- #1
Poirot
- 94
- 3
Homework Statement
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)]
Homework 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]
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!