Conservation of Energy and Momentum in Photon-Electron Interactions

[quietrain]

Homework Statement

A photon strikes an electron of mass m that is initially at rest, creating an electron-positron
pair. The photon is destroyed and the positron and two electrons move
off at equal speeds along the initial direction of the photon. The energy of the
photon was ?

The Attempt at a Solution

are we suppose to use momentum conservation?

or kinetic energy conservation?

do we have to factor in relativistic effects?

the answer is 4mc²

but i have totally no idea at all how to get that

i think the final mass = 1.5 m ? where m = electron mass

because positron and electron pair = 0.5 m , then add in the other stationary electron so 1.5m ?

this is confusing . greatly appreciate any help thanks!

 

[Mindscrape]

I haven't worked it out myself, but see if you can first. You know that momentum is conserved and energy is conserved (or at least I'm telling you that it is a valid strong interaction that conserves energy if you don't know). You should use relativistic effects.

No idea what you are talking about with masses. The positron has the same mass as the electron, they are anti-particles.

 

[quietrain]

oh ok. will try it. thanks!