Question

If the electron e − and the positron e + both have rest energy 0.51 MeV, nd the minimum energy a particle of light γ (a photon) can have in the reaction e + + e − = γ + γ. Why can't there be a reaction producing only one photon, e + + e − = γ? Assume the center-of-mass frame.

Answer 1

For Total energy and momentum to be conserved, the minimum energy of the photons released is equal to twice the rest mass energy of an electron that is
`2 * 0.51 MeV = 1.02 MeV`

The annihilation of electron -positron cannot produce a single photon. It is prohibited by the law of conservation of energy and momentum.