The problem is listed as follows: Show that conservation of energy and momentum require at least two gamma rays to e emitted in the annihilation of an electron by a positron.
p(initial) = p(final)
E(initial) = E(final)
Total rest mass = 1.0218 MeV/c^2
The Attempt at a Solution
I'm checking to see whether my answer to this question is sufficient. The book (Wong) introduces the idea of a proton and anti-proton annihilation at rest, so I assumed that this process could occur at rest as well. Is that ok?
I first tried the production of a single gamma ray. However, since initial p=0, final p=0 as well. However, since initial E=/=0, and initial E = final E, then final E =/=0. These two are in contradiction to each other, since p=hf/c and E=hf. Combining, this gives p=E/c. Since c=/= 0, this equation is impossible.
I then explained that if the rays were travelling in opposite directions, this would allow for final p=0, fulfilling initial p=final p.
Do you guys believe that this is a sufficient answer? It is based upon the presumption that such an interaction can occur at rest.
Let me know, thanks.