Answer
0.34 MeV
Work Step by Step
The final energy of the photons equals the total energy (KE plus rest mass energy) of the initial particles.
The electron and the positron have a rest mass energy of 0.511 MeV each.
The photons have an energy of 0.85 MeV each.
The electron and the positron must have carried 0.85 MeV – 0.511 MeV = 0.34 MeV of kinetic energy per particle.
Check: the final momentum of the photons is 0, so the 2 particles started with equal and opposite momentum vectors, as expected, and had the same initial kinetic energy. Momentum and mass energy are both conserved.
