Find max E of a photon in Compton Collision

[Tyst]

Homework Statement

Find the energy of an x-ray photon that can impart a max energy of 50keV to an electron by compton collision

Homework Equations

∆λ=h/mc(1-cos(theta)) where m = mass of electron
E=hf
(to be honest, not entierly sure if these are all you need, or if you need them... sorry :( )

The Attempt at a Solution

∆λ=2.43*10^-12 (set theta to 90 because i am dealing with a maximum)

corresponding change in f = c/2.43*10^-12 from above
and since E=hf
∆E=510551 eV which is unfortunately, larger than the E delivered to the electron... so CLEARLY I've stuffed up... I was planning on being able to say that the energy was 50keV + ∆E so i guess I'm on the wrong track... very wrong... any hints would be very greatly appreciated :!)

 

[Dick]

You are changing an equation like f-f'=c/lambda-c/lambda' into f-f'=c/(lambda-lambda'). This is WRONG! Right?