Conservation laws and particle equations

The quantities to check

In every interaction these are conserved:

• charge Q
• baryon number B: +1/3 per quark, -1/3 per antiquark (+1 for baryons, -1 for antibaryons, 0 for mesons and leptons)
• lepton number L: +1 for leptons, -1 for antileptons, 0 for hadrons and photons

Energy and momentum are conserved too. If any one fails, the interaction cannot happen.

Beta decay as an example

• β- decay: n → p + e- + anti-ν_e. At quark level, d → u + e- + anti-ν_e. Check: Q 0 = +1 - 1 + 0; B 1 = 1; L 0 = 0 + 1 - 1.
• β+ decay (inside a nucleus): p → n + e+ + ν_e; at quark level, u → d + e+ + ν_e.

The neutrino or antineutrino is needed to conserve lepton number (and energy and momentum).

Writing and interpreting equations

• Write each particle with its symbol; make a table of Q, B and L on each side.
• An unknown particle X can be identified from what is needed to balance the equation.
• Remember antiparticles have opposite values of every quantity.

Worked example

Can p + p → p + n + π+ happen?

1. Q: 1 + 1 = 2; 1 + 0 + 1 = 2 ✓
2. B: 1 + 1 = 2; 1 + 1 + 0 = 2 ✓
3. L: 0 = 0 ✓

Answer: Yes: charge, baryon number and lepton number are all conserved

Check yourself

1. In β- decay, which particle is emitted along with the electron?
   • An electron antineutrino
   • An electron neutrino
   • A positron
   • A proton
   Show answer

   An electron antineutrino. The electron has L = +1, so an antineutrino (L = -1) keeps the total L at 0.

2. Which interaction is NOT allowed?
   • n → p + e- + anti-ν_e
   • p + p → p + p + π0
   • p + p → p + n + π0
   • π+ → μ+ + ν_μ
   Show answer

   p + p → p + n + π0. Charge: 2 on the left but 1 + 0 + 0 = 1 on the right.

3. What is the baryon number of a meson?
   Show answer

   0. A quark (+1/3) and an antiquark (-1/3) give 0.

4. What is the baryon number of an antiproton?
   Show answer

   -1. It is made of three antiquarks, each -1/3, so B = -1.

5. In the interaction n + ν_e → p + X, what is the charge of particle X, in units of e?
   Show answer

   -1. Charge on the left is 0, so 0 = +1 + Q_X and Q_X = -1. X is an electron.

6. What happens to the quarks in β+ decay?
   • A down quark changes into an up quark
   • A strange quark changes into an up quark
   • The quarks do not change
   • An up quark changes into a down quark
   Show answer

   An up quark changes into a down quark. A proton (uud) becomes a neutron (udd), so u → d.

7. What is the lepton number of a positron?
   • +1
   • -1
   • 0
   • +1/3
   Show answer

   -1. The positron is an antilepton.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.