In pair annihilation, an electron and a positron destroy each other to produce gamma radiation. How is the momentum conserved?

During pair annihilation of electron and positron the result of the annihilation is generation of two gamma ray photon. Now when electron and positron come at each other they carry kinetic energy and the equation of the collision is

where

is the kinetic energy of the positron, is the kinetic energy, m is the mass of the particles apart from positron and electron, c is the speed of light = h is the planks constant = . v is the frequency.

So the energy equation before the collision is

_____________1

With both as initial kinetic energy was zero, therefore the energy equation before collision is

And the energy equation after collision is

_____________2

With

The equation formed is

The gamma photons created have equal energy of 0.511 MeV making the motion of gamma photons in opposite direction, now according to the law of conservation of momentum, when two objects in an isolated condition have same momentum before and after collision then the system’s momentum is conserved. As you can see that both equation (1) and (2) are equal; hence, proving that the momentum is conserved both before and after collision.