In gamma-ray astronomy, the existence of positrons (e+) can be inferred by a characteristic gamma ray that is emitted when a positron and an electron (e−) annihilate. For simplicity, assume that the electron and positron are at rest with respect to an Earth observer when they annihilate and that nothing else is in the vicinity.
(a) Consider the reactions e− + e+ → γ, where the annihilation of the two particles at rest produces one photon, and e− + e+ → 2γ, where the annihilation produces two photons.
Explain why the first reaction does not occur, but the second does.
(b) Suppose the reaction e− + e+ → 2γ occurs and one of the photons travels toward Earth. What is the energy of the photon?