examples
Worked example 1. An aluminum atom holds 13 protons, 14 neutrons, and 13 electrons. Why is nearly all of its mass in its nucleus?
Step 1
The 13 protons and 14 neutrons weigh about 1 amu each — about 27 amu, all packed in the nucleus.
Step 2
Each electron is nearly 2000 times lighter, so all 13 together contribute only a tiny fraction of 1 amu.
Step 3
The nucleus holds the 27 heavy particles, so it holds nearly all of the atom's mass.
Worked example 2. If a magnesium atom could lose all 12 of its electrons, about how much of its mass would it lose?
Step 1
Each electron is nearly 2000 times lighter than a proton or a neutron.
Step 2
Almost none — a small fraction of 1% of its mass.
You can now explain why nearly all of an atom's mass is in its nucleus: because each proton and neutron outweighs an electron by a factor of nearly 2000, the electrons add almost nothing to the total.
Check your understanding
Why does an atom's nucleus hold nearly all of the atom's mass?
AEach proton and neutron outweighs an electron by nearly 2000 times, so the electrons add almost nothing.correct
BThe nucleus sits at the exact center of the atom, and an atom's mass naturally gathers at its center.
This option is wrong — you made position the cause — the nucleus is heavy because of what is packed there, not because centers attract mass.
CElectrons have no mass at all, so everything the atom weighs is in the nucleus.
This option is wrong — you gave electrons zero mass — they have mass, just nearly 2000 times less than a proton or a neutron.
DThe nucleus's positive charge pulls the atom's mass inward.
This option is wrong — you turned charge into a mass magnet — charge attracts charge, and mass simply sits with the heavy particles.
Compare the particles' masses. Each proton and each neutron outweighs an electron by nearly 2000 times. The heavy particles are packed in the nucleus, so the nucleus holds nearly all the mass.
Check your understanding
A silicon atom holds 14 protons, 14 neutrons, and 14 electrons. About what share of the atom's mass do its 14 electrons contribute?
AFar less than 1%.correct
BExactly one third — 14 of the atom's 42 particles.
This option is wrong — you shared the mass by particle count — mass follows each particle's weight, and an electron weighs nearly 2000 times less.
CAbout half.
This option is wrong — you split the mass between nucleus and electrons — the electrons together carry only a tiny fraction of 1%.
DAbout 10%.
This option is wrong — you gave the electrons a small but real share — even 14 of them add up to far less than 1% of the mass.
The 28 protons and neutrons weigh about 1 amu each. Each electron is nearly 2000 times lighter, so 14 electrons total well under 0.01 amu. That is far less than 1% of the atom's roughly 28 amu.
Check your understanding
Removing one electron from an atom changes the atom's mass by about how much?
AAlmost nothing — about 1/2000 of 1 amu.correct
BAbout 1 amu.
This option is wrong — you gave the electron a proton's mass — an electron weighs nearly 2000 times less than 1 amu.
CExactly nothing — electrons have no mass.
This option is wrong — you zeroed the electron's mass — it has mass, just a tiny one, so the change is almost nothing rather than nothing.
DAbout half the atom's mass.
This option is wrong — you gave one electron half the atom — nearly all of the mass stays in the nucleus, untouched.
An electron is nearly 2000 times lighter than a proton or a neutron. So one electron weighs about 1/2000 of 1 amu. Removing it changes the atom's mass by almost nothing — but not exactly nothing.
Lesson 13 of 65 · ATM-013
What holds electrons in the atom
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Have You Ever Wondered?
Wonder this:
Electrons race through the space around the nucleus — so why don't they simply fly off and leave the atom behind?
The answer is a pull between charges: opposite charges attract.
The idea
The nucleus is positive, and every electron is negative.
The negative electrons are pulled toward the positive nucleus, because opposite charges attract, and the attraction is stronger when the charges are larger or closer together.
That pull is what holds each electron in the atom.
An electron near a lithium nucleus, for example, is pulled toward the nucleus's 3+ charge.
Worked examples
Worked example 1. Why does an electron in a fluorine atom stay in the atom instead of drifting away?
Step 1
The fluorine nucleus, with its 9 protons, carries a 9+ charge; the electron carries 1−.
Step 2
Opposite charges attract, so the nucleus pulls the electron toward itself.
Step 3
The attraction to the nucleus holds the electron in the atom.
Worked example 2. Two electrons sit the same distance from two different bare nuclei — one nucleus is 4+, the other 2+. Which electron feels the stronger pull?
Step 1
The attraction is stronger when the charges are larger.
Step 2
At the same distance, the 4+ nucleus is the larger charge.
Step 3
The electron near the 4+ nucleus feels the stronger pull.
You can now explain why electrons stay bound to an atom: the negative electrons are pulled toward the positive nucleus, because opposite charges attract, and the attraction is stronger when the charges are larger or closer together.
Check your understanding
What holds an electron inside an atom?
AThe pull between the negative electron and the positive nucleus — opposite charges attract.correct
BThe neutrons hold the electron in place.
This option is wrong — you used the neutrons — they carry no charge, so they have nothing to pull the electron with.
CThe atom has a firm outer edge, and that edge blocks the moving electron from leaving.
This option is wrong — you built a wall around the atom — nothing surrounds the electrons; only the nucleus's pull keeps them.
DThe electron's weight keeps it from floating away.
This option is wrong — you used weight — the holding force is the attraction between opposite charges, not gravity.
The nucleus is positive; the electron is negative. The electron is pulled toward the nucleus, because opposite charges attract, and the attraction is stronger when the charges are larger or closer together. That pull is what holds the electron in the atom.
Check your understanding
Two oxygen atoms are compared. One electron sits close to the first atom's nucleus; another electron sits much farther from the second atom's identical nucleus. Which electron is held more strongly?
AThe closer electron — the attraction is stronger when the charges are closer together.correct
BThe farther electron — the pull grows as the electron moves away.
This option is wrong — you grew the pull with distance — the attraction is stronger when the charges are CLOSER together.
CBoth equally — distance does not change the attraction.
This option is wrong — you dropped distance from the rule — the attraction is stronger when the charges are closer together.
DNeither — electrons are held by the neutrons, which sit at a fixed distance.
This option is wrong — you used the neutrons — they carry no charge; the pull comes from the positive nucleus.
The two nuclei are identical, so only the distance differs. Opposite charges attract, and the attraction is stronger when the charges are larger or closer together. The closer electron feels the stronger pull.
Check your understanding
One electron sits at a certain distance from a sodium nucleus, whose charge is 11+. Another electron sits at the same distance from a boron nucleus, whose charge is 5+. Which electron is pulled more strongly?
AThe electron near the sodium nucleus — the attraction is stronger when the charges are larger.correct
BThe electron near the boron nucleus — a smaller nucleus grips its electrons harder.
This option is wrong — you flipped the charge rule — at the same distance, the LARGER charge gives the stronger pull.
CBoth equally — every nucleus pulls an electron with the same force.
This option is wrong — you dropped charge size from the rule — the attraction is stronger when the charges are larger.
DNeither — a nucleus only pulls on the electrons that belong to its own atom.
This option is wrong — you gave the pull an ownership test — a positive nucleus pulls on any negative charge near it.
The distances are the same, so only the charges differ. Opposite charges attract, and the attraction is stronger when the charges are larger or closer together. 11+ is the larger charge, so the sodium nucleus pulls its electron more strongly.
Lesson 14 of 65 · ATM-014
Why atoms are neutral
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Have You Ever Wondered?
Wonder this:
An atom is built from charged particles — every proton carries 1+ and every electron carries 1−. Yet you can touch a doorknob, a glass of water, or your own arm and feel no jolt at all. How can matter packed with charge carry no charge?
The answer is in the counts.
The idea
A whole atom contains equal numbers of protons and electrons.
Each proton's 1+ charge cancels one electron's 1− charge.
With equal counts, every 1+ is cancelled by a 1−, so the total charge is 0.
Neutrons carry no charge, so they never tip the balance either way.
An oxygen atom has 8 protons and 8 electrons — 8 charges of 1+ against 8 charges of 1−, for a total charge of 0.
Worked examples
Worked example 1. A nitrogen atom has 7 protons, 7 neutrons, and 7 electrons. Why does the whole atom have no overall charge?
Step 1
The 7 protons carry a total charge of 7+.
Step 2
The 7 electrons carry a total charge of 7−.
Step 3
The 7 neutrons carry no charge at all.
Step 4
7+ and 7− cancel exactly.
Step 5
The atom's total charge is 0.
Worked example 2. A whole calcium atom has 20 protons. How many electrons does it have?
Step 1
A whole atom has no overall charge, so its proton and electron counts are equal.
Step 2
20 protons means 20 electrons.
Step 3
The atom has 20 electrons.
You can now explain why a whole atom has no overall charge: because it contains equal numbers of protons and electrons, the 1+ and 1− charges cancel exactly.
Check your understanding
A sulfur atom has 16 protons and 16 electrons. Why does the whole atom have no overall charge?
AThe 16 charges of 1+ and the 16 charges of 1− cancel exactly.correct
BThe protons and electrons are too small for their charges to matter.
This option is wrong — you made the charges disappear by size — every proton and electron carries a full charge; the counts cancel, not the particles.
CThe neutrons absorb the charges of the protons and electrons.
This option is wrong — you gave the neutrons a job they cannot do — a neutron carries no charge and cannot absorb any.
DThe charges only cancel while the atom is not touching other atoms.
This option is wrong — you made cancellation depend on the surroundings — equal counts of 1+ and 1− cancel in any atom, anywhere.
Each proton carries 1+ and each electron carries 1−. The atom has equal counts: 16 protons and 16 electrons. Every 1+ is cancelled by a 1−, so the total charge is 0.
Check your understanding
A neutral atom has 12 protons and 13 neutrons. How many electrons does it have?
Answer: 12electrons
A neutral atom has equal numbers of protons and electrons. The atom has 12 protons, so it has 12 electrons. The 13 neutrons carry no charge and do not change the balance.
Check your understanding
An atom contains 15 protons, 16 neutrons, and 15 electrons. What is its overall charge?
A0correct
B1−
This option is wrong — you counted the extra neutron as a negative charge — a neutron carries no charge at all.
C1+
This option is wrong — you counted the extra neutron as a positive charge — a neutron carries no charge at all.
D31+
This option is wrong — you added the protons and neutrons as positive charges — only the 15 protons carry 1+ each, and the 15 electrons cancel them.
Count only the charged particles: 15 protons at 1+ and 15 electrons at 1−. Equal counts cancel exactly, so the total charge is 0. The 16 neutrons carry no charge and never tip the balance.
Lesson 15 of 65 · ATM-015
The atomic number defines the element
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Did You Know?
Wonder this:
Every atom of carbon has exactly 6 protons. Give one of them a 7th proton, and it is not carbon any more — it is nitrogen.
One count in the nucleus decides everything about which element an atom is.
The idea
The number of protons in an atom's nucleus decides which element the atom is.
The proton count of an atom is called its 'atomic number'.
Every atom with 6 protons is a carbon atom — no matter how many neutrons it has.
Change the proton count, and the atom becomes an atom of a different element.
Change the neutron count, and the atom stays an atom of the same element.
Worked examples
Worked example 1. Every atom of fluorine has 9 protons. What is fluorine's atomic number?
Step 1
The atomic number is the proton count.
Step 2
Fluorine's atomic number is 9.
Worked example 2. One atom has 7 protons and 7 neutrons. Another has 7 protons and 8 neutrons. Are they atoms of the same element?
Step 1
Both atoms have 7 protons.
Step 2
The proton count decides the element, and the neutron count does not.
Step 3
Yes — both are nitrogen atoms.
You can now state that the number of protons in an atom's nucleus, called its atomic number, determines which element the atom is.
Check your understanding
Which count decides which element an atom is?
AThe number of protons.correct
BThe number of neutrons.
This option is wrong — you used the neutron count — neutrons can vary without changing the element.
CThe number of electrons.
This option is wrong — you used the electron count — the deciding count sits in the nucleus, and it is the protons.
DThe number of protons plus neutrons.
This option is wrong — you used the whole nucleus — only the proton part of that total decides the element.
The proton count decides which element an atom is. That count is the element's atomic number. Neutron counts can differ between atoms of one element.
Check your understanding
One atom has 17 protons and 18 neutrons. Another atom has 17 protons and 20 neutrons. How do the two atoms compare?
AThey are atoms of the same element.correct
BThey are atoms of two different elements.
This option is wrong — you let the neutron difference change the element — only the proton count decides the element, and both atoms have 17 protons.
CThey are atoms of the same element only if their electron counts also match.
This option is wrong — you added an electron condition — the element is decided by the proton count alone.
DThere is no way to tell without more information.
This option is wrong — you treated the given counts as not enough — the matching proton counts settle it completely.
The proton count decides which element an atom is. Both atoms have 17 protons, so both are atoms of the same element. The different neutron counts do not change the element.
Check your understanding
Every atom with 79 protons is a gold atom. An atom is found with 79 protons and 118 neutrons. What is it?
AA gold atom.correct
BAn atom of a different, heavier element.
This option is wrong — you let the 118 neutrons change the element — neutrons add mass, not identity, and the 79 protons make it gold.
CAn atom that is partly gold and partly another element.
This option is wrong — you split the atom's identity between its particle counts — the proton count alone decides, and it says gold.
DAn atom that belongs to no element.
This option is wrong — you required the proton and neutron counts to match — unequal counts are normal, and the protons still decide the element.
The proton count decides which element an atom is. This atom has 79 protons, and every atom with 79 protons is gold. The 118 neutrons change the atom's mass, not its element.
Lesson 16 of 65 · ATM-016
Reading the atomic number
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Did You Know?
You've already seen that the proton count — the atomic number — decides which element an atom is. The periodic table hands you that count for every element.
The idea
Every element has its own entry on the periodic table.
Oxygen's periodic-table entry. The whole number 8 is the atomic number: every oxygen atom has 8 protons.
The entry shows a whole number: the element's atomic number.
The atomic number tells you the proton count of every atom of that element.
Oxygen's entry shows atomic number 8, so every oxygen atom has 8 protons.
The entry also shows a second number with a decimal point — that number is not the atomic number.
To find any element's proton count, read the atomic number from its entry.
Worked examples
Worked example 1. Potassium's periodic-table entry shows the whole number 19 and the decimal number 39.1. How many protons does a potassium atom have?
Step 1
The atomic number is the whole number on the entry: 19.
Step 2
The atomic number is the proton count.
Step 3
Every potassium atom has 19 protons.
Worked example 2. Silicon's entry shows the whole number 14 and the decimal number 28.1. What is silicon's atomic number?
Step 1
The whole number on the entry is the atomic number.
Step 2
The decimal number is not the atomic number.
Step 3
Silicon's atomic number is 14.
You can now identify an element's atomic number, and so its proton count, from the element's entry in the periodic table.
Check your understanding
The periodic-table entry for phosphorus is shown. How many protons does a phosphorus atom have?
A15correct
B31
This option is wrong — you rounded the decimal number on the entry — that value is not the atomic number, and the proton count is the whole number 15.
C16
This option is wrong — you subtracted the atomic number from the rounded decimal value — no subtraction is needed; the atomic number itself is the proton count.
D46
This option is wrong — you added the two numbers on the entry together — only the whole-number atomic number reports the proton count.
The whole number on the entry is the atomic number: 15. The atomic number is the proton count. Every phosphorus atom has 15 protons.
Check your understanding
The periodic-table entry for calcium is shown. How many protons does a calcium atom have?
Answer: 20protons
The whole number on the entry is the atomic number: 20. The atomic number is the proton count. Every calcium atom has 20 protons.
Check your understanding
The periodic-table entry for zinc is shown. Which number on the entry is zinc's atomic number?
A30correct
B65.4
This option is wrong — you picked the decimal value — the atomic number is a whole count of protons and never carries a decimal point.
C65
This option is wrong — you rounded the decimal value to a whole number — rounding does not turn it into the atomic number.
D35
This option is wrong — you subtracted the two numbers on the entry — the atomic number is read directly, not calculated.
The atomic number is the whole number on the entry: 30. It is a count of protons, so it never carries a decimal point. The decimal value 65.4 is a different quantity.
Lesson 17 of 65 · ATM-017
Mass number
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Did You Know?
You've already seen that protons and neutrons each have a mass of about 1 amu, and that the electrons add almost nothing. So counting the nucleus counts nearly all of the atom's mass.
The equation
The total count of protons plus neutrons in an atom's nucleus is called the atom's 'mass number'.
To find the mass number, add the proton count and the neutron count.
An atom with 11 protons and 12 neutrons has mass number 11 + 12 = 23.
Electrons are not counted — they are nearly 2000 times lighter than the nuclear particles.
The mass number is a whole-number count, so it never carries a decimal point.
Worked examples
Worked example 1. An iron atom has 26 protons and 30 neutrons. What is its mass number?
Step 1
Write down the values in the question
protons = 26
neutrons = 30
Step 2
Write down the equation
mass number = protons + neutrons
Step 3
Substitute in the values, and calculate
mass number = 26 + 30
mass number = 56
Worked example 2. A fluorine atom has 9 protons and 10 neutrons. What is its mass number?
Step 1
Write down the values in the question
protons = 9
neutrons = 10
Step 2
Write down the equation
mass number = protons + neutrons
Step 3
Substitute in the values, and calculate
mass number = 9 + 10
mass number = 19
You can now determine an atom's mass number, the total count of protons plus neutrons in its nucleus, by adding the two counts.
Check your understanding
An atom has 3 protons and 4 neutrons. What is its mass number?
Answer: 7
Write down the values in the question: protons = 3 neutrons = 4 Write down the relationship: mass number = protons + neutrons Substitute in the values, and calculate: mass number = 3 + 4 mass number = 7
Check your understanding
An argon atom has 18 protons and 22 neutrons. What is its mass number?
Answer: 40
Write down the values in the question: protons = 18 neutrons = 22 Write down the relationship: mass number = protons + neutrons Substitute in the values, and calculate: mass number = 18 + 22 mass number = 40
Check your understanding
Which counts are added together to give an atom's mass number?
AProtons and neutrons.correct
BProtons only.
This option is wrong — you stopped at the protons — the neutrons in the nucleus carry mass too and are counted.
CProtons, neutrons, and electrons.
This option is wrong — you added the electrons in — they are nearly 2000 times lighter than the nuclear particles and are not counted.
DNeutrons and electrons.
This option is wrong — you swapped the protons out for electrons — the mass number counts the two nuclear particles, protons and neutrons.
The mass number is the count of protons plus neutrons in the nucleus. Those two particles each have a mass of about 1 amu. Electrons add almost nothing, so they are left out of the count.
Lesson 18 of 65 · ATM-018
Counting neutrons
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Did You Know?
You've already seen that the mass number adds the protons and neutrons, and that the atomic number is the proton count. Often you are handed those two numbers and need the neutron count back.
The equation
The mass number counts the protons plus the neutrons.
The atomic number is the proton count, so mass number = atomic number + neutron count.
To find the neutron count, make it the subject: neutron count = mass number − atomic number.
An atom with mass number 23 and atomic number 11 has 23 − 11 = 12 neutrons.
The subtraction is the same relationship as the addition, rearranged — not a new rule to memorize.
Worked examples
Worked example 1. A potassium atom has mass number 39. Potassium's atomic number is 19. How many neutrons does the atom have?
Step 1
Write down the values in the question
mass number = 39
atomic number = 19
Step 2
Write down the equation
mass number = atomic number + neutron count
Step 3
Make the unknown the subject
neutron count = mass number − atomic number
Step 4
Substitute in the values, and calculate
neutron count = 39 − 19
neutron count = 20 neutrons
Worked example 2. An iodine atom has mass number 127. Iodine's atomic number is 53. How many neutrons does the atom have?
Step 1
Write down the values in the question
mass number = 127
atomic number = 53
Step 2
Write down the equation
mass number = atomic number + neutron count
Step 3
Make the unknown the subject
neutron count = mass number − atomic number
Step 4
Substitute in the values, and calculate
neutron count = 127 − 53
neutron count = 74 neutrons
You can now calculate the number of neutrons in an atom by subtracting its atomic number from its mass number.
Check your understanding
A fluorine atom has mass number 19. Fluorine's atomic number is 9. How many neutrons does the atom have?
Answer: 10neutrons
Write down the values in the question: mass number = 19 atomic number = 9 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 = 19 − 9 neutron count = 10 neutrons
Check your understanding
A silver atom has mass number 109. Silver's atomic number is 47. How many neutrons does the atom have?
Answer: 62neutrons
Write down the values in the question: mass number = 109 atomic number = 47 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 = 109 − 47 neutron count = 62 neutrons
Check your understanding
A strontium atom has mass number 88. Strontium's atomic number is 38. How many neutrons does the atom have?
Answer: 50neutrons
Write down the values in the question: mass number = 88 atomic number = 38 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 = 88 − 38 neutron count = 50 neutrons
Lesson 19 of 65 · ATM-019
Isotopes
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Wonder this:
Two carbon atoms sit side by side. Both have 6 protons and 6 electrons — yet one outweighs the other.
The difference is in the nucleus.
The idea
One of the carbon atoms has 6 neutrons, and the other has 7.
Same 6 protons — different neutron counts
Two carbon nuclei. The proton counts match, so both atoms are carbon; the neutron counts differ, so the atoms are isotopes.
Atoms of the same element can have different numbers of neutrons.
Different neutron counts give the atoms different mass numbers: 12 and 13.
Atoms of the same element with different numbers of neutrons are called 'isotopes'.
Most elements found in nature are a mixture of their isotopes.
Worked examples
Worked example 1. One oxygen atom has 8 protons and 8 neutrons. Another has 8 protons and 10 neutrons. What word names their relationship?
Step 1
Same element — both have 8 protons.
Step 2
Different neutron counts — 8 and 10.
Step 3
They are isotopes of oxygen.
Worked example 2. One atom has 6 protons and another has 7 protons. Are they isotopes of one element?
Step 1
Different proton counts mean different elements — carbon and nitrogen.
Step 2
Isotopes must be atoms of the SAME element.
Step 3
No — they are atoms of two different elements, not isotopes of one element.
You can now state that isotopes are atoms of the same element that have different numbers of neutrons, and so different mass numbers.
Check your understanding
Which statement describes isotopes of an element?
AAtoms with the same number of protons but different numbers of neutrons.correct
BAtoms with different numbers of protons but the same number of neutrons.
