Problem:
A photon of energy E strikes an electron at rest and undergoes pair production, producing a positron and another electron.
photon + e^{} > e^{+} + e^{} + e^{}
The two electrons and the positron move off with identical linear momentum in the direction of the initial photon. All the electrons are relativistic.
a) Find the kinetic energy of the final three particles.
b) Find the initial energy of the photon.
Express your answers in terms of the rest mass of the electron m_{o} and the speed of light c.
I set the problem up this way:
For part a)
E is conserved before and after the collision.
E_{photon} = 3E_{e} + 3KE_{e}
hc/&lambda = 3m_{o}c^{2} + 3KE_{e}
I then solved for KE_{e} and found:
KE_{e} = 1/3hc/&lambda  m_{o}c^{2}
Is this the correct method to find the kinetic energy of one of the electrons after the collision?
The problem says "state your answer in the rest mass of the electron and the speed of light", however if I don't know the wave length of the photon, how do I eliminate that energy term. Since they say the electrons are moving relativistic, do I just assume their speed is equal to 1/10c and then work backward to find the photons wavelength?
I may be way off, any help is appreciated!
Thanks
Edit: I need to use mc^{2}(&gamma  1) for KE!
The biggest question I have is linear momentum conserved. I would assume it is, and the problem hints at linear momentum.
