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Kinetic energy of electron: Quantization of angular momentum

  1. Oct 23, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the quantization of angular momentum implies that the kinetic energy of the electron is quantized as K=nhforb/2, where forb is the frequency of rotation. Assume circular orbit.

    2. Relevant equations
    Radial acceleration:
    arad = v2/r = (4π2r/T = 2*π*v/Tr = nħ

    KE = mv2/2

    We have covered the Bohr model of the atom, as well as the Rutherford model.

    3. The attempt at a solution

    I did a bunch of moving around of variables and have been able to get to the following expressions, but not the one I need:

    K = m*arad*vforb/2nh = ½mnħr = vmforb/4π

    Your input is much appreciated!
     
  2. jcsd
  3. Oct 23, 2015 #2
    This has been solved using the DeBroglie relationship, the idea that in a Bohr atom, the angular moment of an electron is
    L = mvr = nħ
    as well as classical definition of angular momentum
    L = Iω, where I = mr2

    Thank you for looking!
     
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