Energy of resulting Gamma Rays after particle annihilation

[Fronzbot]

Homework Statement

An electron and a positron are moving side by side in the +x direction at 0.50c when they annihilate each other creating two gamma rays. What is the energy of each photon?

Homework Equations

(mc² + K₊) + (mc² + K_-) = E₁ + E₂

The Attempt at a Solution

I solved out that K = mc² = 0.511MeV ( $$\gamma$$ - 1 ) where $$\gamma$$ = 1.155. Therefore K should equal 79.1keV. Plug this into the equation up in that "relevant equations" section and I get E₁ + E₂ = 1.18MeV.

I know the answer is E₁ = .885 MeV in the +x direction and E₂ = .295 MeV in the -x direction as my prof gave us the answers. These values verify that the calculations I performed earlier are correct.

However, I don't know how to obtain the answers. It seems like it should be stupidly simple, but I just can't figure it out. I tried using hc/$$\lambda$$ = E to solve for wavelength and then tried plugging stuff in again to get energy but that doesn't work. And even if it did, how would I know direction? If anyone can just give me that slight push in the right direction I'd be very grateful!

 

[nickjer]

You have one equation and two unknowns (E_1, E_2). So you might want to use conservation of momentum to help solve for both unknowns.