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Compton Effect, angle of deflection

  1. Jan 1, 2013 #1
    1. The problem statement, all variables and given/known data
    The scientist changes the frequency of the incident X-ray to 4.50 x 10^19 Hz and measures the deflected X ray frequency of 4.32 x 10^19 Hz. What was the angle of deflection?

    Fi = 4.50 x 10^19 Hz
    Ff = 4.32 x 10^19 Hz

    2. Relevant equations
    Δλ = λf - λi
    Δλ = (h/mc)(1-cosθ)
    λ = c/f

    3. The attempt at a solution

    First, I found the wavelength of the X ray before and after it is deflected.

    λi = c/f
    = (3.00 x 10^8 m/s) / (4.50 x 10^19 Hz)
    = 6.818181812 x 10^-12 m

    λf = c/f
    = (3.00 x 10^8 m/s) / (4.32 x 10^19 Hz)
    = 6.9444444444 x 10^-12 m

    Then found the change in wavelength

    Δλ = λf - λi
    = (6.944444444 x 10^-12 m) - (6.818181812 x 10^-12 m)
    = 1.26262626 x 10^-13 m

    Then I used the change in wavelength to find the angle

    Δλ = (h/mc)(1-cosθ)
    1.26262626 x 10^-13 m = ((6.63 x 10^-34 Js) / (9.11 x 10^-31 kg)(3.00 x 10^8 m/s))(1-cosθ)
    1.26262626 x 10^-13 m = (2.4259056 x 10^-12)(1-cosθ)
    0.052047623 = 1-cosθ
    cosθ = 0.947952377
    cos^-1(0.947952377) = 18.56692499° = 18.6°

    I'm just really unsure of the process that I took...
     
  2. jcsd
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