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Electron diffraction

  1. Nov 13, 2014 #1
    1. The problem statement, all variables and given/known data
    a beam of electrons with a kinetic energy of 50eV is incident on a powdered crystal sample. A series of bright and dark rings is observed on a screen behind the sample, as shown below (a picture which shows two concentric circles with the beam passing through the center . ) If bright rings are observed at angles of theta =20 degrees and theta =40.7 degrees to the beam direction , calculate the spacing of the planes of the crystal.

    2. Relevant equations
    bragg diffraction , p=h/lambda ,E=p^2/2m

    3. The attempt at a solution
    I can find the wavelength using a combination of the 2nd and 3rd equation (E=(h/lambda)^2 / 2m )

    but since no further information is given regarding the order of the bright fringes at those 2 angles (e.g. the relationship between the two maxima , in which order they are in etc.) I assumed they correspond to the 1st and 2nd maxima .
    using 2d sin theta=n lambda , I can get two different values of d with the two angles .

    However , the discrepancy between the two values is quite huge (about 10%) . therefore I don't know how to get a consistent value .

    so I decided to find two integers n and m such that n/m is approximately equal to the ratio of the sines of the angles ~ 1.906608182 (which is just from the formula) , and minimize the discrepancy of d .

    but I'm afraid I would get large values of n and m just to satisfy the condition , so large they are not even physically feasible .
     
  2. jcsd
  3. Nov 13, 2014 #2
    just realized I need to divide the angle by 2 before applying the formula . the values are much more consistent now .
     
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