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Compton shift, lorentz factor

  1. Mar 18, 2010 #1
    Hello everyone! I've got a problem I've been working on for the past two days and can't seem to figure out. The problem is as follows:

    1. The problem statement, all variables and given/known data

    Two different experiments use two different wave lengths for the Comptom Shift. The scattered photons wavelengths and scatter angles (Φ) and the scattered electrons' kinetic energy and scatter angled are measured. The following measurements were obtained:

    λ1: 20 nm Φ1= 60°
    λ2: 500 nm Φ2= 60°

    1.What is the scattered photon's wavelength for the two experiments?
    2.What is the scattered electron's kinetic energy?

    3. The attempt at a solution

    So far, I've managed the first part (I think).

    Δλ= h/mc (1-cos Φ)
    Δλ= ((6.63 *10-34)/ ((9.11*10-31)*(3*108)) * (1-1/2)
    Δλ= ((6.63 *10-34)/(2.27*10-23))
    Δλ≈1.2*10-12

    So there's the wavelength, I think. Next up is the Kinetic energy:

    Kin=mc2(ɣ-1)
    ɣ= (1/√(1-(v/c)2)) (Lorentz factor)

    I end up with
    Kin= (9.11*10-31 * 9*1016) (ɣ-1) when I substitute in the mass of an electron and the speed of light.

    I cannot for the life of me get ɣ. Or, rather, I can't get "v" within ɣ. Since it is relative, I am pretty sure I can't use DeBroglie's stuff (λ=h/p and then P=mv), though I tried. It didn't work out well. Any ideas? Thanks so much for the help!
     
  2. jcsd
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