The big idea: The carbon in a museum's ancient bone is slowly turning into nitrogen, one nucleus at a time — a decaying nucleus becomes a new nucleus (the daughter) and shoots out a small particle. We write this as a nuclear equation.
Two numbers must balance — be the same on both sides:
- the nucleon number A (the top number — protons + neutrons) - the proton number Z (the bottom number — protons)
Balance those two and you have found the daughter nuclide.
New words, plainly: Parent = the nucleus before it decays.
Daughter = the new nucleus made by the decay.
Nuclide = a specific nucleus, written (top = nucleon number, bottom = proton number).
Conserved = the same before and after — it does not change.
- nucleon number (top) = protons + neutrons
- proton number (bottom) = number of protons (sets the element)
- the parent nuclide (before decay)
- the daughter nuclide (the new element formed)
The one rule that does everything: Top row adds up the same. Bottom row adds up the same.
That single check finds the daughter every time — you do not need to memorise long lists.
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There are two decays you must be able to balance. Each emits a different particle, so each changes A and Z in its own fixed way.
Alpha (α) decay throws out an alpha particle — a helium-4 nucleus, 2 protons and 2 neutrons, written . So the top falls by 4 and the bottom falls by 2:
- parent nuclide before decay
- daughter: nucleon number falls by 4, proton number by 2
- alpha particle = a helium-4 nucleus (2 protons + 2 neutrons)
Beta-minus (β⁻) decay happens when a neutron turns into a proton inside the nucleus, firing out an electron (written ) and an antineutrino. The nucleon number stays the same, but the proton number goes up by 1:
- parent nuclide before decay
- daughter: nucleon number unchanged, proton number rises by 1
- beta-minus particle = an electron (created when a neutron becomes a proton)
- antineutrino — emitted with the electron (no charge, ≈ no mass)
How A and Z change: Lock in the two patterns — then you never have to think:
Alpha: A drops by 4, Z drops by 2.
Beta-minus: A stays the same, Z goes up by 1.
| Decay | What leaves the nucleus | Nucleon number A | Proton number Z |
|---|---|---|---|
| Alpha (α) | a helium-4 nucleus (2 p + 2 n) | falls by 4 (A → A − 4) | falls by 2 (Z → Z − 2) |
| Beta-minus (β⁻) | an electron + an antineutrino | unchanged (A → A) | rises by 1 (Z → Z + 1) |
Polonium-210 (A = 210, Z = 84) decays by alpha emission. Find the nucleon number and proton number of the daughter nuclide.
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Caesium-137 (A = 137, Z = 55) decays by beta-minus emission. Find the nucleon number and proton number of the daughter nuclide.
Model answer plan
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How this is tested — balancing decay equations is a guaranteed, quick-mark skill:
Paper 1A
- A one-step determine — given a parent and the decay type, pick the daughter's A and Z.
- Or follow a short chain (alpha then beta-minus) and find the final nucleus.
Paper 2
- Complete a nuclear equation — fill in the missing A, Z or particle.
- Or identify the daughter element from its proton number.
The classic trap: In beta-minus decay, dropping Z by 1 instead of raising it. The electron's −1 charge means Z must go up by 1 to balance.
Decay chains: do one step at a time: If a nucleus emits two particles in a row, apply the changes one after the other.
Keep a running total of A and Z, updating after each emission — never try to do both at once.
Thorium-230 (A = 230, Z = 90) first emits an alpha particle, then the nucleus it forms emits a beta-minus particle. (a) Find the nucleon and proton number after the alpha emission. (b) Find the nucleon number, proton number and neutron number of the FINAL nuclide.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.