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AQA GCSE Physics · Topic 4.4 Atomic structure
Edexcel International GCSE Physics · Section 7 (b) Radioactivity
Nuclear Equations
In this lesson you'll learn to: read the mass number and atomic number off a
nuclide symbol, write alpha, beta and gamma radiation into an equation, say exactly what
alpha, beta and gamma emission does to a nucleus, and balance a decay equation
to find a missing number or element.
In this lesson you'll learn to: read the mass number and atomic number off a
nuclide symbol, describe what alpha, beta, gamma and neutron radiation each do to the
mass number and atomic number of a nucleus, and balance a nuclear equation in terms of
mass and charge to find a missing number or element.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — make a nucleus decay
Don't read anything yet. Pick Alpha, press Decay!, and watch three things at once: which particles leave, what happens to the proton count, and how the equation underneath fills in. Then try Beta and Gamma. Once you can predict the new nucleus before it appears, untick Show the new nucleus and test yourself.
Radioactive decay — alpha emission
▲ Count the protons before and after. That one number tells you the element.
Seen it decay? Now learn to write it down.
The examiner will not ask you to describe the animation. They will give you an equation with a gap in it and ask for the missing number, the missing element, or the type of radiation. The notes below give you the one rule that solves all of them.
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Revision notes
⭐ Read this first — same particle, two symbols
You will see the alpha and beta particles written two different ways in textbooks, mark schemes and exam papers. They mean exactly the same thing, and either one gets the mark.
42α=42He
An alpha particle is a helium nucleus
0−1β=0−1e
A beta particle is an electron
This page writes them as α and β, because the Greek letter tells you straight away which kind of radiation it is.
Edexcel iGCSEYour specification writes the beta particle as β−. The little minus just reminds you it is negative — it is the same particle.
1. Reading a nuclide symbol
Every nucleus in a nuclear equation — and every particle — is written with two numbers in front of its symbol. The top one and the bottom one mean different things, and you need both.
For a particle, the bottom number is really its charge. For a nucleus that is the same as the number of protons — which is why an electron can have −1 down there, even though it isn't a proton at all.
| Radiation | What it is | Symbol | Top (mass) | Bottom (charge) |
|---|---|---|---|---|
| Alpha | 2 protons + 2 neutrons — a helium nucleus | 42α | 4 | +2 |
| Beta | a fast-moving electron, thrown out of the nucleus | 0−1β | 0 | −1 |
| Gamma | electromagnetic radiation — a wave, not a particle | 00γ | 0 | 0 |
| Edexcel iGCSENeutron | a single neutron | 10n | 1 | 0 |
2. The one rule that balances every equation
A nuclear equation is just bookkeeping. Nothing is created or destroyed — the protons and neutrons are only rearranged — so the numbers have to add up.
⭐ Memorise this
The top numbers add up to the same total on both sides of the arrow, and so do the bottom numbers.
Top numbers balance → mass is conserved. Bottom numbers balance → charge is conserved.
That is all "balance a nuclear equation in terms of mass and charge" means. Every question in this topic is this rule, used one way or another.
3. What each type of radiation does to the nucleus
Learn these cards. Every row follows straight from the symbol in the table above — the nucleus loses whatever the radiation carries away.
Alpha
42α
Mass number−4
Atomic number−2
New element?Yes
Beta
0−1β
Mass numberno change
Atomic number+1
New element?Yes
Gamma
00γ
Mass numberno change
Atomic numberno change
New element?No
Neutron
10n
Mass number−1
Atomic numberno change
New element?No
Edexcel iGCSE
4. Alpha decay
The nucleus throws out 2 protons and 2 neutrons stuck together. It loses 4 from its mass number and 2 from its atomic number — and because the number of protons has changed, it has become a different element.
