Compton Scattering in Newtonian Physics

[rpardo]

Homework Statement

Derive the equation non-relativistic equation for Compton scattering

(mc^2) [(1/E2)-(1/E1)]+cos(theta)-[((E1-E2)^2)/(2E1E2)]=1

E1 = Incident Photon's energy
E2 = Scattered Photon's energy
theta= scattering angle
m = mass of electron
c = s

Here is the lab
In other words derive equation 2

http://www.physics.uoguelph.ca/~reception/2440/RelativMech-Compton-Jan10-08.pdf

Homework Equations

Conservation of Energy,conservation of mass, cosine law

The Attempt at a Solution

I've derived the first equation on the lab (relativistic approach)
I am really stumped on how to derive this...its been 4 hours and counting...
Any help at all would be appreciated. I feel like I'm really close but the algebra is the problem

Thanks in advance for your help guys and gals,

Truly appreciated

 

[vela]

How did you set up the problem?

Here are some suggestions to make the algebra easier:

1. Write the kinetic energy of the electron as $p^2/(2m)$.
2. Don't break the conservation of momentum equation into components.
3. Isolate the electron's momentum in the conservation of momentum equation on one side and then square the equation.