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Potential barrier, reflection coefficient

  1. Feb 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Electrons are pushed into a grounded metal tube A by the kinetic energy of 100 eV. After having gone through the tube it passes into another tube, B, at some distance from A. Tube B is kept at a potential of -50V. Calculate how many of the electrons are reflected back into the tube A. ( Assume the potential barrier is discontinuous)

    2. Relevant equations
    If ##E>V_0## for our barrier then we have the wave numbers
    ##k_1 = \sqrt{\frac{2mE}{\hbar^2}}## for ##x<0## and
    ##k_2 = \sqrt{\frac{2m[E-V_0]}{\hbar^2}}##
    for the wave functions
    ##\Psi_1 = Ae^{ik_1x}+Be^{-ik_1x}## for ##x < 0## and
    ##\Psi_2 = Ce^{ik_2x}## for ##x>0##.

    The reflection coefficient is then
    ##R = \left(\frac{k_1-k_2}{k_1+k_2}\right)^2##.

    3. The attempt at a solution
    I have an electric potential difference of ##50V##, somehow I need to convert this into an potential energy but I have no idea how to do that so I don't even know if ##E>V_0## or not and the above formulas are applicable.

    Assuming they are I can simply ##R## as
    ##R = \left( \frac{\sqrt{E}-\sqrt{E-V_0}}{\sqrt{E}-V_0} \right)^2##.
    Now I don't know ##V_0## but let's guess ##V_0 = 50eV## (seeing the number 50 in the question!) then
    ##R=\left( \frac{\sqrt{100}-\sqrt{50}}{\sqrt{100}+\sqrt{50}} \right)^2\approx 0.3##
    which agrees with the answer to the exercise but I have no idea if ##V_0 = 50eV## or why that is.
     
  2. jcsd
  3. Feb 9, 2016 #2

    BvU

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    Potential energy is ##qV## !
     
  4. Feb 9, 2016 #3
    Thanks, I suspected that but wasn't sure!
     
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