This option is wrong — you swapped the counts — changing the proton count changes the element, so those atoms are not versions of one element.
CAtoms with the same number of protons and the same number of neutrons.
This option is wrong — you described identical atoms — isotopes must DIFFER in neutron count.
DAtoms of two different elements whose masses happen to be equal.
This option is wrong — you built the definition on mass alone — isotopes are atoms of one element, and their masses differ.
Isotopes are atoms of the same element, so their proton counts match. Their neutron counts differ, so their mass numbers differ. Same protons, different neutrons — that is the whole definition.
Check your understanding
Atom 1 has 20 protons and 20 neutrons. Atom 2 has 20 protons and 24 neutrons. How are the two atoms related?
AThey are isotopes of the same element.correct
BThey are atoms of two different elements.
This option is wrong — you let the neutron difference change the element — both atoms have 20 protons, so both are the same element.
CThey are identical atoms of one element.
This option is wrong — you overlooked the neutron counts — 20 and 24 differ, so the atoms differ in mass.
DThey are the same atom written two different ways.
This option is wrong — you merged two genuinely different atoms — their neutron counts, and so their masses, are different.
Both atoms have 20 protons, so they are atoms of the same element. Their neutron counts differ: 20 and 24. Same element, different neutrons — they are isotopes.
Check your understanding
Four pairs of atoms are described below. In which pair are the two atoms isotopes of one element?
AAn atom with 6 protons and 6 neutrons, and an atom with 6 protons and 7 neutrons.correct
BAn atom with 7 protons and 7 neutrons, and an atom with 8 protons and 8 neutrons.
This option is wrong — you accepted different proton counts — those are atoms of two different elements, not isotopes of one.
CAn atom with 10 protons and 10 neutrons, and another atom with 10 protons and 10 neutrons.
This option is wrong — you picked identical atoms — isotopes must differ in neutron count.
DAn atom with 18 protons and 22 neutrons, and an atom with 20 protons and 20 neutrons.
This option is wrong — you matched the mass numbers — equal totals do not make isotopes; the proton counts differ, so the elements differ.
Isotopes must match in proton count and differ in neutron count. Only the 6-proton pair matches in protons — 6 and 6 — while differing in neutrons — 6 and 7. Equal mass numbers with different proton counts are two different elements, not isotopes.
Lesson 20 of 65 · ATM-020
Why isotopes behave alike
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Did You Know?
You've already seen that isotopes of an element differ in neutron count. That difference changes surprisingly little about how the atoms behave.
The idea
Isotopes of an element take part in exactly the same chemical reactions and form exactly the same compounds.
That is because chemical behavior depends on the protons and electrons, which are unchanged, while extra neutrons change only the mass.
A carbon atom with 7 neutrons forms the same compounds as a carbon atom with 6 neutrons.
What DOES differ between isotopes is mass: more neutrons make a heavier atom.
Same chemistry, different mass — that is nearly the whole isotope story.
The one caution: the neutron count can decide whether the nucleus itself holds together — some combinations of protons and neutrons are not stable. Stable or unstable, though, the atom's chemical behavior still follows its protons and electrons.
Worked examples
Worked example 1. Chlorine atoms come with 18 neutrons or with 20 neutrons. Both kinds react with sodium to form the same table salt. Why?
Step 1
Both kinds have 17 protons and 17 electrons.
Step 2
Chemical behavior depends on the protons and electrons, which are unchanged.
Step 3
The extra neutrons change only the mass.
Step 4
Both kinds form the same compounds, because their protons and electrons match.
Worked example 2. A hydrogen atom with 1 neutron is about twice as heavy as one with no neutrons. Which property differs between them, and which stays the same?
Step 1
The mass differs — the extra neutron nearly doubles it.
Step 2
The protons and electrons are unchanged, so the chemical behavior stays the same.
Step 3
The mass differs; the chemical behavior stays the same — both kinds form water with oxygen.
You can now explain why isotopes of an element show the same chemical behavior but different masses: because chemical behavior depends on the protons and electrons, which are unchanged, while extra neutrons change only the mass.
Check your understanding
Two oxygen atoms both have 8 protons; one has 8 neutrons and the other has 10. Both combine with hydrogen in exactly the same way to form water. Why?
ABecause chemical behavior depends on the protons and electrons, which are unchanged, while extra neutrons change only the mass.correct
BBecause their neutron counts are too close for the difference to matter — a larger gap between the counts would change how the atoms react.
This option is wrong — you made the behavior depend on the size of the neutron difference — a difference of any size leaves the chemistry unchanged, because neutrons play no part in it.
CBecause water formation happens between whole atoms and does not involve the particles inside the atoms at all.
This option is wrong — you took the particles out of chemistry — reactions do depend on particles, specifically the protons and electrons, and those match here.
DBecause the heavier atom sheds its two extra neutrons during the reaction, leaving both atoms identical by the end.
This option is wrong — you had the reaction change the nucleus — chemical reactions never add or remove neutrons; the extra neutrons simply ride along.
Both atoms have 8 protons and 8 electrons. Chemical behavior depends on the protons and electrons, which are unchanged. The extra neutrons change only the mass.
Check your understanding
A carbon atom with 6 protons and 8 neutrons is heavier than the common carbon atom with 6 neutrons. Will the heavier atom form the same compounds as the lighter one?
AYes — because chemical behavior depends on the protons and electrons, which are unchanged, while extra neutrons change only the mass.correct
BNo — the heavier atom reacts differently, because what an atom does in a reaction depends on how much the atom weighs.
This option is wrong — you made mass the driver of chemical behavior — behavior follows the protons and electrons, and those are the same in both atoms.
CYes, but only in reactions that happen slowly enough for the heavier atom's extra mass to keep up with the lighter one.
This option is wrong — you invented a speed condition — the two atoms form the same compounds in every reaction, fast or slow.
DNo — with 8 neutrons against only 6 protons, the atom has stopped being carbon and behaves as a different element.
This option is wrong — you let the neutron count change the element — 6 protons makes the atom carbon regardless of its neutrons.
Both atoms have 6 protons and 6 electrons. Chemical behavior depends on the protons and electrons, which are unchanged. The extra neutrons change only the mass, so both atoms form the same compounds.
Check your understanding
Changing which count in an atom leaves its chemical behavior unchanged?
AThe neutron count.correct
BThe proton count.
This option is wrong — you picked the count that changes everything — changing protons changes the element itself, and with it the chemistry.
CThe electron count.
This option is wrong — you picked a particle that chemistry depends on — chemical behavior follows the protons and electrons.
DThe proton count and the neutron count together.
This option is wrong — you bundled the protons in — any change to the proton count changes the element and its behavior.
Chemical behavior depends on the protons and electrons. Extra neutrons change only the mass. So the neutron count can change while the chemistry stays the same.
Lesson 21 of 65 · ATM-021
Reading isotope notation
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Wonder this:
'The chlorine atom with 17 protons and 18 neutrons' — that is nine words for one atom. Chemists write all of it in one compact symbol: ³⁵₁₇Cl.
The symbol packs two numbers around the element symbol, and each number has a fixed meaning.
The idea
In symbol form, the superscript before the element symbol is the mass number — the count of protons plus neutrons.
One atom, two written forms: ³⁵₁₇Cl and chlorine-35 carry the same information.
The subscript before the element symbol is the atomic number — the proton count.
In ³⁵₁₇Cl, the 35 is the mass number and the 17 is the atomic number.
The same atom has a name form: the mass number follows the element name, as in chlorine-35.
³⁵₁₇Cl and chlorine-35 name exactly the same atom.
Isotopes of an element share the subscript but differ in the superscript.
Worked examples
Worked example 1. What does each number in ⁶⁵₂₉Cu tell you?
Step 1
The subscript 29 is the atomic number: the atom has 29 protons, so it is copper.
Step 2
The superscript 65 is the mass number: the protons and neutrons together count to 65.
Step 3
⁶⁵₂₉Cu is the copper isotope with mass number 65 — in name form, copper-65.
Worked example 2. What does the name nitrogen-15 tell you?
Step 1
The element name gives the element: nitrogen.
Step 2
The number after the name is the mass number: 15.
Step 3
Nitrogen-15 is the nitrogen isotope with mass number 15.
You can now interpret the two written forms of an isotope: in symbol form the superscript before the element symbol is the mass number and the subscript is the atomic number, and in name form the mass number follows the element name.
Check your understanding
In the symbol ⁴⁰₁₈Ar, what does the 40 report?
AThe number of protons plus neutrons.correct
BThe number of protons.
This option is wrong — you read the superscript as the proton count — the proton count is the subscript, 18.
CThe number of neutrons.
This option is wrong — you read the superscript as neutrons alone — the superscript counts the protons and neutrons together.
DThe number of electrons.
This option is wrong — you read the superscript as an electron count — neither number in the symbol counts electrons.
The superscript before the element symbol is the mass number. The mass number is the count of protons plus neutrons. In ⁴⁰₁₈Ar, that count is 40.
Check your understanding
In the symbol ²⁰⁸₈₂Pb, what does the 82 report?
AThe number of protons.correct
BThe number of protons plus neutrons.
This option is wrong — you read the subscript as the mass number — the combined count is the superscript, 208.
CThe number of neutrons.
This option is wrong — you read the subscript as a neutron count — the subscript is the atomic number, which counts protons.
DThe number of particles in the whole atom.
This option is wrong — you read the subscript as a grand total — it is the atomic number, the proton count alone.
The subscript before the element symbol is the atomic number. The atomic number is the proton count. In ²⁰⁸₈₂Pb, that count is 82.
Check your understanding
What is the mass number of the atom written ¹⁰⁹₄₇Ag?
Answer: 109
The superscript before the element symbol is the mass number. In ¹⁰⁹₄₇Ag, the superscript is 109. The mass number is 109 — no arithmetic needed.
Lesson 22 of 65 · ATM-022
Writing isotope notation
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Did You Know?
You've already seen how to read an isotope's symbol form and name form. Writing them yourself runs the same rules in the other direction, starting from the particle counts.
The idea
Start with the proton count: it is the atomic number, and it goes in the subscript position.
The proton count also picks the element symbol and name from the periodic table.
Add the protons and neutrons to get the mass number: it goes in the superscript position.
Write the superscript and subscript before the element symbol.
An atom with 17 protons and 18 neutrons is written ³⁵₁₇Cl.
For the name form, write the element name, a hyphen, and the mass number: chlorine-35.
Worked examples
Worked example 1. An atom has 8 protons and 10 neutrons. Write its symbol form and its name form.
Step 1
The proton count is 8, so the atomic number — the subscript — is 8, and the element is oxygen, symbol O.
Step 2
mass number = protons + neutrons
Step 3
mass number = 8 + 10 = 18, so the superscript is 18.
Step 4
Symbol form: ¹⁸₈O. Name form: oxygen-18.
Worked example 2. An atom has 92 protons and 146 neutrons. Write its symbol form and its name form.
Step 1
The proton count is 92, so the subscript is 92, and the element is uranium, symbol U.
Step 2
mass number = protons + neutrons
Step 3
mass number = 92 + 146 = 238, so the superscript is 238.
Step 4
Symbol form: ²³⁸₉₂U. Name form: uranium-238.
You can now write an isotope's symbol form and name form from its particle counts.
Check your understanding
An atom has 24 protons and 28 neutrons. What number goes in the superscript of its symbol form?
Answer: 52
The superscript is the mass number. mass number = protons + neutrons mass number = 24 + 28 = 52, so the superscript is 52.
Your turn
An atom has 13 protons and 14 neutrons. Its element is aluminum, symbol Al. On paper, write the atom's full symbol form, then select Continue to compare your answer with the model answer.
Model answer. ²⁷₁₃Al — the superscript 27 (13 + 14) sits before the element symbol at the top, and the subscript 13 sits before the element symbol at the bottom.
The superscript is 27 — the protons and neutrons added together (13 + 14).
The subscript is 13 — the proton count, the atomic number.
Both numbers sit BEFORE the element symbol, superscript above subscript.
The element symbol is Al.
Your turn
An atom has 30 protons and 36 neutrons. Its element is zinc. On paper, write the atom's name form, then select Continue to compare your answer with the model answer.
Model answer. zinc-66 — the element name, a hyphen, then the mass number 66 (30 + 36).
The element name zinc comes first.
A hyphen joins the name to the number.
The number is the mass number, 66 — the protons and neutrons added together (30 + 36).
The number is NOT the proton count 30 or the neutron count 36.
Lesson 23 of 65 · ATM-023
Full particle count from an isotope symbol
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Did You Know?
You've already seen what each number in an isotope symbol means, how to find a neutron count, and why a whole atom's electrons match its protons. One symbol now hands you all three particle counts.
The idea
The subscript is the atomic number, so it gives the proton count directly.
The neutron count comes from the relationship: mass number = atomic number + neutron count.
Make the neutron count the subject: neutron count = mass number − atomic number.
For a neutral atom, the electron count equals the proton count.
So ⁵⁶₂₆Fe describes a neutral atom with 26 protons, 56 − 26 = 30 neutrons, and 26 electrons.
Worked examples
Worked example 1. How many protons, neutrons, and electrons are in a neutral ¹²⁷₅₃I atom?
Step 1
protons = the subscript = 53
Step 2
mass number = atomic number + neutron count
Step 3
Make the neutron count the subject: neutron count = mass number − atomic number
Step 4
neutron count = 127 − 53 = 74
Step 5
electrons = protons in a neutral atom = 53
Step 6
53 protons, 74 neutrons, 53 electrons.
Worked example 2. How many protons, neutrons, and electrons are in a neutral ⁹₄Be atom?
Step 1
protons = the subscript = 4
Step 2
mass number = atomic number + neutron count
Step 3
Make the neutron count the subject: neutron count = mass number − atomic number
Step 4
neutron count = 9 − 4 = 5
Step 5
electrons = protons in a neutral atom = 4
Step 6
4 protons, 5 neutrons, 4 electrons.
You can now determine the numbers of protons, neutrons, and electrons in a neutral atom from its isotope symbol.
Check your understanding
How many neutrons are in a neutral ⁸⁴₃₆Kr atom?
Answer: 48neutrons
Write down the values from the symbol: mass number = 84 atomic number = 36 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 = 84 − 36 neutron count = 48 neutrons
Check your understanding
How many electrons are in a neutral ³¹₁₅P atom?
Answer: 15electrons
The subscript gives the proton count: 15. A neutral atom has equal numbers of protons and electrons. So the atom has 15 electrons.
Check your understanding
How many neutrons are in a neutral ²³²₉₀Th atom?
Answer: 142neutrons
Write down the values from the symbol: mass number = 232 atomic number = 90 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 = 232 − 90 neutron count = 142 neutrons
Lesson 24 of 65 · ATM-024
Isotopes correct Dalton
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Did You Know?
Dalton's atomic theory said that atoms of the same element are identical. You've now seen atoms that break that rule.
The idea
Chlorine-35 and chlorine-37 are both chlorine, yet they differ in neutron count and mass.
So the discovery of isotopes disproved one specific point of Dalton's theory: atoms of the same element are NOT all identical.
The corrected statement: atoms of one element all share the same proton count, but they can differ in neutron count and mass.
Dalton's other points survived — elements still have their own kind of atom, compounds still form in fixed whole-number ratios, and chemical changes still only rearrange atoms.
The theory was corrected, not thrown away.
Worked examples
Worked example 1. Carbon-12 and carbon-13 both occur in every natural sample of carbon. Which point of Dalton's theory does this disprove?
Step 1
Both atoms are carbon, yet their masses differ.
Step 2
Dalton said atoms of the same element are identical.
Step 3
It disproves the point that atoms of the same element are identical.
You can now identify which point of Dalton's theory the discovery of isotopes disproved: atoms of the same element are not all identical, because they can differ in neutron count and mass.
Check your understanding
Neon atoms come in two common versions, neon-20 and neon-22, with different masses. Which point of Dalton's theory does this disprove?
AAtoms of the same element are identical.correct
BEvery element is made of its own kind of atom.
This option is wrong — you picked a point isotopes leave standing — both versions are still neon's own kind of atom, defined by the proton count.
CAtoms combine in fixed whole-number ratios to form compounds.
This option is wrong — you picked the compound-ratio point — isotope masses say nothing about combining ratios, which still hold.
DChemical changes rearrange atoms without creating or destroying them.
This option is wrong — you picked the rearrangement point — isotopes exist in unreacted neon; no chemical change is involved.
Dalton said atoms of the same element are identical. Neon-20 and neon-22 are both neon, yet their masses differ. So that one point had to be corrected — the other points survived.
Check your understanding
After isotopes were discovered, Dalton's identical-atoms point had to be rewritten. Which corrected statement is right?
AAtoms of one element share the same proton count but can differ in neutron count and mass.correct
BAtoms of one element can differ in proton count but never in neutron count.
This option is wrong — you swapped the counts — the proton count is what atoms of one element must share; the neutrons are what can differ.
CAtoms of one element are identical in every way after all.
This option is wrong — you kept Dalton's original point — isotopes show atoms of one element differing in mass.
DAtoms of one element can be created and destroyed in chemical changes.
This option is wrong — you corrected the wrong point — isotopes say nothing against the rearrangement point, which still stands.
Atoms of one element all share the same proton count. Their neutron counts, and so their masses, can differ. That is the isotope correction to Dalton's identical-atoms point.
Check your understanding
Silicon-28 and silicon-30 both occur in ordinary beach sand. Which idea does their existence contradict?
AThat every atom of one element is identical.correct
BThat silicon is a real element.
This option is wrong — you let the two versions undo the element — both are silicon, because both have silicon's proton count.
CThat sand contains silicon atoms in fixed ratios with oxygen atoms.
This option is wrong — you reached for the compound-ratio idea — the fixed ratio of atoms in a compound still holds whichever isotopes are involved.
DThat atoms survive chemical changes without being created or destroyed.
This option is wrong — you reached for the rearrangement idea — both isotopes sit in the sand without any chemical change happening.
Silicon-28 and silicon-30 are both silicon, with different masses. Dalton's theory said atoms of one element are identical. The isotope pair contradicts exactly that idea.
Summary video — Inside the atom — subatomic particles, atomic number, and isotopes
Look up chlorine on the periodic table and its entry shows 35.5 amu. But chlorine atoms have mass numbers 35 and 37 — no chlorine atom anywhere has a mass of 35.5 amu.
So what is the table reporting?
The idea
Natural chlorine is a mixture of its isotopes: chlorine-35 and chlorine-37.
The table's decimal value is the 'average atomic mass' — an average of the element's naturally occurring isotope masses.
It is a weighted average: isotopes that are more 'abundant', meaning more common, count for more in the average.
Chlorine-35 is far more common than chlorine-37, so chlorine-35 counts for more in chlorine's 35.5 amu.
That is why the value is not a whole number — it averages over a mixture, and it is the mass of no single atom.
This is the decimal number you were told to ignore when reading atomic numbers — it has a meaning of its own.
Worked examples
Worked example 1. Silver's periodic-table entry shows 107.9 amu, and natural silver is a mixture of silver-107 and silver-109. What kind of value is 107.9 amu?
Step 1
It is the average atomic mass: a weighted average of the two isotope masses.
Step 2
No single silver atom has that mass.
Step 3
107.9 amu is a weighted average over natural silver's isotope mixture.
Worked example 2. Natural magnesium is mostly magnesium-24, with smaller amounts of magnesium-25 and magnesium-26. Which isotope counts for the most in magnesium's average atomic mass?
Step 1
In a weighted average, the more abundant isotope counts for more.
Step 2
Magnesium-24 is the most abundant of the three.
Step 3
Magnesium-24 counts for the most.
You can now state that the atomic mass shown on the periodic table is a weighted average of the masses of the element's naturally occurring isotopes, in which more abundant, meaning more common, isotopes count for more.
Check your understanding
Rubidium's periodic-table entry shows 85.5 amu. What does that value report?
AA weighted average of the masses of rubidium's naturally occurring isotopes.correct
BThe mass that every individual rubidium atom has, whichever isotope it belongs to.
This option is wrong — you gave every atom the average mass — each atom has its own isotope's mass, and no atom has the in-between value 85.5 amu.
CThe mass of one atom of rubidium's heaviest naturally occurring isotope.
This option is wrong — you picked one isotope's mass — the table value averages over all the natural isotopes.
DThe count of protons plus neutrons in the nucleus of one rubidium atom.
This option is wrong — you read the value as a mass number — a mass number is a whole-number count, and 85.5 has a decimal because it is an average.
The table's decimal value is the average atomic mass. It is a weighted average over the element's naturally occurring isotopes. More abundant isotopes count for more in the average.
Check your understanding
Gallium-69 is described as the more abundant of gallium's two natural isotopes. What does 'abundant' mean here?
AMore common in natural samples.correct
BHeavier than the other isotope.
This option is wrong — you read abundance as mass — abundance is about how common an isotope is, not how heavy.
CMore reactive than the other isotope.
This option is wrong — you read abundance as reactivity — isotopes of an element share the same chemical behavior.
DLarger in size than the other isotope.
This option is wrong — you read abundance as size — abundance counts how often the isotope turns up in nature.
Abundant means common in natural samples. The more abundant isotope makes up more of the element's atoms. That is why it counts for more in the weighted average.
Check your understanding
Antimony's periodic-table entry shows 121.8 amu, yet antimony atoms have the whole mass numbers 121 and 123. Why is the table value not a whole number?
AIt is an average over the isotope mixture, so it lands between the isotope masses instead of on one of them.correct
BThe table value was measured with an imprecise balance, so its decimal digits are measurement error.
This option is wrong — you blamed measurement error — the decimal is real and comes from averaging over a mixture.
CSome antimony atoms contain fractions of a neutron, which puts their masses between the whole numbers.
This option is wrong — you split the neutron — particles come in whole numbers; the fraction comes from averaging whole-mass atoms.
DThe table value includes the mass of the atoms' electrons on top of the protons and neutrons.
This option is wrong — you reached for the electrons — their tiny mass is not what puts the value between 121 and 123; the averaging is.
Natural antimony mixes atoms of mass numbers 121 and 123. The table averages over that mixture, weighted by abundance. An average of different whole values need not be whole — and it is the mass of no single atom.
Lesson 26 of 65 · ATM-026
The average sits near the common isotope
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Did You Know?
You've already seen that the average atomic mass is a weighted average, in which the more abundant isotope counts for more. That tells you WHERE the average must sit.
