1. Not finding help here? Sign up for a free 30min 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!

Compton Scattering: Finding Angle from only Initial Energy

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Gamma rays of energy 1.02 MeV are scattered from electrons that are initially at rest. If the
    scattering is symmetric, that is, if θ = ϕ in Fig. 1, find
    i. the scattering angle θ
    ii. the energy of the scattered photons.

    214owso.jpg

    2. Relevant equations

    λ' - λ = (h/mc)[1 - cos(θ)]

    3. The attempt at a solution

    I'm not entirely sure where to go on this one. The first thing I did was take the energy of the gamma ray and find its wavelength via the relationship:

    E = hf

    E = hc/λ

    λ = hc/E

    λ = 1.217E-22 m

    I've been scouring every resource I can but I cannot find a relationship for scattering angle dealing only with energy. I am certain that the fact that the scattering is symmetric has something to do with it, but I do not know how to apply that fact.

    Does anyone know how I can approach this problem?
     
  2. jcsd
  3. Sep 11, 2011 #2

    diazona

    User Avatar
    Homework Helper

    I would try starting from conservation of energy and momentum.
     
  4. Sep 13, 2011 #3
    So I tried applying the conservation of momentum with a bit of help from a book I found in the study room. This was my attempt to solve for the angle, however I ended up with sec(theta) = 0, which is impossible. I know I must be missing a term or something somewhere.

    szylxj.jpg
     
  5. Sep 13, 2011 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Why are you using the same angle for both the electron and the photon? Also, one of the terms in the y-equation should be negative, right?
     
  6. Sep 14, 2011 #5
    I'm using the same angle because the problem states that "the scattering is symmetric, that is, θ = ϕ in Fig. 1". Am I interpreting this part incorrectly?

    I realized that the term describing the momentum of the scattered photon should be negative. It helped a bit, but I now arrive at a point where I cannot eliminate either the recoiling electron's velocity and the scattered photon's wavelength at the same time.

    72zsir.jpg
     
  7. Sep 14, 2011 #6

    diazona

    User Avatar
    Homework Helper

    It looks like you haven't used conservation of energy...
     
  8. Sep 14, 2011 #7
    I've solved the problem. I friend of mine told me that you only need to use conservation of momentum in the x-direction, and the Compton shift equation. Then you solve both for scattered photon wavelength and set them equal.

    I hate it when I look for help with a problem on Google and find a thread where someone says they solved their problem without showing how, so here's my workings for all you people who found this thread via Google: (although I forgot to rotate it so you'll have to either tilt your head or rotate it yourself)

    2dr5274.jpg
     
  9. Sep 14, 2011 #8

    diazona

    User Avatar
    Homework Helper

    Yeah, that works because the Compton scattering equation incorporates conservation of both momentum and energy already.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Compton Scattering: Finding Angle from only Initial Energy
Loading...