Barriers & Tunneling: Find No Reflection & Max. Reflection Thresholds

[zbhest123]

1. Let 11.0-eV electrons approach a potential barrier of height 3.8 eV.
2. (a) For what barrier thickness is there no reflection? (b) For what barrier thickness is the reflection a maximum?
3. For part (a) I tried using kL=npi where k=sqrt(2m(E-V))/hbar, because this is where the Probability of transmission T=1.
The equation for probability of transmission is given by T=(1+V^2sin^2(kL)/(4E(E-V)))^-1. V is the potential barrier, 3.8 eV
I solved for L, getting: L=npi*hbar/sqrt(2m(E-V)), but I still don't know n. (n is an integer) And when ignoring n I get the wrong answer.
The answer I get is 7.623e-19.
The answer in the book is L=.229nm or any integer multiple thereof.
I have no idea what to do from here, I also multiplied the top and the bottom by c=3e8 due to electron mass m=.511e6 eV/c^2.

 

[ideasrule]

I solved for L, getting: L=npi*hbar/sqrt(2m(E-V)), but I still don't know n. (n is an integer) And when ignoring n I get the wrong answer.

n is just any integer, because if pi*hbar/sqrt(2m(E-V)) satisfies the equation sin(k1*L)=0, so do all of its integer multiples.

The answer I get is 7.623e-19.
The answer in the book is L=.229nm or any integer multiple thereof.
[/b]

Check over your algebra. Did you remember to convert E and V to joules?

 

[zbhest123]

Nevermind! I got it using the equation: T=(1+V^2sin^2(kL)/(4E(E-V)))^-1

Simplifying to sin^2(kL)=0

Originally I put it in my calculator to find arcsin(0) equal to 0. It was then pointed out to me that it can also equal pi. So I used Lk=pi, simplified to L=pi/k, which gave me a correct answer.

Thanks!