What Is the Incident Photon Wavelength in Maximum Energy Compton Scattering?

[zing478]

Homework Statement

If the maximum energy transferred to an electron during Compton Scattering is 50KeV, what is the wavelength of the incident photon?

Homework Equations

$$\lambda$$' - $$\lambda$$$$_{o}$$ = h/(Me*c)(1-cos$$\theta$$)

The Attempt at a Solution

We know that the maximum energy transfer for compton scattering occurs when:
$$\theta$$ = 180
$$\phi$$ = 0

So when $$\theta$$=180
$$\lambda$$' - $$\lambda$$$$_{o}$$ = 0.00486nm

Everything I've tried looking up involves the scattered photon as well (like the momentum, energy, wavelength equations)

Any tips on where to look/where I can go next?

 

[Astronuc]

Apply the conservation of momentum and energy.

One has the energy of the electron, from which one can obtain the momentum.

p_ph = E/c

 

[zing478]

I'm still stuck at finding the momentum of the electron. I know it's going to have 50 000ev of Kinetic Energy, but I'm not sure how to relate it to momentum.

 

[Astronuc]

One could do it either classically, e.g. p = mv and KE = 1/2 mv² = 1/2 p²/m, where m is the rest mass, or relativistically where m = $\gamma$m_o, taking into account the change in mass with velocity.

50 keV is ~0.1 of the rest energy 0.511 MeV.

 

[ini]

I can't solve this problem too! Please help me! I am taking exams next week and i 'm supposed to know what happens! my prof gave us a little help by saying these:

1). 1239.8/E=... (and i think from this we have λο)
2). ΔΕ -> Εφ=Εφ'+Εmax(e) -> 50keV=Εφ-Εφ' (where Eφ=photon's energy)
3) θ=π since (1-cosθ)=max

Can anybody help??