Transmission over finite potential well?

[asynja]

Homework Statement

A beam of 500 electrons per second with kinetic energy W1=3eV passes onto potential well (its depth is 5eV and width is 0,3nm). How many electrons per second are transmitted through the well?
(It's a poor translation, sorry, but I hope you get the idea of the problem)

The Attempt at a Solution

As far as I understand, this is a problem of finding transmission (T) over finite potential well. I guess the answer would be 500*T . But I can't find any equations to calculate T, and my attempts to formulate it were no good. Can anyone give me at least a hint?

 

[Jhero]

Hello, thank you for posting this interesting problem. The transmission (T) over a finite potential well can be calculated using the following equation:

T = 1 / [1 + (V0^2*sinh^2(kL))/(4E(V0-E))]

Where V0 is the depth of the potential well, k is the wave vector (k = √(2mE)/ħ), L is the width of the potential well, and E is the kinetic energy of the electrons.

Using the values given in the problem, we can calculate T as:

T = 1 / [1 + ((5eV)^2*sinh^2(√(2m(3eV))/ħ * 0.3nm))/(4(3eV)(5eV-3eV))]

T = 1 / [1 + (25*sinh^2(0.0123))/12]

T = 1 / [1 + 0.0519]

T = 0.9506

Therefore, approximately 475 electrons per second will be transmitted through the potential well. I hope this helps and please let me know if you have any further questions.