# Why is the binding energy per nucleon not zero for hydrogen atom?

The lone proton has not to be worked on against any electrostatic force. So where does the energy come from? What is mass defect for a hydrogen nucleus?

• If you are talking about the "average" naturally occurring hydrogen atom then you have a weighted average that includes the occasional deuteron with it's 2.2 MeV binding energy (i.e. 1.1 MeV per nucleon). Commented Nov 7, 2012 at 13:51
• I think this question would be much better if there was a clearly identified reference. Doing a Google image search, it looks like most graphs define a proton to be the baseline. I don't doubt you could find one that shows what the question asks, it might be relative to the average binding energy or something else. Commented Nov 7, 2012 at 14:05
• @dmckee : yes, perhaps you are right. perhaps i am talking about the average.it is right if i think that the binding energy per nucleon of hydrogen atom, 1H1 only, is zero, right? Commented Nov 11, 2012 at 14:55
• but it is zero,per nucleon, at least in the binding energy tables :upload.wikimedia.org/wikipedia/commons/5/53/… Commented Nov 12, 2012 at 10:06

The hydrogen nucleus has exactly zero nuclear binding energy, for the reason you gave in your question. The nuclear binding energy is the energy it takes to separate all the nucleons in a nucleus from each other. Since there is only the one nucleon, it's already separated from any other nucleons. For the same reason, a bare neutron has zero nuclear binding energy.

You could look at the energy binding the constituent quarks in the proton, and calculate a binding energy from that. But that's not comparable to (for example) the energy binding the protons and neutrons in a carbon nucleus, and it probably has a different name. Nuclear binding energy charts typically take the nucleons themselves as given, and use the proton as the reference state.

Going the other direction a hydrogen atom has a non-zero electron binding energy. This is the electrostatic energy binding the electron to the proton in the hydrogen atom. This is about 1000 times smaller than even the smallest nuclear binding energies.

The nuclear binding energy per nucleon(Ebn) for Hydrogen depends on its isotopes.

The 1H has only one proton as a nucleon and so there is no mass defect which implies that the Ebn for 1H is zero. While Ebn for 2H and 3H are non zero .

The electron is bound to the proton by about -13.6058 eV. A naked proton is not a hydrogen atom.

• This seems ideal for a comment but doesn't really make for a good answer. The question is a bit broad and hard to understand though. Commented Feb 17, 2014 at 21:53
• The question is titled for an atom and then describes a proton then asks about a hydrogen nucleus. A hydrogen atom has binding energy, as above. A proton in vacuum free fall simply has its rest mass. If you diddle the proton in a field, that will show up. What else is there to be had? Commented Feb 18, 2014 at 0:24