Compton scattering and the energies of incident and scattered photons ?

[lavenderblue]

Compton scattering and the energies of incident and scattered photons...?

Hey guys! I'm alittle stuck...Hope you can shed light on this for me!
The question is: 'In a head-on compton encounter, the total energy (i.e the rest mass plus the kinetic energy) of the scattered electron is 10.22MeV. The rest mass energy of the electron is 0.511MeV.
(a) Apply the laws of conservation of energy and momentum to the encounter and thus find the energies, in eV, of the incident and scattered photons.
(b) Show that the change in wavelength is d(lambda)=(2h)/(m(electron)*C)

Homework Equations

The equations I was thinking of using were:

For energy: (hc/lamda) + (m(electron)*c^2) = (hc/lambda2) + Y(m(electron)*c^2)

For momentum: (h/lambda) + 0 = Y(m(electron)*v) - (h/lambda2)

Where Y = the lorentz factor = (1-(v/c))^-1/2

The Attempt at a Solution

I was thinking of combining the above equations and rearranging the lorentz factor to find the speed, but don't know where to start to be honest. Every equation involving the compton scattering involves an angle, so since i don't have an angle to play with, i have no idea where to start!

 

[malawi_glenn]

Do it with vectors.

Draw the situation in the xy-plane. And use the relation for energy and momentum for the electron. Also you need to know some vector algebra, dot-product. hint: cut the lorentz factor, you don't need it here - just vectors, and energy - momentum relation.