# B What causes mass defect in the nucleus?

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1. Sep 11, 2017

### Karagoz

Hi.

I read that the mass of nucleons in nucleus of Oxygen-16 (or nucleus of another atom) is less than the sum of its nucleons if they were separated (also the mass of 8 protons and 8 neutrons).

But why does nucleons have less energy in nucleus of atoms than if they were separated? What causes that "mass defect" of nucleons?

The nucleons on atoms have less mass because part of their mass is converted to nuclear force to bind nucleons together in nucleus of an atom?

Or the nucleons release some energy ( and hence mass ) when binding together?

If nucleus of an atom is split in two, the mass of the nucleons will increase?

2. Sep 11, 2017

### Staff: Mentor

Yes, if you have a bunch of free nucleons and assemble a nucleus (nuclear fusion) then it will release energy. This released energy is the mass deficit.

Yes, this is why fission requires net energy for nuclei lighter than iron

3. Sep 11, 2017

For the smaller nuclei, they are a lower energy state than the separate components. Fusion is possible where they go to a state of lower energy when they combine. In the process, this energy released in the fusion process accounts for the mass difference with $E=\Delta m \, c^2$.

4. Sep 11, 2017

### Karagoz

Fission of nuclei lighter than iron won't release energy (ulike in the case of fission of Uranium)?

5. Sep 11, 2017

That is correct. I believe unstable isotopes would be an exception to this.

6. Sep 11, 2017

### Karagoz

Bu the mass of a proton is ca 1.0072 u and a neutron is ca 1.0086 u. The mass of nucleons is less when these nucleons are part of a nucleus, or part of an atom.

Why their mass is less in atoms? Is it because they lose energy to bind to each other (to form a nuclei)?

7. Sep 11, 2017

Yes. The attractive nuclear forces brings them to a state of lower energy. Basically, in a fusion reaction, they get pulled towards each and speed up towards each other and then are brought to a stop. This kinetic energy gets released in the form of photons, etc., x-rays, uv, etc.. $\\$ And I do believe the neutron is generally slightly more massive than a proton, (you have it reversed), partly because it also contains an electron. The electron and proton of the neutron are attracted to each other, so again, in combining there will be a small mass deficiency. $\\$ It may interest you in the larger atoms that release energy in a fission reaction that the nuclei are bound together in a state that is a lower energy than if they were separated by a small distance=it is a stable potential well, (like a small valley high up on a large mountain), but the lower and more stable energy state is when the atom gets split into parts, and when this occurs, there is the release of energy from Coulomb repulsion as the protons of the component nuclei repel each other and drive each other apart. (Once the atom configuration gets pushed out of the high valley=the potential well, it then goes much lower down the hill).

Last edited: Sep 11, 2017
8. Sep 11, 2017

### Karagoz

If I did get it right, atoms that weigh lower than Fe (iron) give up energy in fusion and absorb energy in fission. But atoms that weigh higher than Fe give up energy in fission and absorb energy in fission. This is not without exception (according to the graph below taken from Wikipedia, as the line goes up and down between He, Li, C etc.).

But what I didn't get is, why is it that? That fusion and fission sometimes absorbs energy but sometimes gives away energy?

9. Sep 11, 2017

Helium 4 is extremely stable in its binding energy, but if you fuse a neutron or two and a proton onto helium to make lithium, I believe it still is a state of lower energy and will release energy in the process. (Not certain of this=it would require detailed calculations and might turn up to be one of the exceptions. Editing: See below, where I computed it for Lithium 6.) $\\$ Likewise Carbon 12 and Oxygen 16 are very stable, but making nitrogen from Carbon 12 should still be a lower energy state. $\\$ The calculation is more complicated than just taking the average binding energy per nucleon. You need to compute the total binding energy and compare to the total binding energy of the component parts. Any extra binding energy is energy that gets released in the fusion process. $\\$ In the case of He 4 vs. Li 6, the calculation is quite simple. Since an isolated proton and an isolated neutron each have zero binding energy, the question is, if 6x binding energy per nucleon for Li 6 is greater than 4 times the binding energy per nucleon for Helium 4. The answer is yes. $(6 )(5.3) > (4)(7.2)$.

