# Why mass defect?

Why is there a mass defect in the nucleus?

I think about mass defect in this way - A comparatively unstable nucleus( i.e. low binding energy) converts to a stabel nucleus( high binding energy)

Intially internal energy was U1 and then it became U2.
So when it converts then some energy should be released which should have a value
U1 - U2

Eg:- two protons far apart have some potential energy, when they get closer potential energy decreases so the lost energy is seen as kinetic energy right?

Similarly when a neutron converts to another why the change in internal energy is seen as a mass defect and not kinetic energy or something else?

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Eg:- two protons far apart have some potential energy, when they get closer potential energy decreases so the lost energy is seen as kinetic energy right?
There are other places the energy can go (light can be emitted, etc), but yes what you have described is basically true. You seem to understand what is going on, so is your question just about the terminology? Why call it a mass defect? Well it is a sensible name, I mean the mass of the combined nucleus is less than the mass of its component parts, so some mass has vanished. It is just the conventional terminology though; one could imagine alternatives.

Ok so let me see if i get this right :- In case of neutrons, when its (internal)energy changes it compensates that lost energy by reducing its mass and releasing energy(photons) right?

So does it always emit photons or can it emit some other particles too?

tom.stoer
remark: two protons (di-proton) or two neutrons (di-neutron) are not stable bound states; you need a proton and a neutron (deuteron)

It's possibly easier to think of (eg) a free proton and a neutron as each having zero potential energy, but if they fuse to form a deuteron they then gain negative potential energy as a result of the binding of the (strong) nuclear force. When they fuse, this extra energy is released, eg as a gamma ray.

The result is that the combined mass of the deuteron (E/c2) is less that the sum of those of the free particles, because its total energy is lower. It is convenient to quantify the negative binding energy using the difference between the mass of the combined nucleus and the sum of the individual nucleons' free masses, as these masses are the easiest quantities we can measure. Hence the concept of mass defect.

Ok so let me see if i get this right :- In case of neutrons, when its (internal)energy changes it compensates that lost energy by reducing its mass and releasing energy(photons) right?

So does it always emit photons or can it emit some other particles too?
Err sort of. The mass of these particles is not actually seperate from their internal energy. Their mass is associated intimately with the configuration of the quark and gluon fields that they are made up of, which is what I expect you mean by their internal energy. When these things get close to each other the quark and gluon fields get reconfigured, and if they end up in a lower energy state, then the system has less mass, E=mc^2 and all that. The energy has to go somewhere though, so it goes into some other field, i.e. some photons get produced.

I have not studied at all what happens when bound states form, so I don't know exactly what happens, but if the energy difference is large enough to create particles other than photons I see little reason why they should not be produced sometimes. I think the energy difference would not be enough to allow much more than electron-positron pairs to be produced though. Looking at wikipedia, it says the deuteron binding energy is 2.2 MeV, which indeed is enough to produce a couple of electron-positron pairs (1.022 MeV needed each pair), but nothing else.

Astronuc
Staff Emeritus
Ok so let me see if i get this right :- In case of neutrons, when its (internal)energy changes it compensates that lost energy by reducing its mass and releasing energy(photons) right?

So does it always emit photons or can it emit some other particles too?
Err sort of. The mass of these particles is not actually seperate from their internal energy. Their mass is associated intimately with the configuration of the quark and gluon fields that they are made up of, which is what I expect you mean by their internal energy. When these things get close to each other the quark and gluon fields get reconfigured, and if they end up in a lower energy state, then the system has less mass, E=mc^2 and all that. The energy has to go somewhere though, so it goes into some other field, i.e. some photons get produced.

I have not studied at all what happens when bound states form, so I don't know exactly what happens, but if the energy difference is large enough to create particles other than photons I see little reason why they should not be produced sometimes. I think the energy difference would not be enough to allow much more than electron-positron pairs to be produced though. Looking at wikipedia, it says the deuteron binding energy is 2.2 MeV, which indeed is enough to produce a couple of electron-positron pairs (1.022 MeV needed each pair), but nothing else.
When nuclei absorb neutrons, it is most often that gamma rays (photons) are emitted. The resulting nuclide may emit a beta particle, but usually the initial energy is emitted as a gamma ray.

In the case of two protons 'fusing', e.g., in the p-p fusion chain of stars, a positron is emitted in conjunction with the transformation of a proton (uud) into a neutron (udd) - or rather the transformation of an u (up quark) to a d (down quark).

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qrkdec.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/quark.html#c3
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c4