Explain beta-decay neutrinos and particle energies
Relate continuous beta-particle energies to energy sharing with neutrinos and distinguish alpha spectra.
Section 11 · Particle physics
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 11. These original particle models and equations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use atomic number, nucleon number, electric charge and conservation with signed values.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which neutral lepton is emitted with an electron in beta-minus decay?
What you will learn
- State the antineutrino emitted in beta-minus decay and neutrino in beta-plus decay
- Explain continuous beta energy using energy sharing
- Contrast discrete alpha energies with continuous beta energies
Beta decay emits a neutrino partner
In beta-minus decay, an electron antineutrino is produced with the electron. In beta-plus decay, an electron neutrino is produced with the positron.
The emitted (anti)neutrino carries away some of the decay energy and momentum. The beta particle therefore does not receive one fixed share of energy in every decay.
Alpha and beta energy distributions differ
Alpha particles from a given nuclear transition have discrete energies: the allowed nuclear energy changes give particular alpha energies.
Beta particles have a continuous range of energies because the available energy is shared variably between the beta particle and the (anti)neutrino, while the daughter nucleus also recoils. The neutrino's share can vary from one decay to another.
Pause and explain
Why is the beta-particle energy continuous?
Worked example
Why does beta-minus radiation have a continuous energy spectrum while alpha particles from a given transition have discrete energies?
Show the worked solution
- Beta-minus decay emits an electron and electron antineutrino.
- The energy share between these particles varies from decay to decay.
- An alpha transition has a specified discrete nuclear energy change, so alpha energies are discrete.
Answer The electron antineutrino shares beta-decay energy variably, giving beta particles a continuous range; alpha transitions give discrete alpha energies.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Complete the emitted neutral-particle label: β⁺ decay produces a positron and an electron _____. Explain the energy-spectrum consequence for β particles.
Give me a hint
Use the beta-plus partner and the variable energy sharing model.
Compare my reasoning
- Beta-plus decay produces an electron neutrino.
- The available energy is shared with the positron and neutrino.
- A variable share gives positrons a continuous range of kinetic energies.
Electron neutrino; variable energy sharing gives beta-plus particles a continuous energy range.
Look for these in your work
- Correct neutrino stated
- Energy sharing described
- Spectrum consequence derived
State the energy-spectrum difference between alpha particles and beta particles and give the reason for the beta distribution.
Give me a hint
Recall discrete alpha transitions and the additional lepton in beta decay.
Compare my reasoning
- Alpha particles from a given transition have discrete energies.
- Beta particles have a continuous energy range.
- The beta particle shares energy variably with an emitted (anti)neutrino.
Alpha energies are discrete; beta energies are continuous because the (anti)neutrino carries a variable share of the decay energy.
Look for these in your work
- Both spectra contrasted
- Neutrino included
- Energy reason stated
A beta particle is measured with less than the maximum available decay energy. Explain how conservation of energy can still hold.
Give me a hint
Include all products and nuclear recoil in the energy account.
Compare my reasoning
- The beta particle does not receive all the available energy.
- The (anti)neutrino carries a variable share, and the daughter nucleus can recoil.
- Together the products account for the energy released.
Energy is conserved because the neutrino or antineutrino and recoiling daughter carry the energy not received by the beta particle.
Look for these in your work
- Partial beta energy recognised
- Other carriers included
- Conservation restored
Common mistakes
- Saying antineutrinos are emitted in beta-plus decay
- Claiming beta particles all receive the same energy
- Explaining the continuous spectrum as a range of parent isotope masses
What can you explain now?
Which neutral lepton is emitted with an electron in beta-minus decay?
Compare with the explanation
Electron antineutrino
β⁻ decay produces e⁻ and ν̄ₑ.
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Make it stick
What extra decay product explains why beta particles do not all have one energy?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.