Why is a hydrogen atom lighter than a electron and a proton

[enotstrebor]

I don't think that's correct. If you measure the mass of the system with the proton and electron before capture and after capture the mass will be less once the electron has been captured by the proton. The missing mass will be radiated away as energy in the EM field, aka light. Light does contribute to gravitation and to the mass of the system.

However, if you measure the mass of the system with the electron nearly an infinite distance away from the proton, and then again right before the electron is captured by the proton, there will be no change in the mass. (Unless the acceleration of the two particles emits EM radiation)

Does that make sense?

From any measurements I have seen, the measured mass of the hydrogen atom is not sufficiently accurate to tell if it is 13.6 eV lower in mass. Can you give me an experimental measurement reference?

If you calculate the energy gained going to the Bohr radius, i.e. e^2/R_bohr you get 27.2 eV. This also means you have to put in 27.2 to move it back out to infinity, yet a photon of 13.6 eV will do the trick, this to me says 13.6 eV must already be in the spread out over space "orbiting electron" to make up the difference and this is in keeping with QM.

Though the specifics are different than using the Schrödinger equation/QM, you can use the simplistic Bohr model as a quick check http://en.wikipedia.org/wiki/Bohr_model which uses E=KE+PE seven equations down and see that the Kinetic Energy = .5M_e v^2. Substituting the previous equation for v the kinetic energy of the electron = .5 e^2/R_bohr, i.e 13.6 eV of kinetic energy.

Is there something wrong with this?

So you see my dilemma, if in the hydrogen atom the electron has more energy and momentum, how can the hydrogen atom be lighter?

 

[Drakkith]

Is there something wrong with this?

So you see my dilemma, if in the hydrogen atom the electron has more energy and momentum, how can the hydrogen atom be lighter?

I'd guess that potential energy is the difference, as has been explained already.