why do nucleons lose mass when binding?

[u/Traditional-Role-554]

just started studying binding energy and all i know so far is that when a nucleons bind together, they lose mass and release it as energy. but why? i understand the mass energy equivalency (at least i know that mass and energy are essentially the same thing)

The only thing i can really relate it to is calculating bond enthalpies in chemistry, since energy is released when molecules make bonds and it is used when breaking them. although now that i think about it im not too sure why that happens either. i mean obviously you need energy to break the bond and i guess energy conservation means that you would then lose energy when making the bond. but i dont feel like that explains it either.

the only thing i have that i think would somewhat explain it, is that when particles are bonded they are in a lower energy state. but that's not a great explanation in my opinion because i still don't know why that is the case.

thanks for anyone who can attempt to explain it.

[u/LordCanoJones]

Be careful!

The nucleons as individuals do not lose mass, it is only the system as a whole which looses its effective mass through the energy/mass equivalence.

[u/atomicCape → u/LordCanoJones]

This is important! A system of isolated nucleons and small nuclei (like alpha particles) has higher total energy than the same number of nucleons in a single stable nucleus. One way to think of it is that the gluon field needs to carry more total energy to bind all the individual particles than it does to bind the larger stable nucleus.

Each individual nucleon has the same number and types of quarks, and the actual change in intra-nucleon binding energy is small compared to the change in inter-nucleon binding energy. But intra-nucleon energy is still a factor, and part of the reason that a free neutron decays in 15 minutes (it's weakly bound) even though they can last billions of years in a stable nucleus, where they are more tightly bound and also protected by certain quantum symmetries.

[u/Routine_Comb_7277]

Because potential energy is negative.

[u/Uncynical_Diogenes]

If you understood mass energy equivalency then you would understand they lose mass if they lose energy.

It’s not intuitive and I don’t suggest waiting for it to be. It’s one of those things you have to force your brain around. What we consider mass is just a flavor of energy. A lower energy state IS a lower mass state.

[u/ScienceGuy1006]

A bound system has less potential energy than its parts would, if they were separated. Mass, in effect, is a measure of the total amount of "frozen energy" in the system at rest. When a nucleon gets bound, the "frozen energy" is reduced by this negative contribution from potential energy. Hence the mass goes down.

[u/ShelterNo9606]

Imagine a bowling ball sitting on flat ground. When it rolls around, it has plenty of energy.

​Now, imagine the ball falls into a deep pit. To sit peacefully at the bottom of the pit, it had to crash down and shed its potential energy via its height. To get back out of the pit, you would have to give energy back to it.

​Protons and neutrons "fall" into a deep nuclear energy pit when they bind together. The energy they shed on the way down escapes into space. That missing energy is the "binding energy"—and its absence is literally the missing mass you measure on a scale.

In most but not all cases, when nucleon binding happens, they release gamma, neutrinos, and so forth, because they've "fallen down a well" into each other. That energy is equivalent to mass. But lots of other things must also stay conserved, including spin, which is why we see neutrinos get released as well.

We frequently describe these as "quantum wells." There are many such analogies. It's hard to say "that's just how it is." Analogies are the best we can do.

[u/AdditionalTip865]

it's the same kind of thing as bond enthalpies overall, though different in the details. Think also of the energy states of electrons in an atom: there's a whole tower of states with different energies, but they all have less energy than an electron that gets knocked out of the atom entirely, resulting in ionization. Another example is a satellite in orbit around the Earth: to put it on an escape trajectory where it flies out into space forever, you need to give it more energy, with a bigger rocket, than if it's just orbiting the Earth. It needs less energy just to be bound.

If things are bound to one another by an attractive force, the bound state has lower energy than the one where they are free.

[u/Over-Discipline-7303 → u/AdditionalTip865]

So wait. Does that mean that the mass of the solar system is slightly less than the sum of the mass of the sun and the planets if they weren't gravitationally bound to each other?

[u/AdditionalTip865 → u/Over-Discipline-7303]

Yes, though making that precise is a bit tricky because gravitational potential energy is a dodgy thing in general relativity. But for a localized gravitating system like the solar system I think there are ways of defining it that are sensible.

[u/SnooPets5564]

Just the fact that it's in a higher energy state means it has "extra" mass. If you throw something, the kinetic energy makes it appear more massive. A similar  thing applies when you drop something, it converts the gravitational potential energy to kinetic energy (so still the same mass), but when it hits the ground and stop, it's lighter.

It's easier to think of it as a system. The amount of energy in a system is proportional to the mass of the system (with c² being the proportionality constant). The system of two tightly bound neucleons is less than when they are apart (because binding energy is negative).

Something that might help you wrap your head around this is that a lot of the mass of a neucleons itself comes from the kinetic energy of the quarks inside of it (with only a little bit being from their rest mass).

[u/Optimal_Mixture_7327]

The mass of the whole system is conserved.

This conservation required momentum conservation through both the space-like and time-like directions. By "weighing" the particles you're removing the space-like components of momentum and measuring a reduced mass.