Example 1
Check neutron → proton + electron + electron antineutrino.
Charge: 0=+1−1+0. Baryon number: 1=1. Electron-family lepton number: 0=+1−1. The counts balance.
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Year 12 · SACE Stage 2
Conservation rules and annihilation
Balance charge, baryon and lepton numbers and calculate annihilation energy.
Method and worked examples
In the reactions considered here, conserve electric charge, baryon number and lepton number. A quark has baryon number +⅓ and an antiquark −⅓; a baryon has+1 and an antibaryon −1. A lepton has lepton number +1, its antilepton −1, and other particles zero. At this school level, track electron, muon and tau lepton families separately when the reaction specifies them.
Beta-minus decay changes d to u: a neutron becomes a proton, electron and electron antineutrino. Beta-plus changes u to d: a proton becomes a neutron, positron and electron neutrino when energetically allowed. Particle–antiparticle annihilation can produce photons, carrying the original rest energy and any initial kinetic energy. For an electron–positron pair initially at rest, two opposite photons share 2mec2, conserving both energy and momentum.
Example 1
Example 2
Use me=9.11×10−31kg and c=3.00×108ms−1. Find rest energy released by electron–positron annihilation.
E=2mec2=1.64×10−13J. For an initially stationary pair, each of two opposite photons has 8.20×10−14J.
Watch out: Particle rest energy becomes other forms, commonly photons; total energy and momentum remain conserved.