Photon-electron collision with pair production

[WrongMan]

Homework Statement

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.

Homework Equations

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

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?

 

[mfb]

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.

 

[WrongMan]

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.

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

 

[mfb]

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

 

[WrongMan]

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