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

Johnahh

What exactly is it that makes the energy/mass of a hydrogen atom be lower than that of the electron and proton separately?
I am aware that this process is what causes stars to emit light, during nuclear fusion deuterium has a smaller mass than a proton and a neutron so its extra mass/energy is emitted as light.

DrDu

The binding energy of the electron in hydrogen is 13.6 eV. By Einsteins E=mc^2 this corresponds to a tiny mass difference.

Johnahh

So some energy is taken from the electron and used as binding energy?

jbriggs444

No, that's not it.

When you combine an electron and a proton to form a hydrogen atom, the reaction gives off energy. At least part of that energy comes from the electrostatic attraction between the two component pieces.

Energy is conserved.

That means that once this extra energy has radiated away (as heat, photons or whatever), the resulting hydrogen atom will have less total energy than the electron and the proton from which it was assembled.

By E=mc^2, this lost energy manifests as lost mass. The composite has less mass than the sum of the parts from which it was assembled.

The term "binding energy" refers to how much energy is released when a bond is formed or, equivalently, how much energy would need to be injected to break a bond. If were able to measure carefully enough you would find that binding energy is always accompanied by a "mass defect".

DrDu

No, the energy is taken from the electric field surrounding both the electron and the proton.
The electromagnetic field is smaller in the atom than for the isolated electron and proton.

Johnahh

thank you both :).

sophiecentaur

And that "binding energy" is due to electric fields, in the case of an atom, as stated already. Inside a nucleus there are other forces, so the binding energy is due to them also.

Johnahh

So gluons, W and Z particles are also the cause?

enotstrebor

The hydrogen atom is NOT LIGTER.

Starting with an electron and proton at near infinity, the coulomb potential force causes the electron to accelerate (gain energy) toward the proton and vis-versa and the electron/proton system gains 27.2 eV (e^2/Bohr_R). Only half that energy 13.6 eV, is emitted by the hydrogen stom. So the hydrogen atom is heavier by 13.6 eV. Remember any energy in an object, even heat energy makes the object heavier.

Unfortunately the measured hydrogen-1 mass (that I have seen) is not accurate enough by several orders of magnitude to measure this difference in mass.

Vanadium 50

Of course it is. I have to add energy to separate the electron from the proton.

Nugatory

Then why do I not see hydrogen atoms spontaneously emitting a 13.6 eV photon as they decay into an unbound proton and electron?

Drakkith

The rest mass of the proton and electron compared to the rest mass of the hydrogen atom is what we mean by mass here. In your example you could have the extra energy left over as kinetic energy, but when we slow it down and measure it, it's mass is indeed less.

enotstrebor

Do the calculation to move an electron from the Bohr radius to infinity, i.e e^2/bohr_R = 27.2

It takes 27.2 eV to move an electron from the Bohr radius to infinity !!!

The photon energy you are adding is only 13.6 eV. Where do you think the other 13.6 eV comes from?

enotstrebor

The initial center of mass is not changed by the in-fall of the electron and proton as both accelerate toward each other. As the center of mass does not change, the hydrogen atom itself has no velocity nor kinetic energy.

Thus all of the extra 13.6 eV is internal to the hydrogen atom, i.e. 13.6 eV heavier

Redbelly98

The electron bound in a hydrogen atom already has 13.6 eV of kinetic energy. So you only need to add 13.6 eV to remove the electron.

enotstrebor

Exactly, what I have been saying.

Just as nuclear kinetic energy makes the nucleus heavier than the sum of the proton and neutron masses, likewise the bound electron kinetic energy makes the hydrogen atom heavier than the mass of the isolated electron and proton.

Redbelly98

Now you're forgetting about the hydrogen atom's -27.2 eV of potential energy. Add that to the 13.6 eV of KE, you get a total bound energy of -13.6 eV. So the hydrogen atom has lower energy than and is lighter than the isolated electron and proton by 13.6eV/c²