Electron Energy in Compton Collision

[Quelsita]

Question:
You want to give an electron an evergy of 25kev in a Compton Collision. What is the minimum initial photon energy you need?

Equations:
\Delta\lambda= h/m_ec(1-cos(\theta))
E=mc²
E=hv=hc/\lambda

I'm not really sure where to start from here. I know the answer is 138kev but I am not sure how to go about getting it.

 

[Delphi51]

For the Compton Effect, you have two equations: conservation of momentum and conservation of energy. I would assume the photon hits a stationary electron and bounces straight back, so only one dimension to consider and no doubt this situation gives you the minimum photon energy.

The two equations involve the initial frequency, frequency after the collision, and the velocity of the electron. But you can find the velocity from the given KE, so you have only two unknowns in your two equations. It looks straightforward to solve for hf1.