# Photon-electron collision with pair production

1. Mar 18, 2017

### WrongMan

1. The problem statement, all variables and given/known data
photon collides with an electron producing a electron-positron pair, the three particles ( two electrons and one positron) move together in the same direction of the original photon.
calculate the energy of each particle.

2. Relevant equations
photon:
Ep=hf
p=E/c
electron/positron
1) E=Ke+me*c^2

3. The attempt at a solution
so 2)Ep + me*c^2=3E : photon energy plus electron rest energy equals the energy of the 3 remaining particles and since mass and direction is the same the energy is the same, same goes for momentum
3)Ep/c=3p
so 2 equations 3 unkowns so i wrote eq 2) with 1) and substituted k for 1/2*me*v^2 and in eq 3) i substituted p for me*v, this did not yield a correct answers.
how should i do this?

2. Mar 18, 2017

### Staff: Mentor

You cannot use the nonrelativistic kinetic energy and momentum formulas here. The particles will move at significant speed. You have to use the relativistic formulas.

3. Mar 18, 2017

### WrongMan

so K= m*c2*(1/(1-v2/c2)0.5)-m*c2
and p=m*v*(1/(1-v2/c2)0.5)
thanks!

4. Mar 18, 2017

### Staff: Mentor

I wouldn't introduce the velocity at all. $E^2 = m^2 c^4 + p^2 c^2$

5. Mar 18, 2017

### WrongMan

ok! got the correct answer now... thanks!