The idea
Because the more abundant isotope counts for more, the average is pulled toward that isotope's mass.
Chlorine-35 is about three times as common, so the average sits much closer to 35 than to 37.
So an element's average atomic mass lies closer to the mass of its more abundant isotope.
Chlorine-35 is about three times as common as chlorine-37, so chlorine's average of 35.5 amu sits much closer to 35 than to 37.
The more lopsided the abundances, the closer the average sits to the common isotope's mass.
When two isotopes are nearly equally common, the average sits near the halfway point between their masses.
Worked examples
Worked example 1. Natural lithium is about 92% lithium-7 and 8% lithium-6. Where will lithium's average atomic mass sit?
Step 1
Lithium-7 is far more abundant, so it counts for far more in the average.
Step 2
The average is pulled strongly toward 7.
Step 3
Very close to 7 amu — the table value is 6.9 amu.
Worked example 2. Natural gallium is about 60% gallium-69 and 40% gallium-71. Where will gallium's average atomic mass sit?
Step 1
Gallium-69 is more abundant, but only somewhat — 60% against 40%.
Step 2
The average is pulled toward 69, but not far from the middle.
Step 3
Closer to 69 than to 71, but near the middle — the table value is 69.7 amu.
You can now predict that an element's average atomic mass lies closer to the mass of its more abundant isotope.
Check your understanding
Natural rubidium is about 72% rubidium-85 and 28% rubidium-87. Where will rubidium's average atomic mass sit?
ACloser to 85 than to 87.correct
BCloser to 87 than to 85.
This option is wrong — you pulled the average toward the heavier isotope — the pull follows abundance, and rubidium-85 is the more common one.
CExactly halfway between 85 and 87.
This option is wrong — you averaged the two masses equally — a weighted average leans toward the more abundant isotope.
DAbove 87.
This option is wrong — you placed the average outside the isotope masses — an average of 85s and 87s must land between them.
Rubidium-85 is the more abundant isotope — 72% against 28%. The more abundant isotope counts for more, so the average is pulled toward 85. The table value, 85.5 amu, sits closer to 85.
Check your understanding
Natural thallium is about 30% thallium-203 and 70% thallium-205. Where will thallium's average atomic mass sit?
ACloser to 205 than to 203.correct
BCloser to 203 than to 205.
This option is wrong — you leaned toward the isotope listed first — the pull follows abundance, and thallium-205 is the more common one.
CExactly halfway between 203 and 205.
This option is wrong — you averaged the two masses equally — a weighted average leans toward the more abundant isotope.
DBelow 203.
This option is wrong — you placed the average outside the isotope masses — an average of 203s and 205s must land between them.
Thallium-205 is the more abundant isotope — 70% against 30%. The more abundant isotope counts for more, so the average is pulled toward 205. The table value, 204.4 amu, sits closer to 205.
Check your understanding
Natural nitrogen is about 99.6% nitrogen-14 and 0.4% nitrogen-15. Which value is closest to nitrogen's average atomic mass?
A14.0 amucorrect
B14.5 amu
This option is wrong — you sat the average halfway between the masses — with abundances this lopsided, the average sits almost on top of 14.
C15.0 amu
This option is wrong — you leaned toward the rarer isotope — the average is pulled toward the abundant one, nitrogen-14.
D29.0 amu
This option is wrong — you added the two masses instead of averaging — the average must land between 14 and 15.
Nitrogen-14 makes up nearly all natural nitrogen. The more abundant isotope counts for more, so the average sits almost exactly at 14. The table value is 14.0 amu.
Lesson 27 of 65 · ATM-027
Which isotope is most abundant
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No single copper atom has a mass of 63.5 amu — yet that is the value the periodic table lists. You've already seen why: the table value is a weighted average that sits closer to the mass of the more abundant isotope. Read in reverse, the same fact tells you which isotope fills most of a sample.
The idea
The periodic-table atomic mass sits closer to the mass of the more abundant isotope.
So compare the table value with each isotope's mass.
The isotope whose mass is closer to the table value is the more abundant one.
Copper's isotopes are copper-63 (mass 63.0 amu) and copper-65 (mass 65.0 amu), and the table lists copper's atomic mass as 63.5 amu.
The value 63.5 sits closer to 63.0 than to 65.0.
So copper-63 is the more abundant isotope.
Worked examples
Worked example 1. Chlorine's isotopes are chlorine-35 (mass 35.0 amu) and chlorine-37 (mass 37.0 amu). The periodic table lists chlorine's atomic mass as 35.5 amu. Which isotope is more abundant?
Step 1
35.5 sits closer to 35.0 than to 37.0.
Step 2
The table value sits closer to the mass of the more abundant isotope.
Step 3
Chlorine-35 is the more abundant isotope.
Worked example 2. Lithium's isotopes are lithium-6 (mass 6.0 amu) and lithium-7 (mass 7.0 amu). The periodic table lists lithium's atomic mass as 6.9 amu. Which isotope is more abundant?
Step 1
6.9 sits closer to 7.0 than to 6.0.
Step 2
This time the table value sits nearer the heavier isotope.
Step 3
Lithium-7 is the more abundant isotope.
You can now identify an element's most abundant isotope by comparing the periodic-table atomic mass with the isotope masses.
Check your understanding
Boron's isotopes are boron-10 (mass 10.0 amu) and boron-11 (mass 11.0 amu). The periodic table lists boron's atomic mass as 10.8 amu. Which isotope is more abundant?
ABoron-11correct
BBoron-10
This option is wrong — you picked the lighter isotope by habit — 10.8 sits closer to 11.0, so boron-11 is the more abundant.
CThe two isotopes are equally abundant
This option is wrong — you assumed equal shares — equal shares would put the average exactly halfway, at 10.5, not at 10.8.
DThe atomic mass alone cannot tell you
This option is wrong — you gave up on the average — the weighted average sits closer to the mass of the more abundant isotope, so it does tell you.
The table value sits closer to the mass of the more abundant isotope. 10.8 sits closer to 11.0 than to 10.0. So boron-11 is the more abundant isotope.
Check your understanding
Gallium's isotopes are gallium-69 (mass 69.0 amu) and gallium-71 (mass 71.0 amu). The periodic table lists gallium's atomic mass as 69.7 amu. Which isotope is more abundant?
AGallium-69correct
BGallium-71
This option is wrong — you picked the heavier isotope as if more mass meant more atoms — 69.7 sits closer to 69.0, so gallium-69 is the more abundant.
CThe two isotopes are equally abundant
This option is wrong — you assumed equal shares — equal shares would put the average exactly halfway, at 70.0, not at 69.7.
DThe atomic mass alone cannot tell you
This option is wrong — you gave up on the average — the weighted average sits closer to the mass of the more abundant isotope, so it does tell you.
The table value sits closer to the mass of the more abundant isotope. 69.7 sits closer to 69.0 than to 71.0. So gallium-69 is the more abundant isotope.
Check your understanding
Rubidium's isotopes are rubidium-85 (mass 85.0 amu) and rubidium-87 (mass 87.0 amu). The periodic table lists rubidium's atomic mass as 85.5 amu. Which isotope is more abundant?
ARubidium-85correct
BRubidium-87
This option is wrong — you picked the heavier isotope as if more mass meant more atoms — 85.5 sits closer to 85.0, so rubidium-85 is the more abundant.
CThe two isotopes are equally abundant
This option is wrong — you assumed equal shares — equal shares would put the average exactly halfway, at 86.0, not at 85.5.
DThe atomic mass alone cannot tell you
This option is wrong — you gave up on the average — the weighted average sits closer to the mass of the more abundant isotope, so it does tell you.
The table value sits closer to the mass of the more abundant isotope. 85.5 sits closer to 85.0 than to 87.0. So rubidium-85 is the more abundant isotope.
Lesson 28 of 65 · ATM-028
Calculating average atomic mass
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You've already seen that the periodic-table atomic mass is a weighted average of the isotope masses, and that it sits closer to the more abundant isotope. This lesson is where you calculate that average yourself.
The equation
Write each isotope's percent abundance as a decimal fraction by dividing the percent by 100.
fraction
percent abundance written as a decimal (none)
mass
isotope mass (amu)
Multiply each isotope's mass by its fraction.
Add the results.
The sum is the element's average atomic mass, in amu.
Sanity check: the average must land between the isotope masses, closer to the more abundant isotope.
Worked examples
Worked example 1. Boron is 20.0% boron-10 (mass 10.0 amu) and 80.0% boron-11 (mass 11.0 amu). What is boron's average atomic mass?
Step 1
Write down the values in the question
fraction of boron-10 = 20.0% → 0.200
fraction of boron-11 = 80.0% → 0.800
mass of boron-10 = 10.0 amu
mass of boron-11 = 11.0 amu
Step 2
Write down the equation
average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)
Step 3
Substitute in the values, and calculate
average atomic mass = (0.200 × 10.0) + (0.800 × 11.0) = 2.00 + 8.80
average atomic mass = 10.8 amu
Worked example 2. Chlorine is 75.0% chlorine-35 (mass 35.0 amu) and 25.0% chlorine-37 (mass 37.0 amu). What is chlorine's average atomic mass?
Step 1
Write down the values in the question
fraction of chlorine-35 = 75.0% → 0.750
fraction of chlorine-37 = 25.0% → 0.250
mass of chlorine-35 = 35.0 amu
mass of chlorine-37 = 37.0 amu
Step 2
Write down the equation
average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂)
Step 3
Substitute in the values, and calculate
average atomic mass = (0.750 × 35.0) + (0.250 × 37.0) = 26.25 + 9.25
average atomic mass = 35.5 amu
Worked example 3. Magnesium is 79.0% magnesium-24 (mass 24.0 amu), 10.0% magnesium-25 (mass 25.0 amu), and 11.0% magnesium-26 (mass 26.0 amu). What is magnesium's average atomic mass?
Step 1
Write down the values in the question
fraction of magnesium-24 = 79.0% → 0.790
fraction of magnesium-25 = 10.0% → 0.100
fraction of magnesium-26 = 11.0% → 0.110
mass of magnesium-24 = 24.0 amu
mass of magnesium-25 = 25.0 amu
mass of magnesium-26 = 26.0 amu
Step 2
Write down the equation
average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + (fraction₃ × mass₃)
You can now calculate an element's average atomic mass by writing each percent abundance as a decimal fraction, multiplying each isotope's mass by its fraction, and adding the results.
Check your understanding
Gallium is 60.0% gallium-69 (mass 69.0 amu) and 40.0% gallium-71 (mass 71.0 amu). What is gallium's average atomic mass, in amu? Give your answer to 3 significant figures.
Answer: 69.8amu(tolerance ±0.05)
Write each percent abundance as a decimal fraction: fraction of gallium-69 = 60.0% → 0.600 fraction of gallium-71 = 40.0% → 0.400 Write down the equation: average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) Substitute in the values, and calculate: average atomic mass = (0.600 × 69.0) + (0.400 × 71.0) average atomic mass = 41.4 + 28.4 average atomic mass = 69.8 amu
Check your understanding
Copper is 70.0% copper-63 (mass 63.0 amu) and 30.0% copper-65 (mass 65.0 amu). What is copper's average atomic mass, in amu? Give your answer to 3 significant figures.
Answer: 63.6amu(tolerance ±0.05)
Write each percent abundance as a decimal fraction: fraction of copper-63 = 70.0% → 0.700 fraction of copper-65 = 30.0% → 0.300 Write down the equation: average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) Substitute in the values, and calculate: average atomic mass = (0.700 × 63.0) + (0.300 × 65.0) average atomic mass = 44.1 + 19.5 average atomic mass = 63.6 amu
Check your understanding
Bromine is 50.0% bromine-79 (mass 79.0 amu) and 50.0% bromine-81 (mass 81.0 amu). What is bromine's average atomic mass, in amu? Give your answer to 3 significant figures.
Answer: 80.0amu(tolerance ±0.05)
Write each percent abundance as a decimal fraction: fraction of bromine-79 = 50.0% → 0.500 fraction of bromine-81 = 50.0% → 0.500 Write down the equation: average atomic mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) Substitute in the values, and calculate: average atomic mass = (0.500 × 79.0) + (0.500 × 81.0) average atomic mass = 39.5 + 40.5 average atomic mass = 80.0 amu
Ocean swells roll toward a beach with long stretches of water between them; the ripples from a pebble crowd close together. To compare waves like these, you need a number for the size of one repeat.
Start with the shape every wave shares.
The idea
A wave repeats the same shape over and over.
Each high point of the wave is called a **'crest'**.
The distance from one crest to the next is the wave's **'wavelength'**.
On the drawn wave in the figure, the crest-to-crest distance is 2 cm, so its wavelength is 2 cm.
To read any drawn wave's wavelength, measure from one crest to the next.
Worked examples
Worked example 1. On a drawing of a water wave, the distance from one crest to the next is 4 cm. What is the wave's wavelength?
Step 1
Wavelength is the crest-to-crest distance.
Step 2
The wavelength is 4 cm.
Worked example 2. Ocean swells pass a buoy with 12 m of water from one crest to the next. What is their wavelength?
Step 1
Wavelength is the crest-to-crest distance, whatever the size of the wave.
Step 2
The wavelength is 12 m.
You can now identify a wave's wavelength as the distance from one crest, or high point, to the next.
Check your understanding
The figure shows a wave drawn on a centimeter grid. What is the wave's wavelength?
A3 cmcorrect
B1.5 cm
This option is wrong — you measured from a crest to the neighboring low point — that is only half of one repeat; measure crest to crest.
C2 cm
This option is wrong — you measured the wave's full height, from its lowest point to its highest — wavelength runs along the wave, from one crest to the next.
D6 cm
This option is wrong — you measured across two full repeats — wavelength is the distance across one repeat, crest to crest.
Wavelength is the distance from one crest to the next. On the grid, neighboring crests sit 3 cm apart. So the wavelength is 3 cm.
Check your understanding
The figure shows a wave drawn on a centimeter grid. What is the wave's wavelength?
A5 cmcorrect
B2.5 cm
This option is wrong — you measured from a crest to the neighboring low point — that is only half of one repeat; measure crest to crest.
C2 cm
This option is wrong — you measured the wave's full height, from its lowest point to its highest — wavelength runs along the wave, from one crest to the next.
D10 cm
This option is wrong — you measured across two full repeats — wavelength is the distance across one repeat, crest to crest.
Wavelength is the distance from one crest to the next. On the grid, neighboring crests sit 5 cm apart. So the wavelength is 5 cm.
Check your understanding
What does a wave's wavelength measure?
AThe distance from one crest to the nextcorrect
BHow tall the wave is from its lowest to its highest point
This option is wrong — you described the wave's height — wavelength runs along the wave between crests, not up and down.
CHow fast the wave travels across the water
This option is wrong — you described the wave's speed — wavelength is a distance frozen in the wave's shape, not a rate of travel.
DHow long the wave lasts before it dies away
This option is wrong — you described a time — wavelength is a distance, measured crest to crest.
A wave repeats the same shape over and over. The distance from one crest to the next is the wave's wavelength.
Lesson 30 of 65 · ATM-030
Frequency
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Wonder this:
Watch waves hit a post at the end of a pier. Some days wave after wave slaps it with barely a pause; other days there is a long wait between arrivals. Wavelength is a distance — it cannot capture how often the waves arrive.
Counting the arrivals needs its own quantity.
The idea
Pick one fixed point, such as the post, and count the complete waves that pass it in one second.
That count is the wave's **'frequency'**.
A wave's frequency is the number of complete waves that pass a point each second.
Frequency is written in waves per second.
In the figure, 5 complete waves pass the flag in one second, so the frequency is 5 waves per second.
Worked examples
Worked example 1. A cork floats on a pond. In one second, 3 complete waves pass it. What is the wave's frequency?
Step 1
Frequency is the number of complete waves that pass a point each second.
Step 2
The frequency is 3 waves per second.
Worked example 2. In one second, 20 complete ripples pass a floating leaf. What is the ripples' frequency?
Step 1
Frequency is the number of complete waves that pass a point each second, however fast they come.
Step 2
The frequency is 20 waves per second.
You can now identify a wave's frequency as the number of complete waves that pass a point each second.
Check your understanding
What is a wave's frequency?
AThe number of complete waves that pass a point each secondcorrect
BThe distance from one crest to the next
This option is wrong — you described wavelength — that is the distance quantity; frequency is a count per second.
CHow fast a single crest travels across the water
This option is wrong — you described the wave's speed — frequency counts arrivals at a point, not how fast a crest moves.
DHow tall the wave is from its lowest to its highest point
This option is wrong — you described the wave's height — frequency is a count of waves passing each second.
Pick one fixed point and count the complete waves that pass it in one second. That count is the wave's frequency, written in waves per second.
Check your understanding
In one second, 7 complete waves pass a harbor post. What is the wave's frequency?
A7 waves per secondcorrect
B14 waves per second
This option is wrong — you counted each high point and each low point as separate waves — count complete waves only.
C7 cm
This option is wrong — you answered with a distance — frequency is a count of waves each second, not a length.
D7 waves per minute
This option is wrong — you attached the wrong time — the 7 waves passed in one second, so the frequency is 7 waves per second.
Frequency is the number of complete waves that pass a point each second. 7 complete waves passed the post in one second. So the frequency is 7 waves per second.
Check your understanding
Each second, 3 complete waves pass a rock in stream A, and 9 complete waves pass an identical rock in stream B. Which wave has the higher frequency?
AThe wave in stream B — more complete waves pass each secondcorrect
BThe wave in stream A — fewer arrivals means each wave counts for more
This option is wrong — you inverted the count — frequency IS the count of waves per second, so 9 beats 3.
CThey are equal, because the rocks are identical
This option is wrong — you judged by the measuring point — frequency belongs to the wave, and the counts differ.
DIt cannot be compared without the waves' wavelengths
This option is wrong — you reached for wavelength — frequency needs only the count per second, which is given for both.
Frequency is the number of complete waves that pass a point each second. Stream B's count is 9 per second; stream A's is 3 per second. So the wave in stream B has the higher frequency.
Lesson 31 of 65 · ATM-031
Longer wavelength, lower frequency
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Light is a wave too, so it has both of the numbers you've already seen — a wavelength and a frequency. And light has one more property that changes everything: in empty space, every light wave travels at exactly the same speed.
The idea
Picture trucks and cars all driving past a gate at the same speed.
Fewer trucks pass the gate each minute than cars, because each long truck takes longer to go by.
Light waves passing a point work the same way.
Because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency.
As the wavelength gets longer, the frequency gets lower.
Red light has a longer wavelength than blue light, so red light has the lower frequency.
Worked examples
Worked example 1. Green light has a longer wavelength than violet light. Which has the lower frequency?
Step 1
Both travel at the same speed in empty space.
Step 2
Green light's waves are longer, so fewer of them pass a point each second.
Step 3
Green light has the lower frequency.
Worked example 2. Yellow light has a higher frequency than orange light. Which has the longer wavelength?
Step 1
Both travel at the same speed in empty space.
Step 2
Yellow light's higher frequency means more waves pass a point each second, so each of its waves must be shorter.
Step 3
Orange light has the longer wavelength.
You can now state that because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency.
Check your understanding
Orange light has a longer wavelength than green light. Which light has the lower frequency, and why?
AOrange — at the same speed, longer waves pass a point less oftencorrect
BGreen — at the same speed, shorter waves pass a point less often
This option is wrong — you reversed the trade-off — shorter waves pass MORE often; the longer-wavelength light has the lower frequency.
COrange — longer waves travel more slowly through empty space
This option is wrong — you changed the speed — all light travels at the same speed in empty space; only the wavelength and frequency trade off.
DNeither — lights sharing one speed must share one frequency
This option is wrong — you let the shared speed fix the frequency — the shared speed is exactly why different wavelengths force different frequencies.
Because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency. Orange light's waves are longer than green light's. So orange light has the lower frequency.
Check your understanding
The figure shows two light waves, A and B, drawn over the same one-second window. Which wave has the lower frequency?
AWave A — its longer waves pass a point less oftencorrect
BWave B — its shorter waves pass a point less often
This option is wrong — you reversed the trade-off — shorter waves pass MORE often; the longer-wavelength wave has the lower frequency.
CWave A — it is drawn first, so it arrives first
This option is wrong — you read the stacking order as timing — position on the page says nothing about frequency; wavelength does.
DThey are equal, because both waves travel at the same speed
This option is wrong — you let the shared speed fix the frequency — the shared speed is exactly why different wavelengths force different frequencies.
Because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency. Wave A's crests sit farther apart than wave B's. So wave A has the lower frequency.
Check your understanding
Light P has a lower frequency than light Q. Which light has the longer wavelength?
ALight P — fewer waves pass each second, so each wave must be longercorrect
BLight Q — more waves pass each second, so each wave must be longer
This option is wrong — you reversed the trade-off — more waves fitting past a point each second means each wave is SHORTER.
CThey have the same wavelength, because they travel at the same speed
This option is wrong — you let the shared speed fix the wavelength — at one shared speed, different frequencies force different wavelengths.
DIt cannot be found without knowing each light's speed
This option is wrong — you asked for the speeds — in empty space all light already travels at the same speed, so the frequencies alone settle it.
Because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency. Run it in reverse: the lower-frequency light is the longer-wavelength light. Light P has the lower frequency, so light P has the longer wavelength.
Lesson 32 of 65 · ATM-032
Higher frequency, higher energy
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Did You Know?
Wonder this:
You can sit beside a glowing campfire all evening and your skin is fine. An hour of midday summer sun can leave it burned. The difference is in the light itself.
Frequency is the number that separates the two.
The idea
A beam of light delivers its energy as a stream of tiny bursts — far too small and too many to notice one at a time.
As the frequency of light increases, the energy each tiny burst of the light delivers also increases.
So burst for burst, the higher-frequency light delivers more energy; brightness only sets how many bursts arrive each second.
Sunshine contains **'ultraviolet'** light — light your eyes cannot see.
Ultraviolet light has a higher frequency than visible light, so each burst of it delivers more energy.
Each ultraviolet burst delivers enough energy to damage skin — no burst of the campfire's visible glow carries that much, however bright the fire.
Worked examples
Worked example 1. Violet light has a higher frequency than red light. Burst for burst, which delivers more energy?
Step 1
As the frequency of light increases, the energy each tiny burst of the light delivers also increases.
