This paper completes the analysis of the 1/r and a/r2 Coulomb and nuclear potential functions through a consequent analysis of the mass-energy equivalence using the standard orbital energy formula (Kepler’s third law) and ensuring (physical) dimensional consistency. The function yield the desired crossing of potentials and the expected combined potential well function. Further analysis of the qe/m and gN/m charge/mass-energy ratios and the different nature of the singularities at the center may explain the rather enormous proton/neutron energy/mass when accepting a Yukawa/Schrödinger-type nuclear force and potential. The model has the advantage of not introducing new fundamental constants (except for the nuclear charge gN), respecting relativity theory (no superluminal speeds), and confirming Planck’s quantum of action as the fundamental unit of physical action (h) and angular momentum (ħ) in particle-field exchanges of energy and momentum.