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How many peaks in the interference pattern?

  1. Oct 11, 2015 #1
    1. The problem statement, all variables and given/known data
    In a diffraction experiment in which electrons of kinetic energy 110 eV are scattered from a crystal, a first maximum in the intensity of the scattered electrons occurs at an angle θ=10.7
    a) How many peaks will there be in the interference pattern?
    b) What is the spacing between the atom planes?

    2. Relevant equations
    2d sinθ = nλ
    λ = h/p = h/√(2m KE)

    3. The attempt at a solution
    From the kinetic energy of the electron I found the wavelength to be 1.17*10^-10 m , then I don't understand how to use it in that equation, I believe n is the number of peaks, and d is the spacing, so how would I solve this equation while two variables are missing?
     
  2. jcsd
  3. Oct 11, 2015 #2

    gneill

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    Staff: Mentor

    n is the number of a given peak (well, the pair of peaks placed symmetrically about the centerline, where the central peak is for n = 0).

    You're given the angle of the first peak for which n = 1. That should get you going. For more detail, take a look at the Hyperphysics entry on diffraction gratings.

    http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html
     
  4. Oct 11, 2015 #3
    Oh ok, so having n=1 will help me solve for the d, but how do I find how many peaks there are then?
     
  5. Oct 11, 2015 #4

    gneill

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    Staff: Mentor

    Usually you'd look for values of n where the equations start giving un-physical results (like imaginary angles, or impossible (real) values for a trig function).
     
  6. Oct 11, 2015 #5
    Solving for the angle θ, I start getting imaginary numbers at n=6, so that means there are 5 peaks?
     
  7. Oct 11, 2015 #6

    gneill

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    Staff: Mentor

    Sounds reasonable. Those would be pairs of peaks, and don't forget symmetry and the central peak.
     
  8. Oct 11, 2015 #7
    Okay, thank you very much for the help
     
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