Step 2
Violet light has the higher frequency.
Step 3
Burst for burst, violet light delivers more energy.
Worked example 2. Each burst of light X delivers less energy than each burst of light Y. Which light has the lower frequency?
Step 1
Burst energy rises and falls with frequency.
Step 2
The light whose bursts deliver less energy must be the one with the lower frequency.
Step 3
Light X has the lower frequency.
You can now state that as the frequency of light increases, the energy the light delivers also increases.
Check your understanding
Blue light has a higher frequency than orange light. Burst for burst, which light delivers more energy?
ABlue light — its frequency is highercorrect
BOrange light — its frequency is lower
This option is wrong — you reversed the relationship — as frequency increases, the energy each burst delivers increases, so the higher-frequency light delivers more, burst for burst.
CThey deliver the same energy, because both are visible
This option is wrong — you let visibility level the energies — being visible says nothing about burst energy; the frequencies differ, so the burst energies differ.
DIt cannot be compared without knowing which light is brighter
This option is wrong — you reached for brightness — brightness only sets how many bursts arrive each second; burst for burst, the higher-frequency light delivers more energy.
As the frequency of light increases, the energy each tiny burst of the light delivers also increases. Blue light has the higher frequency. So burst for burst, blue light delivers more energy.
Check your understanding
A lamp gives off light at two different frequencies. Burst for burst, which light delivers more energy?
AThe higher-frequency lightcorrect
BThe lower-frequency light
This option is wrong — you reversed the relationship — as frequency increases, the energy each burst delivers increases.
CBoth deliver the same energy, because one lamp made them
This option is wrong — you let the source level the energies — energy follows each light's frequency, not where it came from.
DThe one given off first
This option is wrong — you tied energy to timing — when the light left the lamp plays no part; its frequency decides.
As the frequency of light increases, the energy each tiny burst of the light delivers also increases. So burst for burst, the higher-frequency light delivers more energy, whatever the source.
Check your understanding
Each burst of light M delivers more energy than each burst of light N. Which light has the higher frequency?
ALight M — more energy per burst means a higher frequencycorrect
BLight N — delivering less energy leaves it more frequency
This option is wrong — you traded energy against frequency — they rise together; the light whose bursts deliver more energy has the higher frequency.
CThey have the same frequency, because both are light
This option is wrong — you leveled the frequencies — different burst energies force different frequencies.
DIt cannot be found without each light's wavelength
This option is wrong — you reached for wavelength — burst energy rises with frequency, so the energy comparison alone answers it.
As the frequency of light increases, the energy each tiny burst of the light delivers also increases. Run it in reverse: the light whose bursts deliver more energy is the higher-frequency light. Light M's bursts deliver more energy, so light M has the higher frequency.
Lesson 33 of 65 · ATM-033
The electromagnetic spectrum
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Did You Know?
Wonder this:
Press a TV remote and nothing visible leaves it — yet the TV responds. The remote is shining light your eyes cannot see.
Visible light is one slice of a much bigger family.
The idea
The full family of light is called the **'electromagnetic spectrum'**.
From lowest energy to highest, its regions run: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Moving along that order, each region's light carries more energy than the one before's — burst for burst, as always.
Infrared light, for example, carries less energy, burst for burst, than visible light.
Every region is light — the same kind of wave, differing in the energy each burst of it carries.
Worked examples
Worked example 1. Which carries more energy — microwave light or X-ray light?
Step 1
In the energy order, microwave sits second from the bottom and X-ray sits second from the top.
Step 2
X-ray light carries more energy.
Worked example 2. Put these regions in order of increasing energy: ultraviolet, radio, visible.
Step 1
Pick the three out of the full order: radio comes first, visible later, ultraviolet after visible.
Step 2
radio, visible, ultraviolet
You can now state the order of the regions of the electromagnetic spectrum from lowest to highest energy: radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma.
Check your understanding
Burst for burst, which carries more energy — ultraviolet light or visible light?
AUltraviolet lightcorrect
BVisible light
This option is wrong — you reversed the neighbors — ultraviolet sits above visible in the energy order.
CThey carry equal energy
This option is wrong — you leveled two different regions — each region along the order carries more energy than the one before.
DIt cannot be compared without their wavelengths
This option is wrong — you reached for wavelengths — the region order alone ranks the energies.
From lowest to highest energy: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Ultraviolet comes after visible in that order. So ultraviolet light carries more energy.
Check your understanding
Which list orders the regions from lowest to highest energy?
ARadio, infrared, ultraviolet, gammacorrect
BGamma, ultraviolet, infrared, radio
This option is wrong — you ran the order backwards — radio is the low-energy end and gamma the high-energy end.
CRadio, ultraviolet, infrared, gamma
This option is wrong — you swapped infrared and ultraviolet — infrared sits below visible, ultraviolet above it.
DInfrared, radio, gamma, ultraviolet
This option is wrong — you shuffled the ends — radio starts the order and gamma finishes it.
The full order, lowest to highest energy: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Picking out the four: radio, infrared, ultraviolet, gamma.
Check your understanding
Which region of the electromagnetic spectrum carries the least energy?
ARadiocorrect
BGamma
This option is wrong — you named the highest-energy end — gamma finishes the order; radio starts it.
CMicrowave
This option is wrong — you stopped one step short — microwave sits second; radio sits below it.
DInfrared
This option is wrong — you started the order at infrared — radio and microwave both sit below it.
From lowest to highest energy: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Radio starts the order, so radio light carries the least energy.
Lesson 34 of 65 · ATM-034
What each region is used for
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Did You Know?
You've already seen the spectrum's order. Each region also has its own everyday job or effect.
The idea
Radio waves carry broadcast signals to radios and televisions.
Microwaves heat the water in food.
Infrared light is given off by warm objects — you feel it as heat.
Visible light is the only region your eyes can detect.
Ultraviolet light is energetic enough to burn skin and to kill germs.
X-rays pass through skin but not bone, so they photograph the inside of the body.
Gamma rays carry the most energy of all and are used to kill cancer cells.
Worked examples
Worked example 1. A security scanner photographs the objects inside a closed suitcase. Which region of the spectrum does it use?
Step 1
The task is photographing through a solid covering — the X-ray job.
Step 2
X-rays.
Worked example 2. A rescue camera finds a lost hiker in the dark by the warmth of her body. Which region does the camera detect?
Step 1
Warm objects give off infrared light, and that is what the camera picks up.
Step 2
Infrared light.
You can now identify a common use or effect of each region of the electromagnetic spectrum.
Check your understanding
A restaurant lamp keeps plates of food warm from above. Which region of the spectrum is doing the warming?
AInfraredcorrect
BMicrowave
This option is wrong — you reached for the food-heating region — microwaves heat food inside an oven by heating its water; a warming lamp works by giving off infrared, the heat you feel from warm objects.
CUltraviolet
This option is wrong — you picked the sunshine region — ultraviolet burns skin and kills germs; it is not the warmth you feel from a hot lamp.
DRadio
This option is wrong — you picked the broadcast region — radio waves carry signals to radios and televisions, not felt heat.
Infrared light is given off by warm objects — you feel it as heat. The lamp warms the plates the same way: by giving off infrared.
Check your understanding
A hospital wand is passed over surgical tools to kill any germs on them. Which region of the spectrum does the wand shine?
AUltravioletcorrect
BVisible
This option is wrong — you picked the region eyes detect — seeing the tools does not sterilize them; killing germs is ultraviolet's job.
CInfrared
This option is wrong — you picked the felt-heat region — warmth alone is not what the wand delivers; killing germs is ultraviolet's job.
DX-ray
This option is wrong — you picked the photographing region — X-rays image the inside of the body; killing germs is ultraviolet's job.
Ultraviolet light is energetic enough to burn skin and to kill germs. The wand kills germs by shining ultraviolet light.
Check your understanding
Music travels from a broadcast tower to cars across a city. Which region of the spectrum carries it?
ARadiocorrect
BMicrowave
This option is wrong — you went one region up the order — microwaves heat the water in food; broadcast signals ride on radio waves.
CVisible
This option is wrong — you picked the region eyes detect — visible light cannot reach every car through buildings and weather; broadcasting is radio's job.
DInfrared
This option is wrong — you picked the felt-heat region — infrared is the warmth from hot objects; broadcasting is radio's job.
Radio waves carry broadcast signals to radios and televisions. The tower's music rides on radio waves to every car.
Lesson 35 of 65 · ATM-035
Emission spectra
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Have You Ever Wondered?
Wonder this:
A neon sign glows a vivid red-orange — never white like a flashlight. The gas in the tube seems to pick its colors. What exactly is in its light?
To find out, spread a light into its colors and look at what appears.
The idea
White light from a flashlight spreads out into a full rainbow — every color, unbroken.
Light from an energized gas of one element behaves differently.
The energized gas gives off light at only a few exact colors.
Spread out, those colors appear as separate bright lines with darkness between them — not a full rainbow.
This pattern of lines is the element's **'emission spectrum'**.
Energized hydrogen, for example, shows four separate lines in visible light.
Worked examples
Worked example 1. A tube of energized neon gas glows. Spread its light into a spectrum — what appears?
Step 1
An energized gas gives off light at only a few exact colors.
Step 2
Separate bright lines — for neon, mostly reds and oranges — with darkness between them, not a full rainbow.
Worked example 2. Energized helium gives off light at a few exact colors only. What does helium's emission spectrum look like?
Step 1
Each exact color appears as its own bright line.
Step 2
A few separate bright lines with darkness between them.
You can now describe what an element's emission spectrum shows: a gas of the element that has been given energy gives off light at only a few exact colors, which appear as separate bright lines rather than a full rainbow.
Check your understanding
The figure shows the spectrum of light from a tube of energized mercury vapor. What does it show about the light?
AThe gas gives off only a few exact colors, which appear as separate bright linescorrect
BThe gas gives off every color, but most are too dim to see
This option is wrong — you turned the dark gaps into dim light — the gaps are darkness because those colors are simply not given off.
CThe gas gives off one single color of light
This option is wrong — you collapsed the lines into one — each separate line is its own exact color, and the figure shows several.
DThe spreading removed most of the gas's colors
This option is wrong — you blamed the spreading — spreading light only sorts its colors by position; it takes none away.
An energized gas gives off light at only a few exact colors. Spread out, those colors appear as separate bright lines with darkness between them. The figure shows exactly that: mercury's few lines, nothing between.
Check your understanding
The figure shows two spectra, panel A and panel B, from two different light sources. Which panel shows the emission spectrum of an energized gas?
APanel Bcorrect
BPanel A
This option is wrong — you picked the full rainbow — an energized gas gives off only a few exact colors, so its spectrum is separate lines, not an unbroken rainbow.
CBoth panels
This option is wrong — you counted the rainbow as an emission spectrum too — a full unbroken rainbow is what white light gives, not an energized gas of one element.
DNeither panel
This option is wrong — you rejected the line pattern — separate bright lines with darkness between them are exactly what an energized gas gives.
White light spreads into a full rainbow — every color, unbroken. An energized gas gives off only a few exact colors, appearing as separate bright lines. Panel B shows separate lines, so panel B is the emission spectrum.
Check your understanding
What is an element's emission spectrum?
AThe separate bright lines of exact colors its energized gas gives offcorrect
BThe full rainbow any glowing object spreads out
This option is wrong — you gave the white-light picture — an energized gas of one element gives only a few exact colors, not a full rainbow.
CThe colors the gas soaks up from light shone through it
This option is wrong — you described light being taken in — an emission spectrum shows the light the energized gas itself GIVES OFF.
DThe single brightest color the gas gives off
This option is wrong — you kept only one line — the spectrum is the whole pattern of separate lines, not its brightest member.
An energized gas gives off light at only a few exact colors. Spread out, those colors appear as separate bright lines with darkness between them. That pattern of lines is the element's emission spectrum.
Lesson 36 of 65 · ATM-036
Line patterns identify elements
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Every energized gas gives off separate bright lines — but not the same lines.
The idea
Each element's emission spectrum has its own line pattern: its own exact colors, in its own positions.
No two elements share the same pattern.
So a line pattern identifies an element.
To identify an unknown gas, compare its lines with reference spectra, element by element.
The unknown is the element whose reference matches every line — same positions, same count.
In 1868, astronomers spread out sunlight and found lines that matched no element known on Earth.
The pattern belonged to a new element — helium, found in the Sun before it was found on Earth.
Worked examples
Worked example 1. In the figure, unknown X's spectrum sits below the reference spectra of hydrogen, sodium, and neon. Which element is X?
Step 1
Compare X's lines with each reference in turn.
Step 2
X's lines sit exactly where sodium's lines sit — same positions, same count.
Step 3
Neither hydrogen's nor neon's pattern matches.
Step 4
Unknown X is sodium.
Worked example 2. Which element is unknown Y in the same figure?
Step 1
Compare Y's lines with each reference in turn.
Step 2
Y's positions match none of the three references.
Step 3
Y is none of these three elements — its pattern belongs to some other element.
You can now identify an element by matching its emission-line pattern to a reference, because each element's pattern is unique.
Check your understanding
The figure compares an unknown gas's emission spectrum with three labeled reference spectra. Which element is the unknown gas?
AMercurycorrect
BHelium
This option is wrong — you matched a single line — one shared position is not a match; every line must sit where the reference's lines sit.
CLithium
This option is wrong — you matched the overall color family — a general hue is not a match; the exact positions decide.
DNone of the three
This option is wrong — you missed the full agreement — the unknown's lines sit exactly where mercury's sit, same positions and same count.
Compare the unknown's lines with each reference in turn. The unknown's lines sit exactly where mercury's lines sit — same positions, same count. So the unknown gas is mercury.
Check your understanding
The figure compares an unknown gas's emission spectrum with three labeled reference spectra. Which element is the unknown gas?
AHeliumcorrect
BHydrogen
This option is wrong — you matched a single line — one shared position is not a match; every line must sit where the reference's lines sit.
CNeon
This option is wrong — you matched the overall color family — a general hue is not a match; the exact positions decide.
DNone of the three
This option is wrong — you missed the full agreement — the unknown's lines sit exactly where helium's sit, same positions and same count.
Compare the unknown's lines with each reference in turn. The unknown's lines sit exactly where helium's lines sit — same positions, same count. So the unknown gas is helium.
Check your understanding
The figure compares an unknown gas's emission spectrum with three labeled reference spectra. Which element is the unknown gas?
ANone of the threecorrect
BSodium
This option is wrong — you matched the general region of the strip — the unknown's positions do not sit where sodium's lines sit.
CLithium
This option is wrong — you matched the line count — the unknown and lithium both show three lines, but the positions differ, and positions decide.
DMercury
This option is wrong — you matched a single nearby line — one close position is not a match; every line must agree.
Compare the unknown's lines with each reference in turn. The unknown's positions match none of the three references — a shared count or a nearby line is not a match. So the unknown is none of the three; its pattern belongs to some other element.
Lesson 37 of 65 · ATM-037
Bohr's model
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Did You Know?
Wonder this:
Rutherford's model put a tiny, dense nucleus at the center of the atom, with electrons somewhere in the space outside — but it never said where. The separate lines of an emission spectrum were a clue: whatever electrons do, they cannot be just anywhere.
In 1913, Niels Bohr proposed a stricter model.
The idea
In Bohr's model, electrons travel around the nucleus only in specific allowed orbits.
Each allowed orbit has its own fixed energy.
Because of that, the orbits are called **'energy levels'**.
Between the levels there is nowhere to be: in hydrogen, an electron can occupy energy level 1 or energy level 2, but nothing in between.
The levels work like the rungs of a ladder — you can stand on a rung, never between rungs.
Worked examples
Worked example 1. In Bohr's model, can an electron circle the nucleus halfway between energy level 2 and energy level 3?
Step 1
Electrons travel only in the specific allowed orbits, and no allowed orbit sits between the levels.
Step 2
No — between the levels there is nowhere to be.
Worked example 2. In Bohr's model, what does every energy level have?
Step 1
Each allowed orbit has its own fixed energy — that is what makes it an energy level.
Step 2
Its own fixed energy.
You can now describe Bohr's model of the atom: electrons travel only in specific allowed orbits around the nucleus, each with a fixed energy, called energy levels, and cannot exist between them.
Check your understanding
In Bohr's model of the atom, where can electrons travel?
AOnly in specific allowed orbits, each with a fixed energycorrect
BAnywhere in the space outside the nucleus
This option is wrong — you kept Rutherford's vagueness — Bohr's point is the restriction: only the specific allowed orbits exist.
COnly inside the nucleus, packed beside the protons
This option is wrong — you moved the electrons into the nucleus — electrons orbit the nucleus; protons and neutrons live inside it.
DIn any orbit, with the energy changing smoothly from orbit to orbit
This option is wrong — you smoothed the energies out — each allowed orbit has its own fixed energy, and no orbits exist between them.
In Bohr's model, electrons travel around the nucleus only in specific allowed orbits. Each allowed orbit has its own fixed energy — the orbits are energy levels. Between the levels there is nowhere to be.
Check your understanding
The figure shows a drawing of Bohr's model. According to the model, what is wrong with the drawing?
AThe electron is drawn between two energy levels, where no allowed orbit existscorrect
BThe nucleus should not sit at the center
This option is wrong — you moved the nucleus — Bohr kept Rutherford's central nucleus; the error in the drawing is the electron's position.
CThe levels should all have the same energy
This option is wrong — you leveled the energies — each allowed orbit has its own fixed energy; that part of the drawing is fine.
DNothing — electrons may pause between levels while moving
This option is wrong — you gave the electron a resting place between levels — between the levels there is nowhere to be, even briefly.
Electrons travel only in the specific allowed orbits. The drawing places an electron between energy level 1 and energy level 2. No allowed orbit sits there, so the electron's position is the error.
Check your understanding
According to Bohr's model, what does each allowed orbit have?
AIts own fixed energycorrect
BA slowly changing energy that depends on the electron's speed
This option is wrong — you let the energy drift — an allowed orbit's energy is fixed; that is what makes it an energy level.
CThe same energy as every other orbit
This option is wrong — you leveled the orbits — each level has its OWN fixed energy, different from the others.
DA fixed electric charge
This option is wrong — you gave the orbit a charge — charge belongs to particles; what an orbit carries is a fixed energy.
Each allowed orbit has its own fixed energy. That fixed energy is why the orbits are called energy levels.
Lesson 38 of 65 · ATM-038
How atoms give off light
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Did You Know?
You've already seen that an atom's electrons sit on energy levels, with nowhere to be between them. The levels are also the machinery behind a glowing gas: here is how an atom gives off light.
The idea
Give an atom energy — from electricity in a glass tube, or from heat — and an electron absorbs it.
The electron jumps up to a higher energy level.
It does not stay there: the electron soon falls back down to a lower level.
As the electron falls, the atom gives off light.
The light carries exactly the energy difference between the two levels — no more, no less.
A bigger drop between levels gives off light carrying more energy; a smaller drop, less.
In hydrogen, an electron falling from level 3 to level 2 gives off light of one exact color.
Worked examples
Worked example 1. In a helium atom, an electron absorbs energy and jumps from level 2 to level 4. What happens next, and what does the atom give off?
Step 1
The electron does not stay at level 4 — it falls back down to a lower level.
Step 2
As it falls, the atom gives off light carrying exactly the energy difference between the levels.
Step 3
The electron falls back down, and the atom gives off light carrying exactly the energy difference between the two levels.
Worked example 2. In one atom an electron falls from level 4 to level 1; in another, from level 2 to level 1. Which fall gives off light carrying more energy?
Step 1
The light carries exactly the energy difference between the levels.
Step 2
The fall from level 4 to level 1 crosses the bigger energy difference.
Step 3
The fall from level 4 to level 1 gives off the higher-energy light.
You can now explain how an atom gives off light: an electron first absorbs energy and jumps to a higher energy level, and when it falls back to a lower level the atom releases light carrying exactly the energy difference.
Check your understanding
An energized neon atom gives off light. Which sequence of events produces that light?
AThe electron jumps to a higher level, then falls back down — the light comes out during the fallcorrect
BAn electron absorbs energy and gives off the light during its upward jump
This option is wrong — you put the light on the way up — the jump ABSORBS energy; light is given off only as the electron falls back down.
CAn electron leaves the atom entirely, and the escaping electron is the light
This option is wrong — you turned the electron into the light — the electron stays in the atom; the light is energy given off as it falls.
DThe nucleus splits apart, and the fragments shine
This option is wrong — you reached into the nucleus — the nucleus is untouched; the light comes from an electron falling between energy levels.
Give the atom energy and an electron absorbs it, jumping up to a higher energy level. The electron soon falls back down to a lower level. As it falls, the atom gives off light carrying exactly the energy difference between the levels.
Check your understanding
An electron falls from energy level 5 to energy level 2. How much energy does the light given off carry?
AExactly the energy difference between level 5 and level 2correct
BAll of the electron's energy
This option is wrong — you emptied the electron — it keeps level 2's energy; the light carries only the difference between the two levels.
CThe full energy of level 5
This option is wrong — you gave the light the starting level's whole energy — the light carries the difference between the levels, not one level's value.
DAn amount that varies randomly from fall to fall
This option is wrong — you made the energy random — the same drop always gives exactly the same energy difference.
The light carries exactly the energy difference between the two levels — no more, no less. For a fall from level 5 to level 2, that is the difference between those two levels' energies.
Check your understanding
When does an atom give off light?
AWhen an electron falls from a higher energy level to a lower onecorrect
BWhen an electron jumps up to a higher energy level
This option is wrong — you reversed the direction — jumping up ABSORBS energy; light is given off on the way down.
CWhenever its electrons circle the nucleus
This option is wrong — you made ordinary orbiting glow — an electron staying on its level gives off nothing; the fall between levels makes the light.
DWhen it absorbs energy and holds it
This option is wrong — you stopped at the absorbing step — absorbed energy lifts the electron; the light appears only when the electron falls back.
An electron first absorbs energy and jumps to a higher energy level. When it falls back to a lower level, the atom gives off light carrying exactly the energy difference.
Lesson 39 of 65 · ATM-039
Why the lines are separate
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Did You Know?
You've already seen the two halves of the neon-sign puzzle: an energized gas shows separate bright lines, and an atom gives off light when an electron falls between energy levels. The figure puts the halves together — each of hydrogen's visible lines matches one particular drop between its levels.
The idea
Only specific energy levels are allowed in an atom.
