Question: When a positron and an electron are produced by a Gamma Ray only one ray is needed, but when they annihilate each other two gamma rays are produced. Why is this? Thanks

James M Monk answered on 13 Jun 2011:

This is due to the conservation of mass. The electron and positron have mass, both due to their rest mass and their collision energy (remember E=mc^2). A single photon (gamma ray) is massless, so you need two photons travelling in opposite directions in order to have a mass over-all. So when an electron and positron annihilate there must be two photons as a result.

For the same reason, a single real gamma ray cannot decay spontaneously into an electron-positron pair because mass would not be conserved. When gamma rays from space strike the Earth’s upper atmosphere (or some other material) they interact with the atmosphere, and there is a combined energy/mass of the gamma ray and the particles in the atmosphere, which allows the production of a pair of electron/positron whilst conserving mass.

Interestingly, even in completely empty space there is still the cosmic microwave background of very low energy photons. A single gamma ray can, if it has a sufficiently high energy, interact with the microwave background and thus produce a pair of particles.