The big idea: A nuclear power station can light a whole city from a tiny amount of fuel — because when a nucleus decays, its products come out very slightly lighter than the nucleus you started with.
That tiny bit of missing mass does not vanish — it turns into energy, which the products fly off with.
The link between the missing mass and the energy is one famous equation: E = mc².
Before the decay
- One parent nucleus, sitting still
- It has the larger total mass
- No kinetic energy yet (at rest)
After the decay
- Two products fly apart (e.g. a daughter nucleus + an alpha)
- Their total mass is slightly smaller — some mass has vanished
- That missing mass has turned into kinetic energy of the products
New words, plainly: Mass defect (Δm) = how much lighter the products are than the parent.
Released energy (Q) = the energy that the mass defect turns into; also called the disintegration energy.
u = the unified atomic mass unit, the handy unit for nuclear masses (1 u is about the mass of one proton).
| Nucleus / particle | Mass / u |
|---|---|
| Parent (before) | 226.025410 |
| Daughter (after) | 222.017580 |
| Alpha particle (after) | 4.002600 |
| Mass that vanished (Δm) | 0.005230 |
A shortcut for the energy: You could turn Δm into kilograms and multiply by c² — but the data booklet gives a faster route.
1 u is worth 931.5 MeV of energy. So once you have the mass defect in u, just multiply by 931.5 to get the energy released in MeV.
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To find the energy released you need just two steps: find the mass defect (parent mass − total product mass), then turn that mass into energy with E = mc².
- energy released, called the disintegration energy Q (J)
- mass defect Δm — the mass that disappears in the decay (kg)
- speed of light, 3.00 × 10⁸ m s⁻¹ (given constant)
Two units, one idea: In joules: put Δm in kilograms (1 u = 1.661 × 10⁻²⁷ kg) and multiply by c².
In MeV (faster): keep Δm in u and multiply by 931.5 (because 1 u = 931.5 MeV c⁻²).
Both give the same energy — pick whichever the question asks for.
A nucleus at rest decays by emitting an alpha particle. The masses are: parent = 226.025410 u, daughter = 222.017580 u, alpha = 4.002600 u. Show that the energy released is about 5 MeV. (1 u = 931.5 MeV c⁻².)
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How this is tested — a classic Paper 2 short-answer pair, usually two 'show that' parts:
Paper 1A
- A quick MCQ version — which product gets more kinetic energy, or which way Δm and Q go.
Paper 2
- Show ≈ 5 MeV: from atomic masses, find the mass defect and use E = mc² (the 931.5 shortcut).
- Show ≈ 98%: use conservation of momentum to show the light alpha carries almost all the energy.
The classic trap: Thinking the two products share the energy equally, or that the heavier one gets more. The opposite is true — the lighter one gets most of it.
Why the light product gets most of the energy: The parent starts at rest, so its total momentum is zero. After the decay the two products must have equal and opposite momentum (p) so they still add to zero.
Kinetic energy is KE = p² ÷ 2m. They share the same p, so the one with the smaller mass (the alpha) ends up with the bigger kinetic energy.
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Light product (alpha)
- Same size momentum p as the daughter (opposite direction)
- Small mass m
- KE = p² ÷ 2m → small m on the bottom means a BIG kinetic energy
Heavy product (daughter)
- Same size momentum p (recoils the other way)
- Large mass m
- KE = p² ÷ 2m → large m on the bottom means a small kinetic energy
Momentum sharing — what to compare
- Parent at rest → total momentum = 0 before and after
- Two products → equal and opposite momentum (same size p)
- Same p, but KE = p² ÷ 2m → lighter mass = more energy
- Energy split ratio: KEalpha : KEdaughter = mdaughter : malpha
The same decay gives a daughter of mass 222 u and an alpha of mass 4 u, released from a parent at rest. Show that the alpha particle carries about 98% of the released energy.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.