21084Po→20682Pb+42α
Top: 210 = 206 + 4 ✓ · Bottom: 84 = 82 + 2 ✓ · polonium has become lead
5. Beta decay
Inside the nucleus, a neutron turns into a proton and an electron. The electron is thrown out at high speed — that is the beta particle. The new proton stays behind.
- The mass number does not change: one neutron has been swapped for one proton, so the total number of particles in the nucleus is the same.
- The atomic number goes up by 1: there is one more proton, so it is now the next element along.
146C→147N+0−1β
Top: 14 = 14 + 0 ✓ · Bottom: 6 = 7 + (−1) ✓ · carbon has become nitrogen
💡 Exam tip — why beta makes the number go UP
It feels as if losing a particle should make a number go down. But the bottom numbers on the right must still add up to 6, and the beta particle brings −1 to that sum — so the new nucleus needs 7, because 7 + (−1) = 6. Throwing out a negative charge leaves the nucleus more positive.
6. Gamma emission
A gamma ray is electromagnetic radiation. No protons or neutrons leave — the nucleus simply gets rid of spare energy, often straight after an alpha or beta decay has left it with some.
So gamma emission does not change the mass or the charge of the nucleus: the mass number and atomic number both stay the same. Same element, same isotope — just less energy.
9943Tc→9943Tc+00γ
Top: 99 = 99 + 0 ✓ · Bottom: 43 = 43 + 0 ✓ · still technetium
Edexcel iGCSE7. Neutron emission
Some very unstable nuclei throw out a single neutron. The mass number goes down by 1, but the number of protons is unchanged — so it is the same element, just a different isotope.
134Be→124Be+10n
Top: 13 = 12 + 1 ✓ · Bottom: 4 = 4 + 0 ✓ · still beryllium, one neutron lighter
8. Finding a missing number
Most exam questions give you an equation with a gap. The method never changes:
- Top numbers: work out what the missing mass number must be to make both sides add up.
- Bottom numbers: do the same for the atomic number.
- Name the element from its atomic number, using the periodic table. Never just copy the symbol from the left: if the atomic number has changed, so has the element.
23892U→??Th+42α
Top: 238 − 4 = 234 · Bottom: 92 − 2 = 90 · so it is thorium-234
✗ Loses the mark
“In beta decay the atomic number goes down by 1, because the nucleus loses a negative particle.”
✓ Gets the mark
“In beta decay the atomic number goes up by 1, because a neutron has turned into a proton.”
✗ Loses the mark
“In alpha decay the mass number goes down by 2.”
✓ Gets the mark
“In alpha decay the mass number goes down by 4 and the atomic number goes down by 2.”
✗ Loses the mark
“Gamma emission turns the nucleus into a new element.”
✓ Gets the mark
“Gamma emission does not change the mass number or the atomic number, so the element stays the same.”
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How to write each answer
"Describe the effect on the nucleus" questions want two numbers and a conclusion. These are the sentences that get the marks — learn the shape, then swap in your numbers.
“Describe the effect of alpha decay on the nucleus.”
The mass number decreases by 4 and the
atomic number decreases by 2, so a
new element is formed.
“Describe the effect of beta decay on the nucleus.”
A neutron changes into a proton. The
mass number stays the same and the
atomic number increases by 1, so a
new element is formed.
“Describe the effect of gamma emission on the nucleus.”
The mass number and the atomic number
do not change. The nucleus loses energy.
Edexcel iGCSE“Describe the effect of neutron emission on the nucleus.”
The mass number decreases by 1 and the
atomic number stays the same, so it is the
same element but a different isotope.
“Show that this equation is balanced.”
Top: 210 = 206 + 4, so
mass is conserved. Bottom: 84 =
82 + 2, so charge is conserved.
the numbers you are describing how they change the conclusion
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Worked examples
Cover the answer, try it, then check. Write the top and bottom sums out every time — that is where the marks are.
