- #1

- 333

- 47

## 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.