Question: Can an electron be confined to the volume of a nucleus by the Coulomb attraction between the electron and the nuclear charge?
To answer this, find the approximate average kinetic and potential energies of the electron.
a. Take the nuclear charge to be Z = 100 and estimate the average distance between electron and nuclear charge to be ≈ 1 fm. (This approximation concentrates all the nuclear charge into a tiny sphere of radius less than 1 fm; this is not a good approximation but it won't change the answer.) Calculate the average potential energy of the electron.
b. Estimating the uncertainty Δx to be ≈ 1fm, evaluate the average kinetic energy.
c. Use your answers to (a) and (b) to answer the question.