Particle interactions and equationsEdexcel International A Level Physics: Revision notes
Section 1
Three conserved quantities
In every particle interaction, three quantities must be the same before and after:
- charge
- baryon number
- lepton number
To test an interaction, add up each quantity on the left of the equation and on the right. If any one differs, the interaction cannot happen.
Section 2
Values to use
Use these values when adding up:
- proton: charge +e, baryon number +1, lepton number 0
- neutron: charge 0, baryon number +1, lepton number 0
- electron: charge −e, baryon number 0, lepton number +1
- positron: charge +e, baryon number 0, lepton number −1
- electron neutrino: charge 0, baryon number 0, lepton number +1
- electron antineutrino: charge 0, baryon number 0, lepton number −1
- photon and mesons: baryon number 0, lepton number 0
Do not forget that antileptons count −1. An antineutrino has lepton number −1, not 0.
Section 3
Checking whether an interaction is possible
Work through the three quantities in turn.
Example: is p + e⁻ → n + νₑ possible?
- Charge: (+1) + (−1) = 0 on the left; 0 + 0 = 0 on the right. Conserved.
- Baryon number: 1 + 0 = 1 on the left; 1 + 0 = 1 on the right. Conserved.
- Lepton number: 0 + 1 = +1 on the left; 0 + 1 = +1 on the right. Conserved.
All three are conserved, so the interaction is possible.
If one quantity fails, say which one and give both totals. For example, p → e⁺ + γ fails because the baryon number goes from 1 to 0.
Write the three totals under the equation in a small table. It is quicker and earns the marks for showing working.
Section 4
Writing and completing particle equations
Beta decays are the main examples.
- Neutron decay (β⁻): n → p + e⁻ + ν̄ₑ
- Proton decay in a nucleus (β⁺): p → n + e⁺ + νₑ
- Antineutrino capture: p + ν̄ₑ → n + e⁺
- Electron capture: p + e⁻ → n + νₑ
In neutron decay the electron has lepton number +1, so the particle emitted with it must have −1: an antineutrino. In β⁺ decay the positron has −1, so the neutrino emitted has +1: a neutrino.
To find an unknown particle, calculate the charge, baryon number and lepton number it must carry, then match them to a known particle.
Section 5
Interpreting equations
An equation tells you what the interaction produces, and the conservation laws tell you what it is allowed to produce.
For the pion decay π⁺ → μ⁺ + νμ: charge is +1 on both sides. Baryon number is 0 on both sides, since a pion is a meson. Lepton number is 0 on the left and (−1) + (+1) = 0 on the right.
A reaction that fails a test might be rescued by adding the missing particle. p + p → p + n + e⁺ fails on lepton number, but adding νₑ on the right makes it work.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Particle interactions and equations
- Free neutrons are released inside a research reactor. A free neutron is unstable and decays into a proton, an electron and one other particle, which is almost impossible to detect. Physicists use the conservation laws to work out what that third particle must be. The electron has lepton number +1 and the electron neutrino has lepton number +1; their antiparticles have lepton number −1.Show that charge and baryon number are both conserved in the decay n → p + e⁻ + ν̄ₑ.2 marks
- A detector next to a nuclear reactor identifies reactor antineutrinos by the reaction they cause with protons in a large water tank. The team also considers other reactions that might, in principle, be used. In these questions the proton and neutron each have baryon number +1, the electron and the electron neutrino each have lepton number +1, and the positron and the electron antineutrino each have lepton number −1.Deduce whether the reaction p + e⁻ → n + νₑ is possible, showing your working for each quantity.2 marks
- A cosmic-ray laboratory records two decays. In the first, a proton in a neutron-deficient nucleus changes into a neutron and emits a positron. In the second, a positive pion (a meson) decays into an antimuon, μ⁺, and a muon neutrino, νμ. Muons and muon neutrinos have lepton number +1; antimuons have lepton number −1. The electron has lepton number +1 and the positron −1.Write the particle equation for the first decay, and use lepton number to justify the type of neutrino that must be emitted with the positron.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).