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Homework Help: A Quick Question on Compton Scattering

  1. May 28, 2010 #1
    1. A photon of wavelength 1.000nm is scattered by a muon initially at rest. What is the deflection angle of the photon if its wavelength after scattering is 1.001nm?

    2. Relevant equations

    [tex]\lambda[/tex][tex]^{'}[/tex] - [tex]\lambda[/tex] = [tex]\frac{h}{mc}[/tex] (1 - cos([tex]\vartheta[/tex])

    Assume that the mass of the muon is 200 times that of an electron.

    3. The attempt at a solution

    I have got down to cos([tex]\vartheta[/tex]) = -81.4. I'm not sure what to do now.
  2. jcsd
  3. May 28, 2010 #2

    Doc Al

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    Staff: Mentor

    That's not good. Getting |cosθ| > 1 is a sure sign that you've made an error somewhere.

    Redo your calculation. (Show what you plugged in where.)
  4. May 28, 2010 #3
    Thanks for the quick reply.

    Note - I'm going to change theta to x so I can avoid LaTeX complications. Similarly, I'm going to change lambda to a and lambda-prime to b.

    First, I rearranged the equation to make cos(x) the subject:

    (b - a) = h/mc (1 - cos(x))

    (b - a)mc/h = 1 - cos(x)

    1 - [(b - a)mc/h] = cos(x)

    Now, I'll show you how the value came about:

    b - a = (1.001 - 1.000)x10^-9
    = 1.000x10^-12 (1)

    mc/h = (200 x 9.11x10^-31 x 3x10^8) / (6.63x10^-34) = 8.244x10^13 (2)

    Multiplying (1) and (2) I get 82.44

    Then 1 - 82.44 = -81.44

    Therefore cos(x) = -81.44
  5. May 28, 2010 #4

    Doc Al

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    Staff: Mentor

    Your calculation looks OK to me. That tells us that the assumptions of the problem are not consistent with Compton scattering. You can't have the given change in wavelength when scattering off of a muon! (Either that's a trick question or I'm missing something basic. :uhh: I'll think about it.)