Photon colliding with moving electron

[Giorgi1997]

Homework Statement

Consider Comton scattering of a photon by a moving electron. Before the collision the photon has wave length λ and is moving in the +x direction, and the electron is moving in the -x direction with total energy E. The photon and electron collide head-on. After the collision both are moving in the -x direction. (a) Derive an expression for the wavelength λ' of the scattered photon. (b) Show that for the case E>>mc^2, the result reduces to λ′= hc/E(1+ m^2 c^4 λ/4hcE)

Homework Equations

The Attempt at a Solution

I tried using energy and momentum conservation laws but can't seem to find it

 

[AbhinavJ]

Can you please show your work?

 

[Giorgi1997]

Can you please show your work?

I would but i haven't done much progress
I just need a hint or the direction of the solution

 

[AbhinavJ]

Conserving momentum and energy should get you to the answer, put in the vectors correctly while conserving momentum.

 

[Giorgi1997]

Conserving momentum and energy should get you to the answer, put in the vectors correctly while conserving momentum.

did that
thx anyway

 

[AbhinavJ]

https://www.physicsforums.com/threads/compton-scattering-of-a-photon-by-a-moving-electron.562264/
Try following this for the second part

 

[Giorgi1997]

https://www.physicsforums.com/threads/compton-scattering-of-a-photon-by-a-moving-electron.562264/
Try following this for the second part

yeah I've seen that one and i understand the second part but i can't get to the first part

 

[AbhinavJ]

Einitial=Efinal
pinitial=pfinal
Plug in the values, get an answer, post the equations and somebody will point out what was wrong in them.

 

[Giorgi1997]

Einitial=Efinal
pinitial=pfinal
Plug in the values, get an answer, post the equations and somebody will point out what was wrong in them.

This is how i try to start