Compton effect problem – Find angle and energy of scattered electron

1. The problem statement, all variables and given/known data

2. Relevant equations
From what I’ve read in my text book I believe I should be using the equations:
Photon:
p=E/c

Electron:
E(kinetic) = (Gamma-1)*m*c^2
p= (Gamma)*mass(electron)*velocity(electron)

3. The attempt at a solution
For the first part:
Ok, so first of all I wasn’t entirely sure what energy the 0.7M electron volts was referring to, but I assumed it meant the incident photon. So I took that 0.7M electron volts and worked out the initial momentum of the system, in the x direction. I also noted that the initial y momentum of the system was zero.

Then, using trig and the angles given, seperated this momentum into x and y components for both the photon and the electron. The expressions were in E’, v etc.. Basically unknown quantities. I assume I must equate these knowing that.

Px = P(photon)+P(electron) = 0.7×10^-6eV /c
Simularly, Py = P(Photon)-P(Electron) = 0
Given these both have the angles in them I assume there must be some trick to work out the angle. I’m stuck at that point, assuming I haven’t made some mistake… Which is quite possible as I’m struggling with quantum mechanics lol.

For the second part, I assume that knowing the angles the particles are scattered I can find the velocity of the electron and hence it’s kinetic energy.

Py = P(photon)-P(electron) = 0

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