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Electron Scattering and Bragg's law

  1. Feb 25, 2017 #1
    1. The problem statement, all variables and given/known data

    A beam of thermal neutrons (K = 0.025 eV) scatters from a crystal with interatomic spacing 0.45 nm. What is the φ angle of the first order Bragg peak? (as defined in figure 5.11, φ and the scattering angle add up to 180 degrees).

    2. Relevant equations
    nλ = 2dsinθ
    = DsinΦ
    d = distance between Bragg planes
    D = intermolecular distance
    2θ = scattering angle
    2θ = π = Φ
    K= 1/2mv2
    p=mv=h/λ
    3. The attempt at a solution
    Since K=1/2mv2 and p=mv we can solve K and say
    K=p2/2m = (pc)2/2mc2
    so pc = √(2Kmc2)
    and since p=h/λ we have λ=h/p
    if we multiply top and bottom by c we have

    λ=hc/pc = hc/√(2Kmc2) = DsinΦ since n= 1 for first order.

    Thus sinΦ = (hc/D)(1/√(2Kmc2)
    however when I plug these numbers in I get that
    Φ = sin-1 (17.239) which isn't possible. To me, this makes no sense because my units cancel out properly and I can't see what I did wrong. Thanks!
     
  2. jcsd
  3. Feb 25, 2017 #2
    Never mind I think I solved it. I was putting in the mass of the electron instead of neutron. Can someone check for me that all my steps still make sense?
     
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