So only specific drops can occur — level 3 to level 2, level 4 to level 2, and so on.
Each specific drop gives off light of one specific color.
Because only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appear.
A full rainbow would need every in-between color, and every in-between color would need an in-between drop — but the in-between levels simply do not exist.
An atom's energy is therefore **'quantized'** — restricted to specific amounts.
Worked examples
Worked example 1. Why does an energized neon sign glow only its exact red-orange colors, never white?
Step 1
Because only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appear.
Step 2
Neon's allowed drops give off mostly reds and oranges — white would need every color at once.
Step 3
The sign glows only the exact colors neon's drops can make, so it can never glow white.
Worked example 2. Suppose an atom's electrons could have any energy at all. What would its spectrum look like?
Step 1
Every size of energy drop would then be possible.
Step 2
Every different drop gives light of a different color, so every color would appear.
Step 3
A full, unbroken rainbow — the separate lines exist only because the levels are restricted.
You can now explain why an emission spectrum shows separate lines instead of a full rainbow: because only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appear, showing that the atom's energy is quantized, meaning restricted to specific amounts.
Check your understanding
Why does an energized gas of one element show separate bright lines instead of a full rainbow?
ABecause only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appearcorrect
BBecause the gas contains only a few glowing atoms, and each atom contributes one bright line of its own
This option is wrong — you shared the lines out among atoms — every atom of the element has the same allowed levels and makes the same lines.
CBecause the spreading splits the light unevenly, bunching what would be a rainbow into a few narrow lines
This option is wrong — you blamed the spreading — spreading only sorts colors by position; the gaps exist because those colors are never given off.
DBecause the gas gives off every color, but most of the colors are far too dim for the eye to pick out
This option is wrong — you turned the gaps into dim light — the in-between colors are not dim, they are absent: no drop exists to make them.
Because only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appear. Each allowed drop makes one exact color — one line. The colors between the lines would need drops that no allowed levels can make.
Check your understanding
An atom's energy is quantized. What does that mean?
AThe atom's energy is restricted to specific amountscorrect
BThe atom's energy is extremely small
This option is wrong — you read 'quantized' as tiny — quantized says nothing about size; it says only specific amounts are allowed.
CThe atom's energy runs out after each use
This option is wrong — you made the energy deplete — an atom can absorb energy again and again; quantized means the allowed amounts are restricted.
DThe atom's energy can take any value between two limits
This option is wrong — you kept the in-between values — quantized means exactly the opposite: the values between the allowed amounts do not occur.
Quantized means restricted to specific amounts. An atom's energy can sit at its allowed levels' values and nowhere in between.
Check your understanding
Energized mercury vapor in a streetlamp glows with a few exact colors. Why only those colors?
AOnly specific energy levels are allowed in mercury's atoms, so only specific drops — and only their colors — can occurcorrect
BThe lamp runs too cool to make the other colors, so only the easiest few colors appear in its glow
This option is wrong — you blamed the temperature — more heat energizes more atoms, but the allowed drops, and so the colors, stay the same.
CThe glass tube filters most of the colors out, letting only mercury's few exact colors escape
This option is wrong — you blamed the glass — the missing colors are never given off in the first place; no drop exists to make them.
DOnly some of the atoms in the vapor are energized, and each energized atom makes one of the colors
This option is wrong — you shared the colors out among atoms — every mercury atom has the same allowed levels and can make every mercury line.
Because only specific energy levels are allowed, only specific energy drops can occur, so only specific colors of light appear. Mercury's allowed drops fix its exact colors — no filter, temperature, or atom count changes them.
Lesson 40 of 65 · ATM-040
Bigger drops, higher-energy light
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Did You Know?
You have already seen how an atom gives off light: an electron falls from a higher energy level to a lower one, and the atom releases light carrying exactly the energy difference. Different drops release different amounts of energy — so which drop makes the higher-energy light?
The idea
The energy-level ladder shows two drops that both start at level 3: one lands on level 1, and one lands on level 2.
The drop from level 3 to level 1 spans the larger energy difference.
The drop from level 3 to level 1 spans a larger energy difference than the drop from level 3 to level 2.
So the drop from level 3 to level 1 releases higher-energy light.
Now keep the ending level fixed instead: a drop from level 3 to level 1 spans a larger energy difference than a drop from level 2 to level 1.
Again the drop from level 3 to level 1 releases the higher-energy light.
The rule: the larger the energy difference between the starting and ending levels, the higher the energy of the light released.
To compare two drops, compare their energy differences — nothing else about the drop matters.
Worked examples
Worked example 1. In a hydrogen atom, one electron drops from level 4 to level 2, and another drops from level 4 to level 3. Which drop releases higher-energy light?
Step 1
Both drops start at level 4, so compare where they end.
Step 2
The drop to level 2 spans a larger energy difference than the drop to level 3.
Step 3
The drop from level 4 to level 2 releases the higher-energy light.
Worked example 2. In a hydrogen atom, one electron drops from level 6 to level 2, and another drops from level 4 to level 2. Which drop releases higher-energy light?
Step 1
Both drops end at level 2, so compare where they start.
Step 2
The drop from level 6 starts higher, so it spans the larger energy difference.
Step 3
The drop from level 6 to level 2 releases the higher-energy light.
You can now predict which electron drop releases higher-energy light: the larger the energy difference between the starting and ending levels, the higher the energy of the light.
Check your understanding
In a hydrogen atom, one electron drops from level 4 to level 1, and another drops from level 4 to level 3. Which drop releases higher-energy light?
AThe drop from level 4 to level 1, because it spans the larger energy difference.correct
BThe drop from level 4 to level 3, because it lands on a higher level.
This option is wrong — you flipped the rule — a larger energy difference releases higher-energy light, and landing on level 1 makes the difference larger.
CBoth drops release the same energy, because both start at level 4.
This option is wrong — you compared only the starting levels — the ending levels differ, so the energy differences differ.
DIt cannot be decided without the exact energy of each level.
This option is wrong — you looked for exact numbers — with the same starting level, the drop that ends lower spans the larger difference.
Both drops start at level 4, so compare where they end. The drop to level 1 ends lower, so it spans the larger energy difference. The larger the energy difference, the higher the energy of the light.
Check your understanding
In a hydrogen atom, one electron drops from level 5 to level 2, and another drops from level 5 to level 4. Which drop releases higher-energy light?
AThe drop from level 5 to level 2, because it spans the larger energy difference.correct
BThe drop from level 5 to level 4, because a shorter drop packs its energy into brighter light.
This option is wrong — you flipped the rule — the light's energy comes from the energy difference, and the shorter drop spans the smaller difference.
CBoth drops release the same energy, because both electrons leave level 5.
This option is wrong — you compared only the starting levels — the ending levels differ, so the energy differences differ.
DThe drop from level 5 to level 4, because level 4 holds more energy than level 2.
This option is wrong — you ranked the ending levels by their own energy — the light's energy is set by the difference between the two levels, and ending higher leaves a smaller difference.
Both drops start at level 5, so compare where they end. The drop to level 2 ends lower, so it spans the larger energy difference. The larger the energy difference, the higher the energy of the light.
Check your understanding
In a hydrogen atom, one electron drops from level 6 to level 3, and another drops from level 5 to level 3. Which drop releases higher-energy light?
AThe drop from level 6 to level 3, because it spans the larger energy difference.correct
BThe drop from level 5 to level 3, because level 5 sits closer to level 3.
This option is wrong — you flipped the rule — sitting closer means a smaller energy difference, and a smaller difference means lower-energy light.
CBoth drops release the same energy, because both land on level 3.
This option is wrong — you compared only the ending levels — the starting levels differ, so the energy differences differ.
DIt cannot be decided, because the two drops start from different levels.
This option is wrong — you treated different starting levels as incomparable — with the same ending level, the drop that starts higher spans the larger difference.
Both drops end at level 3, so compare where they start. The drop from level 6 starts higher, so it spans the larger energy difference. The larger the energy difference, the higher the energy of the light.
Lesson 41 of 65 · ATM-041
Reading an emission spectrum
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Did You Know?
You have already seen that an energized element gives off light at only a few exact colors — separate bright lines — and that each bigger drop between energy levels makes higher-energy light. Put those together and an emission spectrum stops being a pretty pattern: it becomes a readable record of the drops happening inside the atom.
The idea
Each bright line in an emission spectrum is the light released by one specific electron drop.
Bigger drops make higher-energy lines — the shortest-wavelength line comes from the biggest drop.
Across visible light, energy rises from the red end to the violet end.
Wavelengths tell the same story with numbers: because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency.
As the frequency of light increases, the energy each tiny burst of the light delivers also increases.
So the line with the shortest wavelength carries the most energy.
Hydrogen's visible spectrum shows lines at 656 nm (red), 486 nm (blue-green), 434 nm (blue-violet), and 410 nm (violet).
The violet 410 nm line carries more energy than the red 656 nm line, so the violet line comes from a larger drop.
To read any emission spectrum: rank the lines by wavelength, shortest first — that is their energy order, and it is also their drop-size order.
Worked examples
Worked example 1. Energized helium shows spectrum lines at 447 nm (blue), 588 nm (yellow), and 668 nm (red). Rank the three lines from highest energy to lowest.
Step 1
Shorter wavelength means higher frequency, and higher frequency means higher energy.
Step 2
Order the wavelengths from shortest to longest: 447 nm, 588 nm, 668 nm.
Step 3
The 447 nm blue line carries the most energy, then the 588 nm yellow line, then the 668 nm red line.
Worked example 2. Energized cadmium shows spectrum lines at 480 nm (blue) and 644 nm (red). Which line comes from the larger electron drop?
Step 1
The 480 nm line has the shorter wavelength, so it carries the higher energy.
Step 2
Higher-energy light comes from a larger energy difference between levels.
Step 3
The 480 nm blue line comes from the larger drop.
You can now interpret an element's emission spectrum by matching lines to electron drops and ranking the lines by energy from their colors or wavelengths.
Check your understanding
The figure shows the emission spectrum of energized neon, with lines at 585 nm (yellow) and 640 nm (red). Which line carries more energy?
BThe 640 nm red line, because a longer wavelength carries more energy.
This option is wrong — you tied energy to wavelength directly — longer wavelength means lower frequency, and lower frequency means lower energy.
CBoth lines carry the same energy, because both come from neon.
This option is wrong — you ranked lines by their element — within one element's spectrum, each line comes from a different drop and carries a different energy.
DThe 640 nm red line, because red light looks brighter to the eye.
This option is wrong — you judged energy by brightness — brightness reflects how much light arrives, not the energy each bit of light carries.
Compare the wavelengths: 585 nm is shorter than 640 nm. Because all light travels at the same speed in empty space, light with a longer wavelength has a lower frequency. As the frequency of light increases, the energy each tiny burst of the light delivers also increases. So the 585 nm yellow line carries more energy.
Check your understanding
The figure shows the emission spectrum of energized mercury, with lines at 436 nm (blue-violet), 546 nm (green), and 578 nm (yellow). Which ranking lists the lines from highest energy to lowest?
A436 nm, then 546 nm, then 578 nm.correct
B578 nm, then 546 nm, then 436 nm.
This option is wrong — you ranked by wavelength from longest to shortest — energy runs the other way, rising as wavelength shortens.
C546 nm, then 436 nm, then 578 nm.
This option is wrong — you put the middle wavelength first — rank strictly by wavelength, shortest first, to get the energy order.
D436 nm, then 578 nm, then 546 nm.
This option is wrong — you started correctly but then ranked the last two by color name instead of wavelength — 546 nm is shorter than 578 nm, so it carries more energy.
Rank the wavelengths, shortest first: 436 nm, 546 nm, 578 nm. Shorter wavelength means higher frequency, and higher frequency means higher energy. So the energy order is 436 nm highest, then 546 nm, then 578 nm.
Check your understanding
Energized barium shows a green spectrum line at 554 nm and an orange line at 614 nm. Which line comes from the larger electron drop?
AThe 554 nm green line, because its higher-energy light comes from a larger energy difference.correct
BThe 614 nm orange line, because a longer wavelength records a longer fall.
This option is wrong — you matched long wavelength to a long fall — a longer wavelength means lower-energy light, which comes from a smaller drop.
CBoth lines come from the same drop, because both belong to barium.
This option is wrong — you gave one drop two colors — each line is the light of one specific drop, so two lines mean two different drops.
DThe 614 nm orange line, because orange sits closer to the middle of the rainbow.
This option is wrong — you ranked by position in the rainbow's middle — energy rises from the red end to the violet end, so the greener line carries more energy.
The 554 nm line has the shorter wavelength, so it carries the higher energy. Higher-energy light comes from a larger energy difference between levels. So the 554 nm green line comes from the larger drop.
Lesson 42 of 65 · ATM-042
Bohr's model reaches its limit
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Wonder this:
Bohr's model earned its place by predicting hydrogen's line spectrum almost perfectly. Then scientists pointed it at the next element on the table — and the model that had just explained hydrogen could not explain helium.
Every model keeps its job only while it matches the evidence.
The idea
Bohr's model correctly predicts the line spectrum of hydrogen.
For any atom with more than one electron, the model's predicted lines do not match the measured spectrum.
Helium, with just two electrons, is already enough to break it — Bohr's model cannot reproduce helium's line spectrum.
That is the limitation: Bohr's model works for hydrogen but fails for atoms with more than one electron.
A model that fails for every element but one had to be replaced.
Worked examples
Worked example 1. Lithium atoms have three electrons. Can Bohr's model predict lithium's line spectrum?
Step 1
No — Bohr's model fails for any atom with more than one electron.
Worked example 2. For which element does Bohr's model predict the line spectrum correctly?
Step 1
Hydrogen — the one element whose atoms have a single electron.
You can now identify the limitation of Bohr's model: it predicts the line spectrum of hydrogen but fails for atoms with more than one electron.
Check your understanding
For which atom does Bohr's model correctly predict the line spectrum?
AHydrogen.correct
BHelium.
This option is wrong — you gave the model helium — helium's two electrons are exactly where the model starts to fail.
CEvery atom.
This option is wrong — you gave the model full credit — its predictions match only hydrogen, the one-electron atom.
DNo atom at all.
This option is wrong — you threw out the model's one success — it predicts hydrogen's line spectrum correctly.
Bohr's model correctly predicts the line spectrum of hydrogen. For any atom with more than one electron, its predicted lines do not match. Hydrogen is the one atom with a single electron.
Check your understanding
Which atoms make Bohr's model fail?
AAny atom with more than one electron.correct
BOnly very large atoms with many electrons.
This option is wrong — you let the model keep the small atoms — helium's two electrons already break it.
CHydrogen atoms.
This option is wrong — you flipped the model's one success and its failures — hydrogen is exactly where it works.
DAtoms with more than one energy level.
This option is wrong — you tied the failure to level count — every atom has many energy levels, including hydrogen, where the model works.
Bohr's model works for hydrogen, the one-electron atom. It fails for any atom with more than one electron. Helium's two electrons are already enough to break it.
Check your understanding
Bohr's model is used to predict a line spectrum for helium, and the prediction is checked against helium's measured spectrum. What is found?
AThe predicted lines do not match the measured lines.correct
BThe predicted lines match the measured lines exactly.
This option is wrong — you extended the hydrogen success to helium — the model fails for any atom with more than one electron.
CHelium turns out to have no line spectrum to compare against.
This option is wrong — you took the spectrum away from helium — every element has its own emission-line pattern.
DHelium's measured spectrum turns out to be a full rainbow with no separate lines.
This option is wrong — you un-quantized helium — its spectrum shows separate lines, just not the lines Bohr's model predicts.
Helium has two electrons. Bohr's model fails for any atom with more than one electron. So its predicted lines do not match helium's measured lines.
Lesson 43 of 65 · ATM-043
Heisenberg's uncertainty principle
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Wonder this:
Bohr drew electrons on exact circular paths, like planets around a sun. To fix his model, scientists first had to face an uncomfortable discovery: for an electron, an exact path is not just hard to measure — it is impossible to have.
The discovery is a principle about what can be known at all.
The idea
Werner Heisenberg showed that an electron's exact position and its exact motion (its 'momentum') cannot both be known at the same time.
This is called 'Heisenberg's uncertainty principle'.
Pinning down exactly where an electron is means losing track of exactly how it is moving.
The limit is a rule of nature, not a weakness of our instruments — no better microscope can beat it.
A mapped path would require knowing position and motion together at every moment, so exact electron paths cannot be mapped.
Bohr's exact orbits are therefore something no atom can actually have.
Worked examples
Worked example 1. A physicist measures an electron's position very precisely. What happens to what can be known about its motion?
Step 1
The electron's exact motion becomes unknowable at that moment — position and motion cannot both be known exactly at the same time.
Worked example 2. Why can no experiment ever map an electron's exact path around the nucleus?
Step 1
A path requires exact position and exact motion together at every moment, and the uncertainty principle forbids knowing both at once.
You can now state Heisenberg's uncertainty principle as it applies to atomic models: an electron's exact position and exact motion cannot both be pinned down at the same time, so exact electron paths cannot be mapped.
Check your understanding
According to Heisenberg's uncertainty principle, which two things can never both be known exactly at the same time for an electron?
AIts position and its motion.correct
BIts charge and its mass.
This option is wrong — you picked the electron's fixed properties — charge and mass are constants and are both known precisely.
CIts energy level and its charge.
This option is wrong — you swapped motion for charge — the principle pairs position with motion, and charge is a known constant.
DIts position and the position of the nucleus.
This option is wrong — you paired the electron with the nucleus — the principle is about one electron's own position and motion.
Heisenberg's uncertainty principle pairs exact position with exact motion. The two cannot both be known at the same time. Pinning down where the electron is means losing track of how it is moving.
Check your understanding
What does Heisenberg's uncertainty principle say about mapping an electron's exact path?
AAn exact path can never be mapped, because a path requires exact position and exact motion together.correct
BAn exact path can be mapped once instruments become precise enough.
This option is wrong — you treated the limit as an equipment problem — it is a rule of nature that no instrument can beat.
CAn exact path can be mapped, but only for the single electron in hydrogen.
This option is wrong — you carried over Bohr's hydrogen success — the principle applies to every electron, including hydrogen's.
DExact paths exist, but electrons move too fast for the paths to be recorded.
This option is wrong — you kept the exact path and blamed speed — the principle says the exact path is not there to record.
A mapped path needs exact position and exact motion at every moment. The uncertainty principle forbids knowing both at once. So exact electron paths cannot be mapped — by anyone, with any instrument.
Check your understanding
A measurement pins down exactly where an electron is at one instant. What is the cost?
AExactly how the electron is moving can no longer be known at that instant.correct
BThe electron drops to a lower energy level and releases light.
This option is wrong — you mixed in the light-emission story — drops release light, but the principle trades knowledge of position against knowledge of motion.
CThe electron's charge can no longer be measured.
This option is wrong — you traded position against charge — charge is a fixed, known property; the trade is against motion.
DThe electron is knocked out of the atom.
This option is wrong — you turned a limit on knowledge into a physical ejection — the principle says what can be known, not that the electron leaves.
The principle pairs exact position with exact motion. Pinning down where the electron is means losing track of how it is moving. Nothing is ejected and nothing glows — the cost is paid in knowledge.
Lesson 44 of 65 · ATM-044
The electron-cloud model
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Bohr's model fails for atoms with more than one electron, and the uncertainty principle rules out exact electron paths altogether. The modern model of the atom is built to respect both findings.
The idea
In the modern model, electrons do not follow fixed orbits.
The modern model replaces exact orbits with the electron cloud — the region where electrons are likely to be found.
Instead, each electron occupies a region around the nucleus where it is likely to be found.
That region is called the 'electron cloud'.
The cloud is not a substance — it is a map of likely places, denser where the electron is more likely to be.
In this model, hydrogen's one electron is somewhere within a fuzzy sphere around the nucleus.
The model gives up exact paths, which is exactly what the uncertainty principle demands.
Worked examples
Worked example 1. In the modern model, where is helium's pair of electrons?
Step 1
Within the electron cloud — the region around the nucleus where they are likely to be found — not on any fixed orbit.
Worked example 2. What does the electron-cloud model show in place of Bohr's orbit circles?
Step 1
A fuzzy region of likely electron locations around the nucleus — the electron cloud.
You can now describe the modern electron-cloud model of the atom: instead of following fixed orbits, electrons occupy the electron cloud, the region around the nucleus where they are likely to be found.
Check your understanding
In the modern model of the atom, what is the electron cloud?
AThe region around the nucleus where the atom's electrons are likely to be found.correct
BThe exact path each electron follows around the nucleus.
This option is wrong — you kept Bohr's fixed paths — the uncertainty principle rules out exact paths, and the cloud is a region of likely places instead.
CA mist of positive charge spread through the atom.
This option is wrong — you rebuilt the plum-pudding picture — the cloud is not a substance at all, and the atom's positive charge sits in the nucleus.
DThe region inside the nucleus where electrons rest between drops.
This option is wrong — you moved the electrons into the nucleus — the cloud surrounds the nucleus, and electrons stay outside it.
In the modern model, electrons do not follow fixed orbits. Each electron occupies a region around the nucleus where it is likely to be found. That region is the electron cloud.
Check your understanding
How does the electron-cloud model differ from Bohr's model?
AElectrons occupy a region of likely locations instead of following fixed orbits.correct
BElectrons are replaced by a smooth spread of negative charge with no particles.
This option is wrong — you dissolved the electrons — they are still particles; the cloud maps where each one is likely to be.
CThe nucleus is removed and the atom's charge spreads evenly throughout.
This option is wrong — you undid the gold-foil discovery — the nucleus stays at the center in the modern model.
DElectrons follow the same orbits, but the orbits are drawn as ovals instead of circles.
This option is wrong — you kept exact paths and only reshaped them — the modern model gives up exact paths entirely.
Bohr drew electrons on fixed orbit paths. The uncertainty principle rules exact paths out. The modern model keeps the nucleus and the electrons, and replaces paths with the electron cloud — a region of likely places.
Check your understanding
In the modern model, which statement describes hydrogen's single electron?
AIt is somewhere inside a fuzzy sphere around the nucleus — likely places, no path.correct
BIt travels a fixed circle whose radius is set by its energy level.
This option is wrong — you described Bohr's hydrogen — the modern model replaces the fixed circle with a region of likely places.
CIt sits at one fixed point a set distance from the nucleus.
