# Homework Help: Elastic scattering question

1. Nov 6, 2016

### Poirot

1. The problem statement, all variables and given/known data
An electron collides with a particle with mass M at rest and scatters elastically through an angle θ (assume electron mass negligible).
Show that the fraction of energy lost by the e- is:

(Ee - Ee')/Ee = 1/[1+ Mc2/Ee(1-cosθ)]

2. Relevant equations
Conservation of Energy: Ee + Mc2 = Ee' + EM
Conservation of momentum: Pe = Pe' + PM

E2 = P2c2 + M2c4

or for electron since mass negligible, E=Pc

Previous parts of the questions required the rearrangements of these to get:
PM2 = 1/c2[Ee2 +Ee'2 - 2EeEe'cosθ]

3. The attempt at a solution
I've tried to solve this so many times but the closest I can get is:

(Ee - Ee')/Ee = Ee'(1-cosθ)/Mc2

I don't know if I'm missing some kind of relation I can use to sub in Ee' for Ee because in the final expression I'm trying to get there seems to be way more Ee's than I would expect.

I've also tried working backwards to find out what I'm missing from the answer but I just don't see it.

I think I have tunnel vision from trying this so often and can't see another way, so thank you in advance for any help, it's greatly appreciated!

2. Nov 6, 2016

### Staff: Mentor

Your situation is equivalent to Compton scattering (just with different particles), you should find derivations for this in textbooks and websites.

3. Nov 6, 2016

### vela

Staff Emeritus
You're not missing any physics here. It's just algebra. Starting from the expression you got, solve for $E_e'$ in terms of $E_e$, $\theta$, and $M$. Then plug the result into $(E_e-E'_e)/E_e$ and simplify.

4. Nov 6, 2016