1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Elastic scattering question

  1. Nov 6, 2016 #1
    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. jcsd
  3. Nov 6, 2016 #2


    User Avatar
    2017 Award

    Staff: Mentor

    Your situation is equivalent to Compton scattering (just with different particles), you should find derivations for this in textbooks and websites.
  4. Nov 6, 2016 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
  5. Nov 6, 2016 #4
    I hope this is helpful.

    Attached Files:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted