Question

Suppose that an electron and a positron collide head-on. Both have kinetic energy of 1.64 MeV and rest energy of 0.511 MeV. They produce two photons, which by conservation of momentum must have equal energy and move in opposite directions. What is the energy Ephoton of one of these photons?

Answer 1

The electron and positron collide and annihilate each other, converting their total energy (sum of kinetic and rest energy) into energy carried by two photons:

2(1.64MeV  + 0.511MeV) = 2$E_{photon}$

$E_{photon}$ = 1.64MeV  + 0.511MeV

$E_{photon}$ = 2.15MeV