A nucleus contains Z protons that on average are uniformly distributed throughout a tiny sphere of radius R.
(a) Calculate the potential (relative to infinity) at the center of the nucleus. Assume that there are no electrons or other
charged particles in the vicinity of this bare nucleus.
(b) Graph the potential as a function of distance from the center of the nucleus.
(c) Suppose that in an accelerator experiment a positive pion is produced at rest at the center of a nucleus containing Z
protons. The pion decays into a positive muon (essentially a heavy positron) and a neutrino. The muon has initial
kinetic energy Ki. How much kinetic energy does the muon have by the time it has been repelled very far away
from the nucleus? (The muon interacts with the nucleus only through Coulomb's law and is unaffected by nuclear
forces. The massive nucleus hardly moves and gets negligible kinetic energy.)
(d) If the nucleus is gold, with 79 protons, what is the numerical value of Kf − Ki in electron volts?