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Homework Statement
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)
Homework 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##.
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.
