Conversion of mass to energy

[K8181]

I have a fundamental question. I am reading this modern physics book, and it says that an electron and a proton that are released and come together into a bound state release a photon. Fine. But the explanation given is that the sum of the individual masses of the proton and electron is greater than the mass of the bound system, and that the extra rest mass was converted to energy in the release of the photon. I am confused because it seems that an equally good explanation is that the electron and proton have a potential energy when they are apart, and it is this energy that is released as a photon. Here there would be no conversion of mass into energy needed to save conservation of energy. Does the bound system behave as though it has less mass than the constituent particles, or is the second explanation just as good? Please help.

 

[mfb]

Both descriptions are correct, they just focus on different things.

Does the bound system behave as though it has less mass than the constituent particles, or is the second explanation just as good?

It doesn't just "behave as though", it actually has less mass. You can put it on a scale to check. Well, there will be experimental difficulties, but at least it is possible in principle.