Question

Suppose a beam of 5.0 eV protons strikes a potential energy barrier of height 5.5 eV and thickness 0.57 nm, at a rate equivalent to a current of 825 A.
(a) How long would you have to wait-on average-for one proton to be transmitted?

(b) How long would you have to wait if the beam consisted of electrons rather than protons?

Answer 1

This is a quantum mechanical "barrier penetration" problem.

See

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html

or any of many other websites about this phenomenon. There you will find the formula you need.

Convert the current to a particle arrival rate. Multiply that by the probability of penetration to get the penetration rate. The reciprocal of that is the time you would have to wait.