When a particle meets its antiparticle, they annihilate: their mass is converted completely into energy, usually in the form of photons. For an electron and a positron:e- + e+ → γ + γ Two photons are produced, not one. If the particles are at rest, their total momentum is zero, so the photons must move off in opposite directions with equal energies, so that momentum is conserved. A single photon always carries momentum, so it could not be the only product.
Energy is conserved: the total energy of the photons equals the rest energy of both particles plus any kinetic energy they had. For an electron and positron at rest, each photon has energy equal to the rest energy of one electron, 0.511 MeV. Charge (–1 + 1 = 0) and lepton number (+1 + (–1) = 0) are also conserved.Annihilation is used in PET (positron emission tomography) scanners: a positron from a tracer annihilates with an electron in the body, and detectors pick up the pair of gamma photons travelling in opposite directions.Worked example: find the frequency of each photon from electron-positron annihilation at rest.
E = 0.511 × 106 × 1.6 × 10-19 = 8.18 × 10-14 J
f = E/h = 8.18 × 10-14 / 6.63 × 10-34 = 1.23 × 1020 HzA proton and antiproton annihilating at rest produce photons with far more energy: 938 MeV each.
Energy is conserved: the total energy of the photons equals the rest energy of both particles plus any kinetic energy they had. For an electron and positron at rest, each photon has energy equal to the rest energy of one electron, 0.511 MeV. Charge (–1 + 1 = 0) and lepton number (+1 + (–1) = 0) are also conserved.Annihilation is used in PET (positron emission tomography) scanners: a positron from a tracer annihilates with an electron in the body, and detectors pick up the pair of gamma photons travelling in opposite directions.Worked example: find the frequency of each photon from electron-positron annihilation at rest.E = 0.511 × 106 × 1.6 × 10-19 = 8.18 × 10-14 J
f = E/h = 8.18 × 10-14 / 6.63 × 10-34 = 1.23 × 1020 HzA proton and antiproton annihilating at rest produce photons with far more energy: 938 MeV each.