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Conservation laws and particle equationsEdexcel A-Level Physics: Revision notes

Section 1

Three quantities to check

In a particle interaction or decay, three quantities are conserved and you check them with simple sums of the values before and after.

  • Charge: total charge in units of e.
  • Baryon number (B): +1 for each baryon (proton, neutron), −1 for each antibaryon, 0 for mesons, leptons and photons. Each quark has +1/3.
  • Lepton number (L): +1 for each lepton (electron, muon, neutrinos), −1 for each antilepton (positron, antineutrinos), 0 for hadrons and photons.

Energy and momentum must also be conserved, but charge, baryon number and lepton number are quick tests.

Key termsbaryon numberlepton numberconservation of charge

Section 2

Deciding whether an interaction is possible

Write the particle equation, then add up charge, B and L on each side.

  • If any of the three changes, the interaction is not possible.
  • If all are conserved, the interaction is allowed by these laws.

Worked example: is p → e⁺ + π⁰ possible? Charge: +1 → +1 + 0, conserved. B: +1 → 0 + 0, not conserved. L: 0 → −1 + 0, not conserved. It is impossible.

Worked example: p + p → p + n + π⁺. Charge: +2 → +1 + 0 + 1, conserved. B: 2 → 1 + 1 + 0, conserved. L: 0 → 0. It is allowed.

Key termsparticle equation
Common mistake

Forgetting that an antilepton has lepton number −1. A positron or an antineutrino counts as −1, not +1.

Section 3

Beta decay and electron capture

  • β⁻ decay: n → p + e⁻ + ν̄e. L: 0 → 0 + 1 − 1 = 0. The antineutrino is needed to balance the electron's lepton number.
  • β⁺ decay: p → n + e⁺ + νe. L: 0 → −1 + 1 = 0. It occurs in a nucleus, e.g. ¹¹₆C → ¹¹₅B + e⁺ + νe.
  • Electron capture: p + e⁻ → n + νe. L: +1 → +1.

In each, charge and baryon number are conserved. Nucleon number does not change, and proton number changes by one.

Key termsβ⁻ decayβ⁺ decayelectron capture

Section 4

Decays of pions and muons

Pions and muons give practice in the conservation laws.

  • π⁺ → μ⁺ + νμ: charge +1 → +1, B 0 → 0, L 0 → −1 + 1 = 0.
  • π⁻ → μ⁻ + ν̄μ: charge −1 → −1, L 0 → +1 − 1 = 0.
  • μ⁻ → e⁻ + ν̄e + νμ: L +1 → +1 − 1 + 1 = +1.

An antiparticle is needed whenever a lepton is created without a balancing antilepton.

Key termspionmuon
Exam tip

When a decay seems to violate lepton number, check whether a neutrino or antineutrino is missing. Choose the one that balances.

Section 5

Finding a missing particle

To find an unknown particle X, use each conservation law in turn.

Worked example: n + νe → p + X. Charge: 0 + 0 → +1 + Q, so Q = −1. B: 1 + 0 → 1 + B, so B = 0. L: 0 + 1 → 0 + L, so L = +1. X has charge −1, B = 0, L = +1, so it is an electron.

Give the particle and its type (lepton, meson or baryon) from the numbers you find.

Key termsinteraction

Must know

  • Check charge, baryon number and lepton number before and after
  • Antiparticles have opposite values; a positron or antineutrino has L = −1
  • If any quantity changes, the process cannot occur
  • β⁻ needs an antineutrino; β⁺ and electron capture need a neutrino

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Conservation laws and particle equations

  1. In β⁻ decay a neutron in an unstable nucleus changes into a proton, and an electron and a third particle X are emitted. The neutron and proton are baryons with baryon number +1, and the neutron, proton and electron have lepton numbers 0, 0 and +1 respectively.
    Write the particle equation for the decay and show that charge and lepton number are conserved.2 marks
  2. A positive pion (π⁺) decays into a positive muon and a muon neutrino, π⁺ → μ⁺ + νμ. The pion is a meson with baryon number 0 and lepton number 0. Muons and neutrinos are leptons with lepton number +1, and their antiparticles have lepton number −1.
    The positive muon decays as μ⁺ → e⁺ + νe + ν̄μ. Show that charge and lepton number are conserved in this decay.2 marks
  3. Particle physicists analyse the products of high-energy collisions between protons. Pions are mesons with baryon number 0 and lepton number 0; the π⁺, π⁻ and π⁰ have charges +1 e, −1 e and 0. An antiproton has charge −1 e and baryon number −1.
    In one collision, p + p → p + n + X, where X is a single particle. Use conservation laws to identify X.3 marks
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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).