Rectangular Well Width and Next Higher Energy for Full Electron Transmission

[njdevils45]

In an experiment involving electron scattering from a finite rectangular well of depth 4 eV, it is found that electrons of energy 5 eV are completely transmitted. What must be the width of the well? At what next higher energy can one expect to again observe T = 1?

My Attempt:

I used the formula T = [1+ (e^k₂L-e^-k₂L)²/(16E/V(1-E/V))]^-1. After rearranging the formula i found that (e^k₂L-e^-k₂L)² = 0, and thus the only way for this to be true is for L = 0. However my book gives the answer of L = 2.045 Angstroms for this part. I haven't even attempted the 2nd part yet, but the answer for that is 32 eV.

How do I go about fixing this dead end?

 

[PeterDonis]

Moderator's note: thread moved to homework forum.

 

[TSny]

I used the formula T = [1+ (e^k₂L-e^-k₂L)²/(16E/V(1-E/V))]^-1.

Is k₂ real or imaginary?

 

[njdevils45]

Is k₂ real or imaginary?

k₂ is real. I found it to = 0.082. I think I found the error. I asked my professor and she said I was using the wrong formula to begin with. I'll try to search through my book and find a better version

 

[TSny]

OK. Your formula will work if you take $k_2$ to be imaginary and maybe change a sign or two in the formula. The formula you are using (with real $k_2$) is probably for a rectangular barrier rather than a well. But the formulas for these two situations are very similar.

 

[njdevils45]

I found my mistake, thank you guys!