Nuclear equations, conservation and beta decay
Key idea: A reviewed, static H2 Physics learning chain for all official Nuclear Physics outcomes, from Rutherford evidence to fusion and fission.
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The core idea
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Big question: Which quantities must balance in a nuclear equation?
Nuclear reactions conserve charge, nucleon number, energy and momentum. In beta-minus decay, a neutron becomes a proton while an electron and antineutrino are emitted; the antineutrino accounts for the continuous beta energy spectrum while preserving energy and momentum. Balance A and Z first, then interpret the energy.
Balance more than the visible symbols
A nuclear equation conserves nucleon number A and charge Z. It must also conserve total mass-energy and momentum. Identify an unknown nuclide from both A and Z, then check whether the proposed reaction is energetically possible.
In beta-minus decay, a neutron changes to a proton and emits an electron and electron antineutrino: n → p + e⁻ + ν̄_e. A stays constant and nuclear Z rises by one. Detailed particle classification is not required.
Check your understanding: Complete ²³⁴₉₀Th → ²³⁴₉₁Pa + X.
X is ⁰₋₁e plus an antineutrino in beta-minus decay; A is unchanged and Z balances.
Use the continuous beta spectrum as evidence
If beta decay produced only a daughter nucleus and electron from a fixed initial state, two-body energy and momentum conservation would give the electron a fixed energy apart from recoil. Experiments instead show a continuous range up to an endpoint.
The antineutrino carries a variable share of energy and momentum, restoring conservation event by event. Energy is not 'lost'; it is distributed among electron, recoil nucleus and antineutrino.
Check your understanding: What key observation motivated the antineutrino proposal?
The continuous beta-electron energy spectrum, together with the need to conserve energy and momentum.
Key ideas to keep
- An emitted beta electron is created in the decay; it was not orbiting inside the nucleus.
- Beta decay changes Z but leaves A unchanged.
- A continuous electron spectrum requires energy shared with another particle.
See the reasoning
Worked example
Identify a reaction product using two conservation counts
Question: Balance ¹⁴₇N + ⁴₂He → ¹⁷₈O + X.
Step 1: Balance nucleon number
Why: Total A is conserved.
Working: 14 + 4 = 17 + Aₓ, so Aₓ = 1.
Step 2: Balance charge number
Why: Total nuclear charge is conserved.
Working: 7 + 2 = 8 + Zₓ, so Zₓ = 1.
Step 3: Identify and complete the equation
Why: A = 1 and Z = 1 identifies a proton.
Working: X = ¹₁H; energy and momentum must also balance even though they are not shown by A and Z.
Answer: Conserving nucleon number gives A = 1 and charge gives Z = 1, so X is ¹₁H. Mass-energy and momentum must also be conserved.
Check: Both sides have total A = 18 and total Z = 9.
Use a hint if needed
Practise with support
Try this
In beta-minus decay, state changes in A and Z.
Hint: A neutron becomes a proton.
Check your answer
A is unchanged and Z increases by one.
Now work without the hint
Practise independently
Your turn
Write and check a nuclear equation and explain antineutrino evidence.
Check your answer
Conserve A and charge explicitly, then conserve mass-energy and momentum. A continuous beta energy spectrum contradicts fixed two-body energy sharing; an antineutrino carries the missing variable energy and momentum.
Avoid these traps
Common mistakes
Common mistake
Only nucleon number must balance.
What is wrong with this reasoning?
Show better thinking
Charge, mass-energy and momentum must also be conserved.
Common mistake
The beta electron alone receives a fixed decay energy.
What is wrong with this reasoning?
Show better thinking
Electron, recoil and antineutrino share energy and momentum.
Write for the examiner
Exam guidance
Balance nucleon and proton numbers on both sides before calculating any energy release.
Exam-style practice [6 marks]
Complete ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + X and name conserved quantities.
Plan before you answer
- Balance A and Z.
- Identify the emitted particle.
- State the other conserved quantities.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
X = ⁴₂He. Nucleon number, charge, mass-energy and momentum are conserved.
Come back in three days
Check what stayed with you
Recall question
Why does beta-minus decay keep nucleon number unchanged?
Check the answer
A neutron changes into a proton; the total number of nucleons is unchanged.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 20 excludes knowledge of positron emission in 20(g) and detailed knowledge of the antineutrino and particle zoo in 20(o). Nuclide equations conserve nucleon number, charge, mass-energy and momentum. Count data require background correction before population-law inference. Applications must relate half-life, penetration and ionisation to benefit and hazard. The binding-energy-per-nucleon curve, not a claim that mass disappears, explains fusion and fission energy release.
- GCE A-Level H2 PhysicsTopic 20(m) / Topic 20(n) / Topic 20(o) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027