This option is wrong — you parked the electron — the cloud gives likely locations, not a single resting spot.
DIt spreads out evenly so that every location in the atom is equally likely.
This option is wrong — you flattened the cloud — the cloud is denser where the electron is more likely to be, so locations are not all equally likely.
The modern model gives hydrogen's electron no path and no parking spot. It occupies the electron cloud — for hydrogen, a fuzzy sphere around the nucleus. The cloud is denser where the electron is more likely to be found.
Lesson 45 of 65 · ATM-045
Energy levels survive the new model
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The electron-cloud model threw out Bohr's exact orbit paths. It did not throw out everything.
The idea
In the electron-cloud model, electrons still occupy numbered main energy levels.
Numbered energy levels remain: higher levels mean higher energy and a greater average distance from the nucleus.
Main energy levels are also called 'electron shells' — two names for the same thing.
A higher-numbered level holds electrons of higher energy.
A higher-numbered level also sits farther from the nucleus on average.
The words 'on average' matter: an electron has no exact mapped position, so only its average distance can be given.
For example, a level-2 electron has more energy than a level-1 electron, and spends its time farther from the nucleus on average.
Worked examples
Worked example 1. In one atom, one electron occupies level 3 and another occupies level 1. Which has more energy?
Step 1
The level-3 electron — higher-numbered levels hold electrons of higher energy.
Worked example 2. Which of those two electrons is found farther from the nucleus on average?
Step 1
The level-3 electron — higher-numbered levels sit farther from the nucleus on average.
You can now state that in the electron-cloud model electrons still occupy numbered main energy levels, also called electron shells, and that higher-numbered levels sit farther from the nucleus on average and hold electrons of higher energy.
Check your understanding
What happened to the numbered main energy levels when the electron-cloud model replaced Bohr's model?
AThey remain — electrons still occupy numbered main energy levels.correct
BThey were abandoned along with the fixed orbit paths.
This option is wrong — you threw the levels out with the paths — only the exact orbits went; the numbered levels survived.
CThey apply only to hydrogen, the one atom Bohr's model handled.
This option is wrong — you shrank the levels to Bohr's one success — every atom's electrons occupy numbered energy levels in the modern model.
DThey became exact circular paths at fixed distances again.
This option is wrong — you turned levels back into orbits — a level fixes an electron's energy, not an exact path or exact distance.
The electron-cloud model dropped the exact orbit paths. It kept the numbered main energy levels. A level fixes an electron's energy and its average distance — not a path.
Check your understanding
Which name means the same thing as 'main energy level'?
AElectron shell.correct
BElectron cloud.
This option is wrong — you named the whole region — the cloud is everywhere the electrons are likely to be, while a shell is one numbered level within it.
CFixed orbit.
This option is wrong — you reached back to Bohr's paths — the modern model has levels but no fixed orbits.
DNucleus.
This option is wrong — you named the atom's center — the nucleus holds protons and neutrons, while shells describe where the electrons' energies sit.
Main energy levels are also called electron shells. The two names point at the same numbered levels. The electron cloud is the whole region of likely places, not one level.
Check your understanding
In the same atom, compare an electron in level 3 with an electron in level 1.
AThe level-3 electron has more energy and is farther from the nucleus on average.correct
BThe level-3 electron has more energy but sits closer to the nucleus on average.
This option is wrong — you flipped the distance half — higher-numbered levels sit farther from the nucleus on average.
CThe level-3 electron has less energy and is farther from the nucleus on average.
This option is wrong — you flipped the energy half — higher-numbered levels hold electrons of higher energy.
DThe two electrons have the same energy, because both belong to the same atom.
This option is wrong — you leveled the levels — within one atom, different numbered levels hold different energies.
Higher-numbered levels hold electrons of higher energy. Higher-numbered levels also sit farther from the nucleus on average. So the level-3 electron wins on both counts over the level-1 electron.
Lesson 46 of 65 · ATM-046
How the atomic model developed
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You have now seen five models of the atom, and every replacement happened for the same kind of reason: a result appeared that the ruling model could not explain. Here is the whole chain in one view.
The idea
Dalton's model: the atom is a solid, indivisible ball.
Each arrow is a piece of evidence the older model could not explain.
Atoms turned out to release electrons — a ball with no parts cannot release a part — so the model changed.
Thomson's plum-pudding model: electrons dotted through a spread-out ball of positive charge.
In the gold-foil experiment, a few fast positive particles bounced nearly straight back — thinly spread positive charge cannot do that — so the model changed.
Rutherford's nuclear model: a tiny, dense, positive nucleus with electrons in the space around it.
Elements' emission spectra showed separate lines, and the nuclear model gave no reason for exact colors — so the model changed.
Bohr's model: electrons on fixed orbits with set energies, which predicted hydrogen's lines.
Bohr's model failed for atoms with more than one electron, and the uncertainty principle ruled out exact paths — so the model changed.
The electron-cloud model: electrons occupy regions of likely locations around the nucleus.
The pattern to keep: a model is replaced when evidence appears that it cannot explain.
Worked examples
Worked example 1. The gold-foil experiment produced rare, nearly straight-back bounces. Which change in the atomic model did this evidence force?
Step 1
Ask which ruling model the evidence contradicts: thinly spread positive charge could not turn a fast positive particle around.
Step 2
The contradicted model is Thomson's plum pudding, so the bounces forced its replacement.
Step 3
The change from the plum-pudding model to Rutherford's nuclear model.
Worked example 2. Which evidence forced the change from Dalton's solid-ball model to Thomson's plum-pudding model?
Step 1
Ask what Dalton's model could not explain: an indivisible ball has no parts to give off.
Step 2
The discovery that atoms release electrons contradicted exactly that.
Step 3
The discovery of the electron — atoms that release smaller charged particles must be built from smaller parts.
You can now match each change in the atomic model, from Dalton to Thomson to Rutherford to Bohr to the electron cloud, to the experimental evidence or principle that forced it.
Check your understanding
Elements' emission spectra show separate lines at exact colors. Which change in the atomic model did this evidence force?
AThe change from Rutherford's nuclear model to Bohr's model.correct
BThe change from Dalton's solid ball to the plum-pudding model.
This option is wrong — you matched the lines to the electron's discovery — the solid ball fell because atoms release electrons, before spectra entered the story.
CThe change from the plum-pudding model to the nuclear model.
This option is wrong — you matched the lines to the gold-foil result — the bounces forced the nuclear model; the lines came for the nuclear model afterward.
DThe change from Bohr's model to the electron-cloud model.
This option is wrong — you moved one step too far — separate lines are what Bohr's model explains; its own failure came from multi-electron atoms and the uncertainty principle.
Ask which ruling model the evidence contradicts. Rutherford's nuclear model gave no reason for light at exact colors only. Bohr's fixed orbits with set energies supplied the reason, so the lines forced the nuclear-to-Bohr change.
Check your understanding
Which evidence or principle forced the change from Bohr's model to the electron-cloud model?
ABohr's model fails past one electron, and the uncertainty principle bans exact paths.correct
BThe rare hard bounces of positive particles fired at gold foil.
This option is wrong — you reached back two changes — the bounces replaced plum pudding with the nuclear model.
CThe discovery that atoms of one element can differ in mass.
This option is wrong — you brought in the isotope discovery — that corrected Dalton's identical-atoms claim without replacing the ruling model of atomic structure.
DThe discovery that hydrogen's spectrum shows separate lines.
This option is wrong — you picked Bohr's founding success — the separate lines built his model rather than breaking it.
Ask what Bohr's model could not explain. It failed for every atom with more than one electron, and its exact orbits clash with the uncertainty principle. Those two findings together forced the move to the electron-cloud model.
Check your understanding
The discovery that atoms can release electrons forced a model change. Which model did the change produce?
AThomson's plum-pudding model.correct
BDalton's solid-ball model.
This option is wrong — you named the model the evidence broke — the released electrons ended the solid ball and produced its replacement.
CRutherford's nuclear model.
This option is wrong — you jumped one change ahead — the nuclear model came later, from the gold-foil bounces.
DThe electron-cloud model.
This option is wrong — you jumped to the end of the chain — the cloud model came from Bohr's failures, long after the electron's discovery.
An atom that releases electrons must be built from smaller parts. Dalton's indivisible ball could not survive that finding. Its replacement was Thomson's plum-pudding model — electrons dotted through a positive ball.
Summary video — Light, emission spectra, and energy levels
Point a better instrument at an element's emission spectrum and some single bright lines split into small groups of lines sitting close together. Drops between whole energy levels cannot make those extra lines — the levels themselves must have smaller steps inside them.
Those smaller steps are the next piece of the modern model.
The idea
Each main energy level is made of one or more smaller levels, called 'sublevels'.
Sublevel capacities
Sublevel
Holds at most
s
2 electrons
p
6 electrons
d
10 electrons
Three letters, three capacities — the same in every main energy level.
Sublevels are named with letters: s, p, and d.
An s sublevel holds at most 2 electrons.
A p sublevel holds at most 6 electrons.
A d sublevel holds at most 10 electrons.
Level 1 contains only an s sublevel.
Level 2 contains an s and a p sublevel, so it holds at most 2 + 6 = 8 electrons.
Level 3 contains an s, a p, and a d sublevel.
Level 4 also contains an s, a p, and a d sublevel — those are all the sublevels this course uses.
Worked examples
Worked example 1. How many electrons can the p sublevel of level 3 hold at most?
Step 1
6 — a p sublevel holds at most 6 electrons in any level.
Worked example 2. Which sublevels make up main energy level 3?
Step 1
An s, a p, and a d sublevel.
You can now state that each main energy level splits into sublevels named s, p, and d, which hold at most 2, 6, and 10 electrons.
Check your understanding
How many electrons can a d sublevel hold at most?
Answer: 10electrons
The capacities are fixed by letter: s holds 2, p holds 6, d holds 10. A d sublevel holds at most 10 electrons.
Check your understanding
Which sublevels does main energy level 3 contain?
AAn s, a p, and a d sublevel.correct
BAn s and a p sublevel only.
This option is wrong — you carried level 2's makeup up a level — level 3 adds a d sublevel.
CAn s sublevel only.
This option is wrong — you carried level 1's makeup up — only level 1 stops at a single s sublevel.
DA p and a d sublevel only.
This option is wrong — you dropped the s sublevel — every main energy level contains an s sublevel.
Level 1 has only s; level 2 has s and p. Level 3 contains an s, a p, and a d sublevel.
Check your understanding
What is the largest number of electrons that can fit in main energy level 2?
Answer: 8electrons
Level 2 contains an s and a p sublevel. The s holds at most 2 and the p holds at most 6. 2 + 6 = 8 electrons at most.
Lesson 48 of 65 · ATM-048
The filling order
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An atom's electrons settle into the sublevels starting from the lowest energy available. To place them correctly, there is exactly one thing to memorize: the order in which the sublevels fill.
The idea
Across the periodic table's first four rows — rows are called 'periods' — electrons fill the sublevels in a fixed order.
Electrons fill left to right: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.
The order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.
Read the surprise in the middle: after 3p is full, the next electron enters 4s, not 3d.
Only after 4s is full does 3d fill, and after 3d comes 4p.
Everything else in the order runs exactly as the level numbers suggest.
Worked examples
Worked example 1. An atom's electrons have filled 3p completely. Which sublevel does the next electron enter?
Step 1
4s — in the filling order, 4s comes before 3d.
Worked example 2. Which sublevel fills immediately after 4s?
Step 1
3d — and after 3d comes 4p.
You can now state the order in which electrons fill the sublevels across the periodic table's first four rows, called periods: 1s, 2s, 2p, 3s, 3p, 4s, 3d, then 4p, noting that 4s fills before 3d.
Check your understanding
Which sublevel fills immediately after 3p?
A4s.correct
B3d.
This option is wrong — you followed the level numbers — the order's one surprise is here: 4s fills before 3d.
C4p.
This option is wrong — you skipped two entries — 4s and then 3d both fill before 4p.
D3s.
This option is wrong — you moved backward — 3s filled before 3p; the order only moves forward.
The order runs 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. After 3p comes the surprise: 4s, not 3d.
Check your understanding
Which sublevel fills immediately after 2p?
A3s.correct
B2d.
This option is wrong — you gave level 2 a d sublevel — level 2 contains only s and p, so the order moves on to 3s.
C3p.
This option is wrong — you jumped straight to the p — each level's s sublevel fills before its p.
D1s.
This option is wrong — you moved backward — 1s filled first of all; the order only moves forward.
The order runs 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. After 2p comes 3s.
Check your understanding
Which sublevel fills immediately after 4s?
A3d.correct
B4p.
This option is wrong — you skipped 3d — after 4s, the order steps back down to fill 3d before 4p.
C4d.
This option is wrong — you stayed in level 4 — the d sublevel that fills here is level 3's, and 4d is beyond this course's order.
D5s.
This option is wrong — you started the next period — the order through period 4 ends 4s, 3d, 4p.
The order runs 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. After 4s the order returns to level 3: 3d fills next, then 4p.
Lesson 49 of 65 · ATM-049
Reading configuration code
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Did You Know?
Wonder this:
Try writing out where argon's 18 electrons sit, in words: two electrons in the s sublevel of level 1, two in the s sublevel of level 2, six in the p sublevel of level 2… It works, but it is slow, and chemists place electrons all day.
Chemists compress all of it into a short code.
The idea
The code that records where an atom's electrons sit is called an 'electron configuration'.
2p⁴ — 4 electrons occupy the p sublevel of energy level 2.
A configuration is built from blocks, and every block has three parts.
The number names the main energy level.
The letter names the sublevel.
The raised number — the superscript — counts the electrons in that sublevel.
So 2p⁴ means 4 electrons occupy the p sublevel of energy level 2.
A full configuration strings blocks together: 1s²2s²2p⁴ places 2 electrons in 1s, 2 in 2s, and 4 in 2p.
Read any configuration block by block — level, sublevel, count.
Worked examples
Worked example 1. What does the block 3s¹ say?
Step 1
The number 3 names main energy level 3.
Step 2
The letter s names the s sublevel.
Step 3
The superscript ¹ counts one electron.
Step 4
One electron occupies the s sublevel of energy level 3.
Worked example 2. What does the block 4p³ say?
Step 1
The number 4 names main energy level 4.
Step 2
The letter p names the p sublevel.
Step 3
The superscript ³ counts three electrons.
Step 4
Three electrons occupy the p sublevel of energy level 4.
Worked example 3. In the configuration 1s²2s²2p⁶3s², how many electrons sit in main energy level 2?
Step 1
Find every block whose number is 2: the blocks 2s² and 2p⁶.
Step 2
Add their superscripts: 2 + 6 = 8.
Step 3
8 electrons sit in main energy level 2.
You can now interpret each part of electron-configuration notation, in which the number names the main energy level, the letter the sublevel, and the superscript the electron count.
Check your understanding
One block of an atom's configuration reads 3d⁷. How many electrons sit in that sublevel?
Answer: 7electrons
Read the block part by part: level, sublevel, count. The superscript is the count, and 3d⁷ carries the superscript 7. 7 electrons sit in that d sublevel.
Check your understanding
In the block 4p³, what does the letter p tell you?
AWhich sublevel the electrons occupy.correct
BWhich main energy level the electrons occupy.
This option is wrong — you swapped the letter's job with the number's — the 4 names the level, the letter names the sublevel.
CHow many electrons the block contains.
This option is wrong — you swapped the letter's job with the superscript's — the ³ counts the electrons, the letter names the sublevel.
DHow many electrons the sublevel could hold when full.
This option is wrong — you read the letter as a capacity statement — the letter only names the sublevel; capacity is a fact about that sublevel, not part of the code.
Every block reads: level, sublevel, count. In 4p³ the number 4 is the level, the letter p is the sublevel, and the superscript ³ is the count.
Check your understanding
Fluorine's configuration is 1s²2s²2p⁵. How many electrons sit in main energy level 2?
Answer: 7electrons
Find every block whose number is 2: 2s² and 2p⁵. Add their superscripts: 2 + 5 = 7. 7 electrons sit in main energy level 2.
Lesson 50 of 65 · ATM-050
Writing configurations, hydrogen to argon
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You can read configuration code block by block, and you have the filling order. Now run the two in the other direction: start from an element and write its configuration yourself. A neutral atom has as many electrons as protons, and the atomic number gives the proton count.
The idea
To write an element's electron configuration, run four steps.
Fill left to right, each sublevel to its capacity, until the electrons run out.
Step 1 — find the electron count: a neutral atom has as many electrons as its atomic number.
Step 2 — write down the filling order: 1s, 2s, 2p, 3s, 3p.
Step 3 — fill each sublevel to its capacity, in order, until the electrons run out.
Step 4 — check that the superscripts total the electron count.
Watch the routine run on sodium, atomic number 11.
A neutral sodium atom has 11 electrons.
1s takes 2 electrons, leaving 9.
2s takes 2, leaving 7.
2p takes 6, leaving 1.
3s takes the last electron.
Write the blocks: 1s²2s²2p⁶3s¹.
Check: 2 + 2 + 6 + 1 = 11 — the count matches, so the configuration is done.
Worked examples
Worked example 1. Write the full electron configuration of nitrogen (atomic number 7).
Step 1
Write down the electron count: a neutral nitrogen atom has 7 electrons.
Step 2
Write the filling order: 1s, 2s, 2p.
Step 3
Fill to capacity until the electrons run out: 1s takes 2 (5 left), 2s takes 2 (3 left), 2p takes the last 3.
Step 4
Check: 2 + 2 + 3 = 7.
Step 5
1s²2s²2p³
Worked example 2. Write the full electron configuration of aluminum (atomic number 13).
Step 1
Write down the electron count: a neutral aluminum atom has 13 electrons.
Step 2
Write the filling order: 1s, 2s, 2p, 3s, 3p.
Step 3
Fill to capacity until the electrons run out: 1s takes 2 (11 left), 2s takes 2 (9 left), 2p takes 6 (3 left), 3s takes 2 (1 left), 3p takes the last 1.
Step 4
Check: 2 + 2 + 6 + 2 + 1 = 13.
Step 5
1s²2s²2p⁶3s²3p¹
Worked example 3. Write the full electron configuration of argon (atomic number 18).
Step 1
Write down the electron count: a neutral argon atom has 18 electrons.
Step 2
Write the filling order: 1s, 2s, 2p, 3s, 3p.
Step 3
Fill to capacity until the electrons run out: 1s takes 2 (16 left), 2s takes 2 (14 left), 2p takes 6 (8 left), 3s takes 2 (6 left), 3p takes the last 6.
Step 4
Check: 2 + 2 + 6 + 2 + 6 = 18.
Step 5
1s²2s²2p⁶3s²3p⁶
You can now write the full electron configuration of any of the first 18 elements by placing its electrons into sublevels in filling order.
Check your understanding
Carbon's atomic number is 6. Write the full electron configuration of a neutral carbon atom.
Accepted answer: 1s²2s²2p²
Write down the electron count: a neutral carbon atom has 6 electrons. Fill in order: 1s takes 2 (4 left), 2s takes 2 (2 left), 2p takes the last 2. Write the blocks: 1s²2s²2p². Check: 2 + 2 + 2 = 6.
Check your understanding
Magnesium's atomic number is 12. Write the full electron configuration of a neutral magnesium atom.
Accepted answer: 1s²2s²2p⁶3s²
Write down the electron count: a neutral magnesium atom has 12 electrons. Fill in order: 1s takes 2 (10 left), 2s takes 2 (8 left), 2p takes 6 (2 left), 3s takes the last 2. Write the blocks: 1s²2s²2p⁶3s². Check: 2 + 2 + 6 + 2 = 12.
Check your understanding
Chlorine's atomic number is 17. Write the full electron configuration of a neutral chlorine atom.
Accepted answer: 1s²2s²2p⁶3s²3p⁵
Write down the electron count: a neutral chlorine atom has 17 electrons. Fill in order: 1s takes 2 (15 left), 2s takes 2 (13 left), 2p takes 6 (7 left), 3s takes 2 (5 left), 3p takes the last 5. Write the blocks: 1s²2s²2p⁶3s²3p⁵. Check: 2 + 2 + 6 + 2 + 5 = 17.
Lesson 51 of 65 · ATM-051
Configurations through period 4
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The same four-step routine writes configurations for the periodic table's fourth row — you only need the longer filling order, with its 4s-before-3d surprise.
The idea
The elements this lesson covers sit in the table's tall left and right columns, and are called 'main-group' or 'representative' elements.
Period-4 configurations use the whole strip — 4s fills before 3d.
For period 4, extend the filling order you use: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.
After 3p is full, the next two electrons enter 4s.
From gallium onward, the 3d sublevel is completely full, so its whole 3d¹⁰ block appears in the configuration.
Write the blocks in filling order — 4s before 3d — and run the same final check.
Watch the routine run on gallium, atomic number 31.
A neutral gallium atom has 31 electrons.
The first 18 fill 1s through 3p exactly as in argon, leaving 13.
4s takes 2, leaving 11.
3d takes 10, leaving 1.
4p takes the last electron.
Write the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p¹.
Check: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 1 = 31.
Worked examples
Worked example 1. Write the full electron configuration of potassium (atomic number 19).
Step 1
Write down the electron count: a neutral potassium atom has 19 electrons.
Fill to capacity until the electrons run out: 1s through 3p take 18 (16 left), 4s takes 2 (14 left), 3d takes 10 (4 left), 4p takes the last 4.
Step 4
Check: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 4 = 34.
Step 5
1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴
You can now write the full electron configuration of a main-group, also called representative, element in period 4, filling 4s before 3d and including the full 3d sublevel from gallium onward.
Check your understanding
Calcium's atomic number is 20. Write the full electron configuration of a neutral calcium atom.
Accepted answer: 1s²2s²2p⁶3s²3p⁶4s²
Write down the electron count: a neutral calcium atom has 20 electrons. Fill in order: 1s through 3p take 18 (2 left), and 4s takes the last 2 — 4s fills before 3d. Write the blocks: 1s²2s²2p⁶3s²3p⁶4s². Check: 2 + 2 + 6 + 2 + 6 + 2 = 20.
Check your understanding
Arsenic's atomic number is 33. Write the full electron configuration of a neutral arsenic atom.
Accepted answer: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³
Write down the electron count: a neutral arsenic atom has 33 electrons. Fill in order: 1s through 3p take 18 (15 left), 4s takes 2 (13 left), 3d takes 10 (3 left), 4p takes the last 3. Write the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³. Check: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 3 = 33.
