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De Broglie wavelength from scattering of neutrons on crystal

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data
    A certain crystal has a set of planes 0.33 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at ∅= 38°. What is the de Broglie wavelength of the neutrons?


    2. Relevant equations
    nλ = Dsin∅ where D = d / sinα and α = ∅/2


    3. The attempt at a solution
    First, I found D: D = .33nm / (sin(38/2)) = 1.014
    This D corresponds to the spacing of the atoms and the d given in the problem statement
    corresponds to the spacing of the planes in the crystal.

    I assume n = 1. Then λ = 1.014 nm * sin(38) = .624
    The answer .59. What am I doing wrong?

    The only thing that I can think of that I might be doing wrong is my n is incorrect.
     
  2. jcsd
  3. Nov 6, 2012 #2

    haruspex

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    There's some confusion here between d and D. Make sure you have clear in your head what each of these is.
    Looks to me like you only need your first equation.
    Btw, n=1 is not an assumption - it is implied by first maximum.
     
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