Positronium Decay: Find Momentum of Gamma Rays

[Newtime]

Homework Statement

Consider positronium decay. Show the magnitude of the momentum for each gamma ray is $$m_0c$$ where $$m_0$$ is the mass of the electron.

Homework Equations

$$E=\sqrt{p^2c^2+m^2c^4}, p=h\nu/v$$

The Attempt at a Solution

I'm not sure how to start this one, though I suspect the solution is elementary. Should I use conservation of energy or momentum or both? Are the above equations relevant? I come from a mathematics background, not a physics background, so problems which require "energy considerations" still confuse me.

 

[Newtime]

Here's a first attempt: we use conservation of momentum and find $$|p_{\text{before}}|=|p_{\text{after}}| \Rightarrow 2\gamma m_0v =2\gamma h\nu / c \Rightarrow m_0v=h\nu/c = |p_i|$$ for each gamma ray $$p_i$$ where the last inequality is from a previous exercise which asks us to show this for each photon. So I end up with *almost* the solution except I have v instead of c. Where did I go wrong?