Example 1 — completing an alpha equation
Uranium-238 decays by alpha emission to form thorium. Complete the equation.2 marks
23892U→??Th+42α
Top — mass number: 238 − 4 = 234
Bottom — atomic number: 92 − 2 = 90
Answer: 23490Th
Bottom — atomic number: 92 − 2 = 90
Answer: 23490Th
Mark scheme: one mark for 234, one mark for 90.
Example 2 — completing a beta equation and naming the element
Strontium-90 is a beta emitter. Find the mass number and atomic number of X, and name the element.3 marks
9038Sr→??X+0−1β
Top — mass number: 90 − 0 = 90
Bottom — atomic number: 38 − (−1) = 38 + 1 = 39
Element: atomic number 39 on the periodic table is yttrium, Y
Answer: 9039Y
Bottom — atomic number: 38 − (−1) = 38 + 1 = 39
Element: atomic number 39 on the periodic table is yttrium, Y
Answer: 9039Y
Common slip: writing 37. Taking away a negative adds — and beta decay always takes the atomic number up, so 37 can't be right.
Example 3 — identifying the radiation
Radon-222 decays to polonium-218. What is particle X?2 marks
22286Rn→21884Po+X
Top — mass number: 222 − 218 = 4
Bottom — atomic number: 86 − 84 = 2
Answer: mass number 4 and atomic number 2 is an alpha particle, 42α (or 42He — the same thing)
Bottom — atomic number: 86 − 84 = 2
Answer: mass number 4 and atomic number 2 is an alpha particle, 42α (or 42He — the same thing)
Tip: work out the two numbers first, then match them to the table in section 1. Don't guess from the names.
Example 4 — two decays in a row
A nucleus of thorium-234, 23490Th, decays by beta emission. The nucleus it forms also decays by beta emission. What nucleus is left at the end?3 marks
First beta decay: mass number stays 234, atomic number 90 + 1 = 91 (protactinium)
Second beta decay: mass number stays 234, atomic number 91 + 1 = 92
Element: atomic number 92 is uranium
Answer: 23492U
Second beta decay: mass number stays 234, atomic number 91 + 1 = 92
Element: atomic number 92 is uranium
Answer: 23492U
Why it works: do one decay at a time. Two betas leave the mass number alone twice and add 1 to the atomic number twice.
Example 4 — neutron emission
A nucleus of beryllium-13 emits a neutron. Complete the equation, and explain why the element does not change.3 marks
134Be→??Be+10n
Top — mass number: 13 − 1 = 12
Bottom — atomic number: 4 − 0 = 4
Answer: 124Be
Bottom — atomic number: 4 − 0 = 4
Answer: 124Be
Explanation: the atomic number is still 4, so the nucleus still has 4 protons and is still beryllium. Only the number of neutrons has changed, so it is a different isotope of the same element.
📘 Now do it in your workbook
Equations with gaps to fill, particles to identify and "describe the effect" questions — with worked answers at the back so you can mark your own.
AQA GCSE Physics Workbook · ATOMIC STRUCTURE · page 8 Edexcel iGCSE Physics Workbook · RADIOACTIVITY · page 7
⬇ Free: page 8 (PDF)
⬇ Free: page 7 (PDF)
Get the full workbook on Amazon
Get the full workbook on Amazon
Free sample = the page for this lesson. The full workbook covers the whole topic for your board, with exam-style questions and worked answers.
✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this spec point.
Don't forget to hit “Mark complete” at the bottom of the lesson.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook page above cover every mark.
▲ In GHL you can also use the lesson's built-in video field instead of this embed.
Now put it into practice
Watching is the easy bit — nuclear equations only become automatic once you have filled in a few gaps yourself. Page 8 of the workbook is free, and the full book covers every spec point in Topic 4 Atomic Structure with worked answers.
Watching is the easy bit — nuclear equations only become automatic once you have balanced a few yourself. Page 7 of the workbook is free, and the full book covers the whole of Section 7 Radioactivity and particles with worked answers.
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