Why Two Gamma Rays is Produced during Annihilation?

 1γ→1e−+1e+ ( pair production)

Then why

1e−+1e+→2γ (annihilation of matter)

Instead of

1e−+1e+−>1γ ?

The process e++e−→γcannot satisfy both momentum and energy conservation at the same time. To see this, consider a reference frame in which the system's total momentum is zero (that is, the electron has the opposite momentum to the positron). A basic Lorentz transformation can always be used to choose this reference frame.

Now, the photon produced must have zero total momentum. However, since photons must still travel at the speed of light, this is impossible. More importantly, if the emitted photon has the frequency ω, then the momentum must  satisfy |k|=ℏω/c. Since ℏω is the energy of the photon, ℏω≥2me   by energy conservation, and so |k|>0.

The e++e−→γ+γmechanism is completely acceptable since the center-of-mass frame can still be perfectly fulfilled even though the outgoing photons have opposite momenta.

I hope this helped you to be more understand!