Solving Potential Barrier Problems with Electron Beams

[jlucas134]

New some help with some problems. I have tried them an listed what I have done so far...

1. A beam of electrons is sent along the x-axis from - with kinetic energy E=7.5eV. The beam encounters a potential barrier of height V'=1eV and width 2a=1.2nm.
What fraction of the incident beam is reflected? [Hint: Assume E>>V0]
I found k and q and from these found |R|^2, but have had no success in getting the correct answer. Am I supposed to do something after I find |R|^2?

2. Suppose a wave function within a barrier is approximately proportional to e-kx. The
probability that a particle will penetrate a barrier of thickness 2a is 0.010. What is the
probability of penetrating a barrier that is twice as thick?
Not even sure where to start here... I know that my thickness will now be 4a, but what now?

3. Suppose electrons with E= 10.0 eV approach a potential barrier of height 2.0 eV.
a. Suppose electrons with E= 10.0 eV approach a potential barrier of height 2.0 eV. in nanometers

b. For what minimum barrier thickness is there no reflection? in nanometers
Not sure where to start. I think i need to solve for 2aq=n*pi for a and for b where n*pi/2.

I am not really looking for the answers, but how to solve them as there is not much help in the text.

Thanks in advance.

 

[physics girl phd]

Can you show us your work on question 1?