Check your understanding
Krypton's atomic number is 36. Write the full electron configuration of a neutral krypton atom.
Accepted answer: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶
Write down the electron count: a neutral krypton atom has 36 electrons. Fill in order: 1s through 3p take 18 (18 left), 4s takes 2 (16 left), 3d takes 10 (6 left), 4p takes the last 6. Write the blocks: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶. Check: 2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 = 36 — every sublevel ends exactly full.
Lesson 52 of 65 · ATM-052
Noble-gas shorthand
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Wonder this:
Bromine's full configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵ — and its first six blocks are identical for every element in bromine's row. Chemists write those repeated blocks thousands of times. They found a way to stop.
The trick uses a special family of elements as bookmarks.
The idea
At the right-hand end of each row of the periodic table sits an unreactive element, called a 'noble gas'.
The first four noble gases
Noble gas
Symbol
Electrons
helium
He
2
neon
Ne
10
argon
Ar
18
krypton
Kr
36
Each bracketed symbol stands in for exactly this many opening electrons.
The noble gases of the first four rows are helium, neon, argon, and krypton.
Their electron counts are 2, 10, 18, and 36.
A noble gas's own configuration is exactly the stretch of blocks every later element starts with.
So the shorthand rule: find the nearest noble gas that comes BEFORE the element in the table, and replace that opening stretch with the noble gas's symbol in square brackets.
The noble gas must come before the element — a noble gas later in the table cannot stand in for electrons the element does not have.
Sulfur's full configuration is 1s²2s²2p⁶3s²3p⁴, and the nearest noble gas before sulfur is neon.
Neon's own configuration, 1s²2s²2p⁶, is sulfur's opening stretch.
Replace it: sulfur's configuration shortens to [Ne]3s²3p⁴.
Worked examples
Worked example 1. Write the noble-gas shorthand configuration of aluminum (atomic number 13).
Step 1
Write the full configuration: 1s²2s²2p⁶3s²3p¹.
Step 2
Find the nearest noble gas before aluminum: neon, with 10 electrons.
Step 3
Neon's own configuration is the opening stretch 1s²2s²2p⁶.
Step 4
Replace that stretch with the bracketed symbol.
Step 5
[Ne]3s²3p¹
Worked example 2. Write the noble-gas shorthand configuration of calcium (atomic number 20).
Step 1
Write the full configuration: 1s²2s²2p⁶3s²3p⁶4s².
Step 2
Find the nearest noble gas before calcium: argon, with 18 electrons.
Step 3
Argon's own configuration is the opening stretch 1s²2s²2p⁶3s²3p⁶.
Step 4
Replace that stretch with the bracketed symbol.
Step 5
[Ar]4s²
Worked example 3. Write the noble-gas shorthand configuration of bromine (atomic number 35).
Step 1
Write the full configuration: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵.
Step 2
Find the nearest noble gas before bromine: argon, with 18 electrons.
Step 3
Argon's own configuration is the opening stretch 1s²2s²2p⁶3s²3p⁶.
Step 4
Replace that stretch with the bracketed symbol — the 4s, 3d, and 4p blocks stay.
Step 5
[Ar]4s²3d¹⁰4p⁵
You can now write a noble-gas shorthand configuration by replacing an element's inner electrons with the bracketed symbol of the nearest earlier noble gas, the unreactive element at the right-hand end of an earlier row3s²3p⁴].
Check your understanding
Phosphorus's atomic number is 15. Write the noble-gas shorthand configuration of a neutral phosphorus atom.
Accepted answer: [Ne]3s²3p³
Write the full configuration: 1s²2s²2p⁶3s²3p³. The nearest noble gas before phosphorus is neon, with 10 electrons. Replace neon's stretch 1s²2s²2p⁶ with [Ne]. The shorthand is [Ne]3s²3p³ — 10 inside the bracket plus 5 shown makes 15.
Check your understanding
Potassium's atomic number is 19. Write the noble-gas shorthand configuration of a neutral potassium atom.
Accepted answer: [Ar]4s¹
Write the full configuration: 1s²2s²2p⁶3s²3p⁶4s¹. The nearest noble gas before potassium is argon, with 18 electrons. Replace argon's stretch 1s²2s²2p⁶3s²3p⁶ with [Ar]. The shorthand is [Ar]4s¹ — 18 inside the bracket plus 1 shown makes 19.
Check your understanding
Silicon's atomic number is 14. Write the noble-gas shorthand configuration of a neutral silicon atom.
Accepted answer: [Ne]3s²3p²
Write the full configuration: 1s²2s²2p⁶3s²3p². The nearest noble gas before silicon is neon, with 10 electrons. Replace neon's stretch 1s²2s²2p⁶ with [Ne]. The shorthand is [Ne]3s²3p² — 10 inside the bracket plus 4 shown makes 14.
Lesson 53 of 65 · ATM-053
Which element is this?
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You've already written electron configurations from the periodic table. This lesson runs the routine backwards: a configuration arrives with no name on it, and you work out which element it belongs to.
The idea
Every electron in a configuration is counted in a superscript, so adding all the superscripts gives the total number of electrons.
A neutral atom has equal numbers of electrons and protons, so the electron total equals the atomic number.
Find that atomic number in the periodic table, and you have the element.
A noble-gas shorthand hides some electrons inside the brackets, so the bracketed noble gas contributes its own electron count: [He] holds 2, [Ne] holds 10, and [Ar] holds 18.
For a shorthand configuration, add the bracketed noble gas's electrons to the superscripts written after it.
The shorthand [Ar]4s² holds 18 + 2 = 20 electrons, so the atomic number is 20 and the element is calcium.
Worked examples
Worked example 1. Which element has the electron configuration 1s²2s²2p⁶3s²3p⁵?
A neutral atom has 17 protons, so the atomic number is 17.
Step 3
Atomic number 17 is chlorine.
Worked example 2. Which element has the electron configuration [Ne]3s²3p²?
Step 1
The bracketed neon contributes 10 electrons.
Step 2
Add the superscripts after it: 10 + 2 + 2 = 14 electrons.
Step 3
A neutral atom has 14 protons, so the atomic number is 14.
Step 4
Atomic number 14 is silicon.
You can now identify the element from a full or noble-gas shorthand electron configuration by finding its total electron count, which equals the atomic number for a neutral atom4s² holds 18 + 2 = 20 electrons, so the element is calcium].
Check your understanding
Which element has the electron configuration 1s²2s²2p⁴?
AOxygencorrect
BBeryllium
This option is wrong — you read the last superscript, 4, as the atomic number — add ALL the superscripts: 2 + 2 + 4 = 8.
CCarbon
This option is wrong — you counted only the level-2 electrons — the total must include the 1s² electrons as well.
DNeon
This option is wrong — you treated the 2p sublevel as full — the superscript says it holds 4 electrons here, not 6.
Add the superscripts: 2 + 2 + 4 = 8 electrons. A neutral atom has 8 protons, so the atomic number is 8. Atomic number 8 is oxygen.
Check your understanding
Which element has the electron configuration [Ne]3s²3p¹?
AAluminumcorrect
BBoron
This option is wrong — you counted only the superscripts after the bracket — the bracketed neon contributes 10 more electrons.
CNeon
This option is wrong — you read the bracketed noble gas as the element itself — the brackets only stand in for neon's 10 inner electrons.
DSodium
This option is wrong — you added only the 3s² after the bracket — the 3p¹ electron counts too: 10 + 2 + 1 = 13.
The bracketed neon contributes 10 electrons. Add the superscripts after it: 10 + 2 + 1 = 13 electrons. Atomic number 13 is aluminum.
Check your understanding
Which element has the electron configuration [Ar]4s²3d¹⁰4p¹?
AGalliumcorrect
BAluminum
This option is wrong — you forgot the bracketed argon's 18 electrons — 2 + 10 + 1 counts only the electrons written after the bracket; the full total is 18 + 2 + 10 + 1 = 31.
CScandium
This option is wrong — you skipped the 3d¹⁰ electrons — every superscript counts toward the total: 18 + 2 + 10 + 1 = 31.
DArgon
This option is wrong — you read the bracketed noble gas as the element itself — the brackets stand in for argon's 18 inner electrons.
The bracketed argon contributes 18 electrons. Add the superscripts after it: 18 + 2 + 10 + 1 = 31 electrons. Atomic number 31 is gallium.
Lesson 54 of 65 · ATM-054
Spotting configuration errors
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You've already written configurations of your own. Now you check other people's: a written configuration can be wrong in exactly three ways, and this lesson trains you to spot which one.
The idea
Check one: capacity — an s sublevel holds at most 2 electrons, a p sublevel at most 6, and a d sublevel at most 10.
The three checks
Check
What to look for
capacity
s holds at most 2, p at most 6, d at most 10
order
1s, 2s, 2p, 3s, 3p, 4s, 3d, then 4p
total
superscripts add up to the atomic number
Run the three checks in order, and name the first one that fails.
A superscript larger than its sublevel's capacity means a sublevel is filled past its capacity.
Check two: order — the sublevels must fill as 1s, 2s, 2p, 3s, 3p, 4s, 3d, then 4p.
An electron placed in a later sublevel while an earlier one still has room means the sublevels are filled out of order.
Check three: total — the superscripts must add up to the element's atomic number.
A total that does not match the element means the electron count is wrong, even if every sublevel looks legal.
Run the three checks in order, and name the first one that fails.
The configuration 1s²2s²2p⁷3s¹, offered for magnesium, fails the capacity check: 2p⁷ places 7 electrons in a p sublevel, one more than it can hold.
Worked examples
Worked example 1. A student writes silicon's configuration as 1s²2s²2p⁶3s¹3p³. What is the error?
Step 1
Capacity: no superscript exceeds its sublevel's capacity.
Step 2
Order: 3p holds electrons while 3s still has room — 3s should be full before 3p starts.
Step 3
The total, 14, does match silicon, so the only error is the filling order.
Step 4
The sublevels are filled out of order.
Worked example 2. A student writes oxygen's configuration as 1s²2s²2p⁵. What is the error?
Step 1
Capacity: 2p⁵ is within the p sublevel's capacity of 6.
Step 2
Order: every earlier sublevel is full before the next begins.
Step 3
Total: 2 + 2 + 5 = 9, but oxygen's atomic number is 8.
Step 4
The electron total does not match the element.
Worked example 3. A student writes calcium's configuration as 1s²2s²2p⁶3s²3p⁶3d². What is the error?
Step 1
Capacity: every superscript is within its sublevel's capacity.
Step 2
Order: after 3p, the filling order goes to 4s, not 3d — so 3d² is out of order.
Step 3
The total, 20, does match calcium, so the only error is the filling order.
Step 4
The sublevels are filled out of order — 4s fills before 3d.
You can now evaluate a supplied electron configuration and identify the error: a sublevel filled past its capacity, sublevels filled out of order, or an electron total that does not match the element.
Check your understanding
A student writes sodium's configuration as 1s²2s²2p⁶3s¹. Evaluate the configuration. What, if anything, is wrong with it?
AThe configuration has no errorcorrect
BA sublevel is filled past its capacity
This option is wrong — you flagged a legal superscript — no sublevel here exceeds 2 for s or 6 for p.
CThe sublevels are filled out of order
This option is wrong — you flagged the half-filled 3s¹ — a sublevel may hold fewer electrons than its capacity when it is the last one filled.
DThe electron total does not match the element
This option is wrong — you miscounted — 2 + 2 + 6 + 1 = 11, which is sodium's atomic number.
Capacity: 2, 2, 6, and 1 are all within their sublevels' capacities. Order: 1s, 2s, 2p, 3s is the correct filling order. Total: 2 + 2 + 6 + 1 = 11, and sodium's atomic number is 11. All three checks pass, so the configuration is correct.
Check your understanding
A student writes nitrogen's configuration as 1s²2s³2p². Evaluate the configuration. What, if anything, is wrong with it?
AA sublevel is filled past its capacitycorrect
BThe sublevels are filled out of order
This option is wrong — you looked past the superscripts — the sequence 1s, 2s, 2p is the correct order; the defect is the 3 electrons crammed into 2s.
CThe electron total does not match the element
This option is wrong — you flagged the total, but 2 + 3 + 2 = 7 does match nitrogen — the defect is where the electrons sit, not how many there are.
DThe configuration has no error
This option is wrong — you missed the 2s³ — an s sublevel holds at most 2 electrons.
Capacity: 2s³ places 3 electrons in an s sublevel, which holds at most 2. The capacity check fails first, so that is the error to name.
Check your understanding
A student writes potassium's configuration as 1s²2s²2p⁶3s²3p⁶3d¹. Evaluate the configuration. What, if anything, is wrong with it?
AThe sublevels are filled out of ordercorrect
BA sublevel is filled past its capacity
This option is wrong — you flagged 3d¹, but a d sublevel holds up to 10 electrons — the problem is that 4s should fill before 3d.
CThe electron total does not match the element
This option is wrong — you miscounted — the superscripts add to 19, which is potassium's atomic number.
DThe configuration has no error
This option is wrong — you accepted 3d before 4s — after 3p the filling order goes to 4s first.
Capacity: every superscript is within its sublevel's capacity. Order: after 3p the next electron enters 4s, not 3d — so 3d¹ is out of order. Potassium's final electron belongs in 4s¹.
Lesson 55 of 65 · ATM-055
Full and shorthand configurations on demand
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You've already written full configurations through period 4 and noble-gas shorthands separately. This lesson puts the whole routine together: any main-group element in the periodic table's first four rows, both forms, on demand.
The idea
Find the element in the periodic table and read its atomic number — for a neutral atom, that is the electron count.
Fill the sublevels in order — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p — until every electron is placed.
Respect each capacity as you fill: s holds at most 2, p at most 6, d at most 10.
That finished string is the full configuration.
For the shorthand, find the nearest noble gas that comes BEFORE the element in the table.
Replace that noble gas's electrons with its bracketed symbol, and keep everything after it unchanged.
Arsenic, atomic number 33, gives the full form 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³ and the shorthand [Ar]4s²3d¹⁰4p³.
Worked examples
Worked example 1. Using the periodic table, write the full and the noble-gas shorthand electron configuration of selenium.
Step 1
Selenium's atomic number is 34, so place 34 electrons.
Step 2
Fill in order: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴.
Step 3
The nearest noble gas before selenium is argon, which covers the first 18 electrons.
Worked example 2. Using the periodic table, write the full and the noble-gas shorthand electron configuration of potassium.
Step 1
Potassium's atomic number is 19, so place 19 electrons.
Step 2
Fill in order: 1s²2s²2p⁶3s²3p⁶4s¹ — after 3p, the nineteenth electron enters 4s.
Step 3
The nearest noble gas before potassium is argon.
Step 4
Bracket argon and keep the rest: [Ar]4s¹.
Step 5
Full: 1s²2s²2p⁶3s²3p⁶4s¹. Shorthand: [Ar]4s¹.
You can now write both the full and the noble-gas shorthand electron configuration of any main-group element in the periodic table's first four rows, using the table4s²3d¹⁰4p³].
Your turn
Using the periodic table, write on paper the full electron configuration AND the noble-gas shorthand configuration of gallium. When you have both, reveal the model answer and check your work against the checklist.
Model answer. Full: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p¹. Shorthand: [Ar]4s²3d¹⁰4p¹. Gallium's atomic number is 31; the first 18 electrons are argon's, and the remaining 13 fill 4s, then all of 3d, then start 4p.
The superscripts of the full form add up to 31, gallium's atomic number.
The sublevels appear in filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.
4s is written and filled before 3d, and 3d carries its full 10 electrons.
The shorthand brackets argon — the nearest noble gas before gallium — and keeps 4s²3d¹⁰4p¹ unchanged.
Check your understanding
Which is the correct full electron configuration of aluminum?
A1s²2s²2p⁶3s²3p¹correct
B1s²2s²2p⁶3p³
This option is wrong — you skipped 3s — after 2p the filling order goes to 3s before 3p.
C1s²2s²2p⁹
This option is wrong — you kept loading the 2p sublevel — a p sublevel holds at most 6 electrons, so the extras move on to 3s and 3p.
D1s²2s²2p⁶3s²3d¹
This option is wrong — you jumped to a d sublevel — after 3s the next sublevel in filling order is 3p.
Aluminum's atomic number is 13, so place 13 electrons. Fill in order: 1s², 2s², 2p⁶, 3s², then the last electron enters 3p. The full configuration is 1s²2s²2p⁶3s²3p¹.
Check your understanding
Which is the correct noble-gas shorthand configuration of phosphorus?
A[Ne]3s²3p³correct
B[Ar]3s²3p³
This option is wrong — you bracketed argon, which comes AFTER phosphorus — the shorthand uses the nearest noble gas before the element.
C[Ne]2s²2p³
This option is wrong — you restarted at level 2 after the bracket — neon already contains the level-2 electrons, so the remainder begins at 3s.
D[Ar]4s²3d¹⁰4p³
This option is wrong — you wrote the shorthand of the element one row below in the same column — check the atomic number: phosphorus has 15 electrons, not 33.
Phosphorus's atomic number is 15. The nearest noble gas before phosphorus is neon, which covers 10 electrons. The remaining 5 electrons give [Ne]3s²3p³.
Arsenic has 33 electrons. When chemists work out how arsenic behaves, they ignore 28 of them and watch just 5. Which 5 — and why those?
When two atoms meet, their outermost electrons meet first — the electrons in the highest energy level do almost all the work in chemistry. Those outermost electrons are the ones chemists watch.
The idea
The electrons in an atom's highest-numbered energy level are called its 'valence electrons'.
Every electron in a lower-numbered level is an inner electron.
To count valence electrons, find the highest level number that appears in the configuration.
Add the superscripts of every sublevel carrying that highest number — and only those.
In a noble-gas shorthand, the bracketed part is all inner electrons, so it never counts.
Watch d sublevels: 3d belongs to level 3, so when level 4 is the highest, 3d electrons are inner electrons.
Sulfur's configuration [Ne]3s²3p⁴ has level 3 as its highest, so sulfur has 2 + 4 = 6 valence electrons.
Worked examples
Worked example 1. Silicon's electron configuration is 1s²2s²2p⁶3s²3p². How many valence electrons does silicon have?
Step 1
The highest level number in the configuration is 3.
Step 2
The level-3 sublevels are 3s² and 3p².
Step 3
Add their superscripts: 2 + 2 = 4.
Step 4
Silicon has 4 valence electrons.
Worked example 2. Selenium's electron configuration is [Ar]4s²3d¹⁰4p⁴. How many valence electrons does selenium have?
Step 1
The highest level number in the configuration is 4.
Step 2
The level-4 sublevels are 4s² and 4p⁴ — the 3d¹⁰ electrons belong to level 3, so they are inner electrons.
Step 3
Add the level-4 superscripts: 2 + 4 = 6.
Step 4
Selenium has 6 valence electrons.
You can now identify an atom's valence electrons, the electrons in its highest-numbered energy level, and count them from its electron configuration3s²3p⁴ shows 2 + 4 = 6 valence electrons in level 3].
Check your understanding
Chlorine's electron configuration is 1s²2s²2p⁶3s²3p⁵. How many valence electrons does chlorine have?
Answer: 7
The highest level number in the configuration is 3. The level-3 sublevels are 3s² and 3p⁵. Add their superscripts: 2 + 5 = 7 valence electrons.
Check your understanding
Boron's electron configuration is [He]2s²2p¹. How many valence electrons does boron have?
Answer: 3
The bracketed [He] holds inner electrons, so it never counts. The highest level number is 2, with sublevels 2s² and 2p¹. Add their superscripts: 2 + 1 = 3 valence electrons.
Check your understanding
Germanium's electron configuration is [Ar]4s²3d¹⁰4p². How many valence electrons does germanium have?
Answer: 4
The highest level number in the configuration is 4. The level-4 sublevels are 4s² and 4p² — the 3d¹⁰ electrons are inner electrons of level 3. Add the level-4 superscripts: 2 + 2 = 4 valence electrons.
Lesson 57 of 65 · ATM-057
Valence electrons from the periodic table
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You've already counted valence electrons by writing out a configuration and reading its highest level. Writing a whole configuration just to get one small number is slow — the periodic table hands you that number directly.
The idea
Each vertical column of the periodic table is called a 'group'.
For a main-group element, the column tells you the valence-electron count.
Columns 1 and 2 give 1 and 2 valence electrons.
Columns 13 through 18 give 3 through 8 valence electrons — subtract 10 from the column number.
Helium is the exception in column 18: it has only 2 electrons in total, so it has 2 valence electrons.
The rule works for a main-group element in any row, because every element in a column has the same number of valence electrons.
Oxygen sits in column 16, and 16 − 10 = 6, so oxygen has 6 valence electrons — exactly what its configuration 1s²2s²2p⁴ shows.
Worked examples
Worked example 1. Calcium sits in column 2 of the periodic table. How many valence electrons does calcium have?
Step 1
Calcium is a main-group element in column 2.
Step 2
Columns 1 and 2 give the column number directly.
Step 3
Calcium has 2 valence electrons.
Worked example 2. Iodine sits in column 17 of the periodic table, in period 5. How many valence electrons does iodine have?
Step 1
Iodine is a main-group element in column 17.
Step 2
Columns 13 through 18 give the column number minus 10: 17 − 10 = 7.
Step 3
The row does not matter — column 17 gives 7 valence electrons in every period.
Step 4
Iodine has 7 valence electrons.
You can now determine a main-group element's valence-electron count from its column, called its group, in the periodic table: columns 1 and 2 give 1 and 2, and columns 13 through 18 give 3 through 8, except helium with 2.
Check your understanding
Nitrogen sits in column 15 of the periodic table. How many valence electrons does nitrogen have?
Answer: 5
Nitrogen is a main-group element in column 15. Columns 13 through 18 give the column number minus 10. 15 − 10 = 5 valence electrons.
Check your understanding
Cesium sits in column 1 of the periodic table, in period 6. How many valence electrons does cesium have?
Answer: 1
Cesium is a main-group element in column 1. Columns 1 and 2 give the column number directly. Cesium has 1 valence electron, whatever its row.
Check your understanding
Xenon sits in column 18 of the periodic table. How many valence electrons does xenon have?
Answer: 8
Xenon is a main-group element in column 18. Columns 13 through 18 give the column number minus 10: 18 − 10 = 8. Only helium breaks this pattern, because it has just 2 electrons in total.
