Kinetic energy of positron/electron collision

[Kreamer]

Homework Statement

A positron is a particle that has the same mass but opposite charge of an electron. An electron and a positron are shot directly toward each other by a particle accelerator. They start very far from each other, each with a kinetic energy of 5 × 10−14 J. When they collide, they disintegrate and completely transform into two photons. What is the total (combined) kinetic energy of the two photons after the collision?

A. 8 × 10−14J
B. 1.6 × 10−14J
C. 1.0 × 10−13 J
D. 2.6 × 10−13J
E. 1.3 × 10−13 J

The attempt at a solution
I know the answer is D. 2.6 x 10-13J from an answer key however I am a little confused as to how to get that answer.
First I started thinking about how momentum is always conserved however photons have no mass so the momentum of the photons is 0 correct? So how is momentum conserved? And how is the answer D?

 

[Bhumble]

The momentum of the positron and electron system is zero since they are equal masses moving at equal speeds in opposite directions so their vectorial sum is zero. Which will be the same for the two photons since they will be equal speeds in opposite directions.

As far as the exact energy this is going to be determined the key to this problem is actually conservation of energy. I didn't double check but I'm assuming the energy needs to be calculated relativistically.

 

[Kreamer]

Ah that does make sense. However I am having a little trouble with the actual calculating of the photons energy. I figured with conservation of energy the initial kinetic energy would equal the final kinetic energy. I still do not fully understand how to calculate the final energy of the photons and how the given answer would be correct.

 

[Bhumble]

E initial = mc^2 + KE = E final

The idea is that the mass energy of the electron/positron pair is converted to additional kinetic energy of the photons.

 

[Kreamer]

Ahhh I am forgetting the basics! Forgot about rest mass energy. Thank You!