Max Energy of UV Light Photon in Compton Collision

[physicsss]

What is the maximum energy a photon of UV light ( lamda= 320 nm) can transfer to an electron in a Compton collision?

I used the Compton eq. and set cos= -1 and found the change in lamda to be 0.00486 nm. then using p=h/lamda where p is the momentum, i found the momentum for when lamda is 320 nm and 0.00486 nm. then I added the two momentums. How do I the energy from here?

 

[Meir Achuz]

E=hc/\lambda.
dE=-hc d\lambda/\lambda^2.

 

[Astronuc]

For light E = h\nu = pc, where E is energy and p is momentum.