Question

a) An electron with 10.0 eV kinetic energy hits a 10.1 eV potential energy barrier. Calculate the penetration depth.

b) A 10.0 eV proton encountering a 10.1 eV potential energy barrier has a much smaller penetration depth than the value calculated in (a). Why?

c) Give the classical penetration depth for a 10.0 eV particle hitting a 10.1 eV barrier.

Answer 1

(a) The penetration depth is the distance outside the barrier where the wavefunction becomes 1/e of its original value. I am starting this answer from basics for better understanding:

Note: The constant 'h cut' is used here which is (h/2π).

(b) The penetration depth is smaller for proton because proton is much heavier than electron. Since the penetration depth is inversely proportional to the mass, hence penetration depth for proton would be smaller.

(c) Since according to classical physics, the particle with lower energy than barrier would not cross the barrier.Hence there will be no penetration. So it is zero in this case.

Hope you like the answer. Have a nice day .Sorry for any calculation mistake :)