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Compton Scattering Question

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Okay, so here's the problem:

    In a Compton scattering experiment, a photon is scattered through an angle of 90.0 and the
    electron is set into motion in a direction at an angle of 20.0 to the original direction of the
    photon.

    (a) Explain how this information is sucient to determine uniquely the wavelength of the
    scattered photon.

    (b) Find this wavelength.


    2. Relevant equations

    λ2 - λ1 = (h/m c)(1 - Cosθ)

    3. The attempt at a solution

    So, with the angle I'm given I can find Δλ, but I won't be able to find λ2 which is what I believe the question is asking me to find. I feel like I should be using the angle of the electron but I don't really see how I can. Can anyone help me out here? :S
     
  2. jcsd
  3. Feb 4, 2013 #2

    rude man

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    Write the x and y component equations for momentum conservation:

    For x, the photon has initial momentum h/λ1 and final momentum is a function of p, scattered electron angle ψ, scattered photon angle θ (actually a new photon!), and λ2. p is the scalar relativistic momentum of the electron after collision so the x component of momentum for the electron would be p*cosψ.

    Similarly, for the y direction, you have 0 = a function of p, the same two angles, and λ2.

    On top of that you also need to invoke energy conservation: initial photon energy plus electron rest energy = new photon energy plus relativistic electron energy which of course is E = √[(pc)2 + E02].

    3 equations, 3 unknowns: λ1, λ2 and p.
     
    Last edited: Feb 4, 2013
  4. Feb 4, 2013 #3
    Well, I'm screwed. Thanks, though.
     
  5. Feb 4, 2013 #4

    rude man

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    Why? It's just basic momentum & energy conservation, and I think I gave you most of the relativistic stuff you need.
     
  6. Feb 4, 2013 #5
    I have a vague idea of what I'm supposed to be doing but I'm just so horrible at this.
    Ok, here's my attempt:

    The initial momentum of the photon in the x direction PLUS the initial momentum of the electron in the x direction (would it be zero??) has to equal the sum of both final x direction momentums.

    Sooooooooo

    Ppix (Momentum photon inital x direction) = h/λ1
    Peix (momentum electron initial x direction) = 0?

    Ppfx = I have no idea

    Pefx = p Cosψ (what is p exactly? Scalar Relativistic momentum? What does that mean?)


    So Ppix + Peix = Ppfx +Pefx

    And likewise with the y components, although I wouldn't have the first clue where to start with that

    And energy. Hmmmmmm. So....


    h f1 + electron rest energy = h f2 + √[(pc)^2 + E0^2]
    ?
    Huh. What's E0? What's electron rest energy? What exactly is this "p"?! Yeah, I'm in bad shape right now :/
     
  7. Feb 4, 2013 #6

    rude man

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    Yeah, you need to review. Relativisically, rest energy derives from the special theory which exchanges energy for mass, and you know the electron has mass ...
     
  8. Feb 4, 2013 #7
    Ok, so would the new x component momentum for the photon be h/λ2 * Cosθ? Or is there something I'm missing?

    And would the initial y components for the photon and electron be zero?

    As for the final y components would they be:

    Ppfy= h/λ2 * sinθ?

    Pefy= p sinψ?

    So, in total:

    h/λ1 + 0 = h/λ2 * cosθ + p cosψ <------x components

    0 = h/λ2 * sinθ + p sinψ ---> -p sinψ = h/λ2 * sinθ <--------y components

    But that's assuming that I got the final x and y components right


    And for energy:

    hc/λ1 + mc^2 = hc/λ2 + √[(pc)^2 + E0^2] ?

    I'm not totally sure how to get the last part. Is E0 rest energy?

    I really do need to review this stuff. Can you let me know if this is right? And I apologize for saying that I was screwed. That was pretty immature of me. I just get so dang frustrated with this stuff!
     
  9. Feb 4, 2013 #8

    rude man

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    So now you see that you can solve for λ1 and λ2, right? Which is what the question seemingly asks for.
     
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