# Electron and Positron Annihilation

1. May 9, 2010

### Krappy

1. The problem statement, all variables and given/known data

An electron traveling at 0.8c annihilates with a positron that is at rest, producing two photons. One of the produced photons travels in the direction of the electron. Determine the energy of each of the photons.

2. Relevant equations

$$p_{photon} = \frac{E}{c}$$

$$P_{electron} = \frac{m_e v}{\sqrt{1-v^2/c^2}}$$

3. The attempt at a solution

$$p_i = p_f$$

$$\frac{m_e v}{\sqrt{1-v^2/c^2}} = 2p_{photon}$$

$$E = \frac{m_e 0.9 c^2}{2 \sqrt{1-0.81}} = 8.46 \times 10^{-14} J$$

First of all, I already searched about this frequent topic, but didn't manage to solve the issues. My "issue" is regarding the final momentum. I assume that both photons will have the same momentum, but I don't think that's right.

Thank You ;)

2. May 9, 2010

### diazona

No, it isn't right. I suppose you mean you assumed that both photons will have the same magnitude of momentum, though? That's only true if the total momentum is zero. You could analyze the problem in a reference frame where that is true.

3. May 10, 2010

### Krappy

Yes, sorry, I meant the same magnitude.

Now I tried to solve this with using both Energy and Momentum conservation and it gave me something like $$10^19 eV$$. But I think there's an easier way to solve it. Could you please post your resolution?

Regards

Last edited: May 10, 2010
4. May 10, 2010

### vela

Staff Emeritus
Do you know how to use four-vectors?

5. May 10, 2010

### Phrak

Go to the center of mass frame. Solve the problem, and transform back.