My book points out that the combined rest mass of an isolated proton + an isolated electron is greater than the mass of a hydrogen atom: mH < mp + me The book then goes on to claim that if the electron is captured into the ground state in order to form a hydrogen atom, the rest mass difference will correspond to exactly 13.6 eV, the ionization potential of hydrogen. Their argument seems to be that if an electron loses 13.6 eV, emitting a photon of that energy in the process, then where did that energy go? My standard response would be that, "it came from the electric potential energy that existed due to the fact that these two opposite charges were initially unbound and separated." Of course, the problem with my viewpoint is that the amount of energy liberated would depend upon initial separations and kinetic energies of the proton and electron, and the electron, once captured, would spiral in, continuously emitting light of ever increasing frequency. We know that this doesn't happen. So I guess my problem stems from the fact that I am using classical physics to try and understand something that should be described by quantum mechanics + special relativity. But in spite of some knowledge of those fields, I cannot really understand the role of "rest energy" and why it is reduced. The book later gives an example of 4 protons undergoing a fusion reaction to create a 4He nucleus. In this case, I am more willing to believe that the 26.731 MeV liberated by this nuclear reaction in the form of photons + neutrinos come at the expense of a reduction in "rest energy." Maybe it's because I know that this reaction involves the strong force, which is something that I really don't understand, but I have this notion that somehow the binding energy of the strong force and "rest energy" are related (since "rest energy" seems to involve how much energy is tied up in things that are made of quarks). Can you lose "rest energy" through electromagnetic interactions? If so, how/why does it differ from the classical picture of something in the presence of some Coulomb potential? I can solve Schrodinger's Equation with the best of them (for simple, 1D, totally unphysical Hamiltonians, LOL), but the more I delve into physics, the less I realize I know.