Question

In Quantum Mechanics there's an interesting phenomenon where an electron and a positron collide. Since these are antiparticles of each other, when they collide they annihilate and produce two equal energy photons. Why must this interaction produce two photons as opposed to one? Use some math in your logic.

Answer 1

Electron and positron are anti particle of each other having equal mass 0.51 Mev. When they colloid in free space they produce two gamma photon having same energy. This collision is governed by conservation laws. Energy and momentum are conserved in this reation but if single photon is formed then energy may remain conserved but momentum can't be conserved. Momentum of photon is given by E₁/C .

Net momentum before collision is zero. Hence net momentum after collision must be zero.

0 = E₁/C - E₂/c

Therefore production of two photons are necessary for pair annhilltion. One photon may be produced when collision occurs in presence of nucleus.