Particle Annihilation: Electron-Positron & Photon Energies

[pyo]

Hey i am doing some studying and when it comes to the subject of nuclear decays it says that when an electron and positron annihilate at rest they produce two photons with equal energys. Can someone try to explain to me why the photons have equal energies and how come there must be two photons produced instead of one in this case? Is the conservation of momentum the answer here?

 

[NewScientist]

Yep, its 4-momentum

 

[Physics Monkey]

Yes, since the initial system (electron and positron at rest) had no momentum, the final system must also have no momentum. Clearly this means that the pair of photons must be emitted in opposite directions and with equal magnitude for their momenta. Now, how is the energy of a photon related to its momentum?

 

[pyo]

Great thanks !