Lesson 58 of 65 · ATM-058
Reading Lewis dot symbols
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Valence electrons matter so much that chemists draw a picture that shows nothing else. You've already counted valence electrons two ways — this lesson teaches you to read the picture built from them.
The idea
A 'Lewis dot symbol' shows an element symbol with dots placed around its four sides.
The element symbol stands for the nucleus plus all the inner electrons.
Each dot is one valence electron — nothing else appears in the picture.
To read a Lewis dot symbol, count the dots: that count is the element's number of valence electrons.
Two dots sitting side by side, both the same distance from the symbol, are a pair of valence electrons — count both.
The symbol Cl surrounded by 7 dots says chlorine has 7 valence electrons: the Cl stands for the nucleus and the 10 inner electrons.
Worked examples
Worked example 1. The Lewis dot symbol shown is for silicon. How many valence electrons does silicon have?
Step 1
Count the dots around the symbol: one on each of the four sides.
Step 2
Each dot is one valence electron.
Step 3
Silicon has 4 valence electrons.
Worked example 2. The Lewis dot symbol shown is for oxygen. How many valence electrons does oxygen have?
Step 1
Count the dots: two pairs and two single dots.
Step 2
Count every dot in a pair: 2 + 2 + 1 + 1 = 6.
Step 3
Oxygen has 6 valence electrons.
You can now interpret a Lewis dot symbol, in which the element symbol stands for the nucleus plus all inner electrons and each surrounding dot is one valence electron.
Check your understanding
The Lewis dot symbol shown is for nitrogen. How many valence electrons does nitrogen have?
Answer: 5
Count every dot, pairs included. One pair and three single dots give 2 + 1 + 1 + 1 = 5. Nitrogen has 5 valence electrons.
Check your understanding
The Lewis dot symbol shown is for potassium. What does the letter K in the symbol stand for?
AThe nucleus plus all of potassium's inner electronscorrect
BOnly potassium's nucleus, with no electrons at all
This option is wrong — you left out the inner electrons — the letters carry everything except the valence electrons.
CAll of potassium's electrons, inner and valence together
This option is wrong — you put the valence electron inside the letters — the dot outside the symbol carries it.
DPotassium's valence electrons, drawn as a single letter
This option is wrong — you swapped the parts — the dots are the valence electrons; the letters are everything else.
A Lewis dot symbol splits the atom into two parts. The element symbol stands for the nucleus plus all the inner electrons. Each dot outside it is one valence electron — potassium's single dot is its 1 valence electron.
Check your understanding
The Lewis dot symbol shown is for calcium. How many valence electrons does calcium have?
Answer: 2
Count the dots around the symbol: 2. Each dot is one valence electron, so calcium has 2.
Lesson 59 of 65 · ATM-059
Drawing Lewis dot symbols
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Did You Know?
You've already read Lewis dot symbols. Now you draw them: given any main-group element, you produce its Lewis dot symbol from scratch.
The idea
Write the element's symbol — it stands for the nucleus and all the inner electrons.
Count the element's valence electrons, from its column or its configuration.
Place the dots around the four sides of the symbol: top, right, bottom, and left.
Put one dot per side until every side has one — so the first four dots all sit alone.
From the fifth dot on, pair the new dot with a dot already there.
Draw each pair as two dots side by side, both the same distance from the symbol.
No side ever holds more than 2 dots, so 8 dots is the most a symbol can carry.
Phosphorus has 5 valence electrons, so its symbol carries one pair plus three single dots.
Worked examples
Worked example 1. Draw the Lewis dot symbol of carbon.
Step 1
Carbon sits in column 14, so it has 4 valence electrons.
Step 2
Four dots means one dot per side — no pairs yet.
Step 3
The symbol C with a single dot on each of its four sides.
Worked example 2. Draw the Lewis dot symbol of sulfur.
Step 1
Sulfur sits in column 16, so it has 6 valence electrons.
Step 2
The first four dots take one side each.
Step 3
The fifth and sixth dots pair up with dots already there.
Step 4
The symbol S with two pairs and two single dots.
You can now draw the Lewis dot symbol of a main-group atom by placing its valence electrons as dots around the four sides of the element symbol, one dot per side before any side gets a second.
Check your understanding
A student is asked to draw the Lewis dot symbol of nitrogen, which has 5 valence electrons. Which drawing is correct?
Acorrect
B
This option is wrong — you paired dots too early — every side takes one dot before any side takes a second.
C
This option is wrong — you drew only 3 dots — nitrogen has 5 valence electrons, and every one gets a dot.
D
This option is wrong — you filled all four sides with pairs — that is 8 dots, but nitrogen has only 5 valence electrons.
Nitrogen has 5 valence electrons, so the symbol carries 5 dots. The first four dots take one side each. The fifth dot forms one pair, leaving three single dots.
Your turn
On paper, draw the Lewis dot symbol of aluminum, which has 3 valence electrons. When your drawing is finished, reveal the model answer and check it against the checklist.
Model answer. The symbol Al with three single dots — one on top, one on the right, one on the bottom — and the left side empty. Any three different sides are equally correct.
The drawing shows the symbol Al with exactly 3 dots.
Each dot sits alone on its own side — no pairs, because no side takes a second dot until every side has one.
The dots sit close to the Al, clearly belonging to it.
Your turn
On paper, draw the Lewis dot symbol of oxygen, which has 6 valence electrons. When your drawing is finished, reveal the model answer and check it against the checklist.
Model answer. The symbol O with a pair of dots on top, a pair on the right, and single dots on the bottom and left. Each pair's two dots sit side by side, both the same distance from the O. Any arrangement with two pairs and two singles on four different sides is equally correct.
The drawing shows the symbol O with exactly 6 dots.
Every side holds at least one dot — the first four dots went one per side.
Exactly two sides hold pairs, and no side holds more than 2 dots.
Each pair's two dots sit side by side, both the same distance from the O.
Lesson 60 of 65 · ATM-060
Ions
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Have You Ever Wondered?
Wonder this:
Rub a balloon on your hair, and the balloon picks up an electric charge — it will stick to a wall. But the balloon is made of atoms, and whole atoms carry no charge at all. Where did the charge come from?
You've already seen why a whole atom is neutral: its protons and electrons cancel exactly. Charge appears when that balance is broken.
The idea
An atom can lose one or more of its electrons, or gain extra ones.
Once that happens, the protons and electrons no longer cancel, so the atom carries an overall electrical charge.
An atom that has gained or lost electrons is called an 'ion'.
A sodium atom that loses one electron becomes an ion.
Gaining or losing electrons is the only change involved — nothing happens to the nucleus.
Worked examples
Worked example 1. A fluorine atom gains one electron. What kind of particle has it become?
Step 1
An ion — an atom that has gained or lost electrons.
You can now state that an ion is an atom that has gained or lost electrons and so carries an overall electrical charge.
Check your understanding
What is an ion?
AAn atom that has gained or lost electronscorrect
BAn atom that has gained or lost protons
This option is wrong — you moved particles in the nucleus — changing protons changes which element the atom is; ions form from electron changes only.
CAn atom that has gained or lost neutrons
This option is wrong — you described an isotope — neutron changes alter the mass, not the charge.
DAny atom that contains charged particles
This option is wrong — you counted the protons and electrons every atom contains — an ion needs an IMBALANCE, made by gaining or losing electrons.
An ion is an atom that has gained or lost electrons. The electron change breaks the proton-electron balance, so the ion carries an overall charge.
Check your understanding
A magnesium atom loses two electrons. What kind of particle is it now?
AAn ioncorrect
BAn isotope
This option is wrong — you filed the change under neutrons — isotopes differ in neutrons; this atom changed its electrons.
CA molecule
This option is wrong — you filed the change under joining — a molecule is atoms joined together; nothing joined here.
DA neutral atom
This option is wrong — you kept the balance — after losing two electrons, the protons and electrons no longer cancel.
The atom gained or lost electrons — here it lost two. An atom that has gained or lost electrons is an ion.
Check your understanding
Which of these particles is an ion?
AA lithium atom that has lost one electroncorrect
BA helium atom with 2 protons and 2 electrons
This option is wrong — you picked a balanced atom — equal protons and electrons cancel, so it carries no charge.
CA carbon atom with one extra neutron
This option is wrong — you picked an isotope — extra neutrons change the mass, not the charge.
DTwo hydrogen atoms joined into one particle
This option is wrong — you picked a molecule — joined atoms are not an ion unless electrons were gained or lost.
Look for the particle that gained or lost electrons. The lithium atom lost one electron, so it is an ion. Balanced atoms, isotopes, and molecules keep their proton-electron balance.
Lesson 61 of 65 · ATM-061
Cations and anions
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Did You Know?
You've already seen that an ion is an atom that has gained or lost electrons. Ions come in two kinds, and chemists name and write them by their charge.
The idea
An ion's charge is written as a superscript after the element symbol.
Na⁺ is an ion of sodium with a positive charge, and Cl⁻ is an ion of chlorine with a negative charge.
A number in the superscript sizes the charge: Ca²⁺ carries a 2+ charge.
An ion with a positive charge is called a 'cation'.
An ion with a negative charge is called an 'anion'.
So Na⁺ and Ca²⁺ are cations, and Cl⁻ is an anion.
A symbol with no charge superscript, like Ne, is a neutral atom — not an ion at all.
Worked examples
Worked example 1. Is K⁺ a cation or an anion?
Step 1
The superscript after K is ⁺, a positive charge.
Step 2
K⁺ is a cation.
Worked example 2. Is O²⁻ a cation or an anion?
Step 1
The superscript after O is ²⁻, a negative charge.
Step 2
O²⁻ is an anion.
You can now classify an ion as a cation if it carries a positive charge, written like Na⁺, or an anion if it carries a negative charge, written like Cl⁻.
Check your understanding
Classify the particle written Al³⁺. Is it a cation, an anion, a neutral atom, or an isotope?
AA cationcorrect
BAn anion
This option is wrong — you read the charge sign backwards — the superscript ³⁺ is positive, and a positive ion is a cation.
CA neutral atom
This option is wrong — you ignored the superscript — a charge superscript means the particle is an ion.
DAn isotope
This option is wrong — you confused the charge superscript with isotope notation — mass numbers sit BEFORE the symbol, charges after.
Read the superscript after the symbol: ³⁺, a positive charge. An ion with a positive charge is a cation.
Check your understanding
Classify the particle written N³⁻. Is it a cation, an anion, a neutral atom, or an isotope?
AAn anioncorrect
BA cation
This option is wrong — you read the charge sign backwards — the superscript ³⁻ is negative, and a negative ion is an anion.
CA neutral atom
This option is wrong — you ignored the superscript — a charge superscript means the particle is an ion.
DAn isotope
This option is wrong — you confused the charge superscript with isotope notation — mass numbers sit BEFORE the symbol, charges after.
Read the superscript after the symbol: ³⁻, a negative charge. An ion with a negative charge is an anion.
Check your understanding
An ion of lithium carries a 1+ charge. Classify it: is it a cation, an anion, a neutral atom, or an isotope?
AA cationcorrect
BAn anion
This option is wrong — you attached 'anion' to the wrong sign — anions are the negative ions.
CA neutral atom
This option is wrong — you overlooked the stated charge — a particle carrying any charge is an ion, not a neutral atom.
DAn isotope
This option is wrong — you reached for the mass label — charge, not neutron count, is what the 1+ describes.
The charge is 1+, which is positive. An ion with a positive charge is a cation, whatever its size or element.
Lesson 62 of 65 · ATM-062
Why the charge appears
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Have You Ever Wondered?
Wonder this:
Losing something usually leaves you with less. Yet when a magnesium atom loses two electrons, it ends up with a charge of 2+ — as if losing gave it something. Why?
You've already classified ions by their charge sign. This lesson explains where that sign comes from.
The idea
Each proton carries a 1+ charge, and each electron carries a 1− charge.
Gaining or losing electrons never touches the nucleus, so the proton count stays fixed.
Because the proton count does not change when electrons are gained or lost, the charge equals protons minus electrons.
Lose electrons, and the protons now outnumber the electrons — the leftover charge is positive.
Gain electrons, and the electrons now outnumber the protons — the extra charge is negative.
A magnesium atom keeps its 12 protons but has only 10 electrons after losing 2, leaving it 2+.
Worked examples
Worked example 1. A chlorine atom gains one electron. Explain why the ion is negative.
Step 1
The proton count stays fixed at 17.
Step 2
The electron count rises from 17 to 18.
Step 3
The 18 electrons now outnumber the 17 protons by one.
Step 4
One extra negative charge is left over, so the ion is 1−.
Worked example 2. A lithium atom loses one electron. Explain why the ion is positive.
Step 1
The proton count stays fixed at 3.
Step 2
The electron count falls from 3 to 2.
Step 3
The 3 protons now outnumber the 2 electrons by one.
Step 4
One positive charge is left over, so the ion is 1+.
You can now explain why losing electrons leaves an ion positive and gaining electrons leaves it negative: because the proton count does not change when electrons are gained or lost, the charge equals protons minus electrons.
Check your understanding
A potassium atom loses one electron. Why does the resulting ion carry a positive charge?
AIts 19 protons now outnumber its 18 electrons, so one positive charge is left overcorrect
BLosing an electron turns one of its 19 protons into an extra positive charge
This option is wrong — you had the protons change — protons are unchanged; the positive charge was always there and is now uncancelled.
CThe atom gains a proton to replace the electron it lost, tipping the balance
This option is wrong — you added a nucleus particle — gaining or losing electrons never touches the nucleus.
DThe lost electron carries the atom's negative charge away, and the neutrons then supply positive charge
This option is wrong — you gave neutrons a charge — neutrons are neutral; the protons alone supply the positive charge.
Because the proton count does not change when electrons are gained or lost, the charge equals protons minus electrons. Potassium keeps its 19 protons and drops to 18 electrons. One proton's charge is left uncancelled, so the ion is 1+.
Check your understanding
An oxygen atom gains two electrons. Why does the resulting ion carry a negative charge?
AIts 10 electrons now outnumber its 8 protons, so two negative charges are left overcorrect
BGaining two electrons removes two protons from the nucleus, leaving it negative
This option is wrong — you took particles out of the nucleus — gaining or losing electrons never touches the nucleus.
CThe added electrons become part of the nucleus and make it negative
This option is wrong — you moved the electrons into the nucleus — electrons stay outside it; the imbalance in counts makes the charge.
DGaining electrons turns two of its neutrons into negative charges
This option is wrong — you gave neutrons a charge — neutrons are neutral; the extra electrons themselves supply the negative charge.
Because the proton count does not change when electrons are gained or lost, the charge equals protons minus electrons. Oxygen keeps its 8 protons and rises to 10 electrons. Two electrons' charges are left uncancelled, so the ion is 2−.
Check your understanding
An ion contains 9 protons and 10 electrons. Is its charge positive or negative, and why?
ANegative, because the electrons outnumber the protons by onecorrect
BPositive, because protons are stronger than electrons
This option is wrong — you ranked the charges by strength — a proton's 1+ and an electron's 1− are equal in size; only the counts decide.
CNegative, because every ion with more than 9 electrons is negative
This option is wrong — you used the electron count alone — the charge compares electrons WITH protons, not with a fixed cutoff.
DPositive, because the protons sit together in the nucleus
This option is wrong — you used the particles' positions — where the particles sit does not matter; the counts decide the charge.
Compare the counts: 10 electrons against 9 protons. One electron's negative charge is left uncancelled. The ion carries a 1− charge.
Lesson 63 of 65 · ATM-063
Charge from particle counts
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Did You Know?
You've already seen why an ion's charge appears: the proton count holds still while the electron count changes. Now you turn that idea into a number.
The equation
Write down the ion's proton count and electron count.
Write down the equation: charge = number of protons − number of electrons.
Substitute the counts and calculate.
A positive result is written with the number before a plus sign, like 2+.
A negative result is written with the number before a minus sign, like 2−.
A result of exactly 0 means the particle is a neutral atom, not an ion.
Worked examples
Worked example 1. An ion contains 13 protons and 10 electrons. What is its charge?
Step 1
Write down the values in the question
protons = 13
electrons = 10
Step 2
Write down the equation
charge = number of protons − number of electrons
Step 3
Substitute in the values, and calculate
charge = 13 − 10
charge = +3, written 3+
Worked example 2. An ion contains 35 protons and 36 electrons. What is its charge?
Step 1
Write down the values in the question
protons = 35
electrons = 36
Step 2
Write down the equation
charge = number of protons − number of electrons
Step 3
Substitute in the values, and calculate
charge = 35 − 36
charge = −1, written 1−
You can now calculate an ion's charge from its proton and electron counts by subtracting electrons from protons.
Check your understanding
An ion contains 11 protons and 10 electrons. Calculate its charge, giving the number and the sign.
Answer: 1+
protons = 11 electrons = 10 charge = number of protons − number of electrons charge = 11 − 10 charge = +1, written 1+
Check your understanding
An ion contains 7 protons and 10 electrons. Calculate its charge, giving the number and the sign.
Answer: 3−
protons = 7 electrons = 10 charge = number of protons − number of electrons charge = 7 − 10 charge = −3, written 3−
Check your understanding
A particle contains 20 protons and 20 electrons. Calculate its charge, giving the number and the sign if there is one.
Answer: 0
protons = 20 electrons = 20 charge = number of protons − number of electrons charge = 20 − 20 charge = 0 — the particle is a neutral atom, not an ion
Lesson 64 of 65 · ATM-064
Electrons in an ion
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Did You Know?
You've already calculated an ion's charge from its particle counts. An ion symbol hands you the charge and hides the electron count — this lesson runs the equation backwards to find it.
The equation
Read the proton count first: it is the element's atomic number, from the periodic table.
Read the charge from the superscript after the symbol.
Start from the equation: charge = number of protons − number of electrons.
Make the number of electrons the subject: number of electrons = number of protons − charge.
A positive charge counts as a positive number, so a 3+ charge means subtracting 3.
A negative charge counts as a negative number, so subtracting a 2− charge ADDS 2 electrons.
In plain words: a cation has lost electrons, so its electron count sits BELOW the proton count; an anion has gained electrons, so its count sits above.
Al³⁺, with aluminum's 13 protons, has 13 − 3 = 10 electrons.
Worked examples
Worked example 1. How many electrons does O²⁻ have? Oxygen's atomic number is 8.
Step 1
Write down the values in the question
protons = 8
charge = −2
Step 2
Write down the equation
charge = number of protons − number of electrons
Step 3
Substitute in the values, and calculate
Make the number of electrons the subject:
number of electrons = number of protons − charge
number of electrons = 8 − (−2)
number of electrons = 10
Worked example 2. How many electrons does Rb⁺ have? Rubidium's atomic number is 37.
Step 1
Write down the values in the question
protons = 37
charge = +1
Step 2
Write down the equation
charge = number of protons − number of electrons
Step 3
Substitute in the values, and calculate
Make the number of electrons the subject:
number of electrons = number of protons − charge
number of electrons = 37 − 1
number of electrons = 36
You can now determine the number of electrons in an ion from its symbol by starting from the proton count and undoing the charge.
Check your understanding
How many electrons does K⁺ have? Potassium's atomic number is 19.
Answer: 18
protons = 19, charge = +1 number of electrons = number of protons − charge number of electrons = 19 − 1 = 18 Direction check: a cation has LOST electrons, so 18 below 19 is right.
Check your understanding
How many electrons does N³⁻ have? Nitrogen's atomic number is 7.
Answer: 10
protons = 7, charge = −3 number of electrons = number of protons − charge number of electrons = 7 − (−3) = 10 Direction check: an anion has GAINED electrons, so 10 above 7 is right.
Check your understanding
How many electrons does Ba²⁺ have? Barium's atomic number is 56.
Answer: 54
protons = 56, charge = +2 number of electrons = number of protons − charge number of electrons = 56 − 2 = 54 Direction check: a cation has LOST electrons, so 54 below 56 is right.
Lesson 65 of 65 · ATM-065
Full particle count for an ion
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Did You Know?
You've already read a full particle count from an isotope symbol, and an electron count from an ion's charge. A symbol can carry both marks at once — and then it tells you everything: protons, neutrons, and electrons.
The idea
The subscript before the symbol is the atomic number: that is the proton count.
The superscript before the symbol is the mass number: neutrons = mass number − atomic number.
The superscript after the symbol is the charge: electrons = protons − charge, exactly as for any ion.
Work the three reads in that order — protons, then neutrons, then electrons.
The charge changes ONLY the electron count; protons and neutrons come from the isotope part alone.
So ⁴⁰₂₀Ca²⁺ has 20 protons, 40 − 20 = 20 neutrons, and 20 − 2 = 18 electrons.
Worked examples
Worked example 1. How many protons, neutrons, and electrons does ³⁷₁₇Cl⁻ have?
Step 1
Protons: the atomic number is 17.
Step 2
Neutrons: mass number − atomic number = 37 − 17 = 20.
Step 3
Electrons: protons − charge = 17 − (−1) = 18.
Step 4
17 protons, 20 neutrons, 18 electrons.
Worked example 2. How many protons, neutrons, and electrons does ²⁵₁₂Mg²⁺ have?
Step 1
Protons: the atomic number is 12.
Step 2
Neutrons: mass number − atomic number = 25 − 12 = 13.
Step 3
Electrons: protons − charge = 12 − 2 = 10.
Step 4
12 protons, 13 neutrons, 10 electrons.
You can now determine the numbers of protons, neutrons, and electrons in an ion from its isotope symbol written with a charge.
Check your understanding
How many electrons does ⁷⁹₃₅Br⁻ have?
Answer: 36
Protons: the atomic number is 35. Electrons: protons − charge = 35 − (−1) = 36. An anion has gained electrons, so 36 above 35 is right — the mass number 79 plays no part in the electron count.
Check your understanding
How many neutrons does ⁶⁴₃₀Zn²⁺ have?
Answer: 34
Neutrons: mass number − atomic number. 64 − 30 = 34 neutrons. The ²⁺ charge changes only the electron count — protons and neutrons come from the isotope part alone.
Check your understanding
How many electrons does ¹⁹₉F⁻ have?
Answer: 10
Protons: the atomic number is 9. Electrons: protons − charge = 9 − (−1) = 10. An anion has gained electrons, so 10 above 9 is right.
Summary video — Valence electrons, Lewis symbols, and ions