Last edited: Sep 11, 2017
10. Sep 11, 2017

### Staff: Mentor

A nucleus is subject to the repulsive electrical (Coulomb) force between protons, and the attractive strong nuclear force among both protons and neutrons. The relative "balance" between these two forces varies with different numbers of protons and neutrons, and determines whether fission or fusion is more "natural".

The details are too long to write in a forum post, but they're in many textbooks and web pages. Google for "semi-empirical binding energy formula" or "semi-empirical mass formula" and you should be able to find something that describes the different terms in that formula and their origin. This is usually derived using the the "liquid drop model" of the nucleus, so you might also Google for that.

11. Sep 11, 2017

### Mister T

That graph shows that Fe56 has the highest binding energy per nucleon, without exception, evidenced by the fact that there's nothing with a higher binding energy per nucleon! The wiggles around He and Li do not demonstrate an exception. They demonstrate that the maximum at Fe56 is not approached smoothly.

Are you asking why the element with the highest binding energy per nucleon is the most stable? Or are you asking what it is about that particular number of nucleons that makes it the one with the highest binding energy per nucleon?

The first question almost answers itself and thus answers your fusion versus fission question. I don't know the answer to the second question beyond what the others have already mentioned.

12. Sep 12, 2017

### Karagoz

In this graph: you see that Fe has least mass per nucleon.
http://dev.physicslab.org/img/7b784857-7639-45de-bd2e-32cdeb2dabdc.gif

But Fe has highest binding energy per nucleon, like you see in this graph:
https://cnx.org/resources/72ec9ed4c72df1425d0318f15a94e3c8247182bb/Figure_32_06_03a.jpg

Is there a relationship between "average mass of per nucleon in nuclei" (or mass / nucleon) and "binding energy per nucleon"?
Also higher binding energy per nucleon, then less "mass / nucleon" will there be be?

If so, why is there such relationship or correlation?

13. Sep 12, 2017

### DrGreg

The binding energy is just the difference between the mass of the nucleus and the sum of the masses of the particles in the nucleus, if those particles were all separated from each other. (And then converted to energy units, if necessary, via $E=mc^2$.)

Edit: deleted some irrelevant and potentially misleading words

Last edited: Sep 12, 2017
14. Sep 12, 2017

### Karagoz

So, the mass of nucleons decrease because that mass is converted to "binding energy"?

15. Sep 12, 2017

The system when it binds, goes to a state of lower energy. Energy is released in the process because the energy is conserved. The quantity of energy that is released (as photons and heat, etc.) is said to be the binding energy for that system. To get the system separated again, this amount of energy (the binding energy) would need to be added to the system. (The binding energy is a measure of how strongly the system is bound. If it is given a negative sign, it can then be considered to be the potential energy of the system. Total energy=E=Kinetic energy +potential energy=mc^2). $\\$ Meanwhile the energy of the system is related to its mass by $E=mc^2$. If some of the energy contained in the mass $m$ of the particle is subsequently converted to energy in the form of radiated photons (electromagnetic waves,etc.), it will then have a lower mass. In the process of binding, energy is given off in the form of photons.

Last edited: Sep 12, 2017
16. Sep 12, 2017

### Staff: Mentor

The individual masses of the nucleons do not change. A proton always has a mass of 938.3 MeV/c2, and a neutron always has a mass of 939.6 MeV/c2. The mass of a system of particles (e.g. a nucleus) does not equal the sum of the masses of the individual particles, in general. The potential energy of the system and the kinetic energies of the individual particles (*) also contribute to the mass of the system.

(*) More precisely, the part of the kinetic energy that is not associated with the motion of the system (nucleus) as a whole.

17. Sep 12, 2017

### Karagoz

You say that the individual masses of the nucleons don't change, but why the mass of a nucleus is less than the sum of the masses of the individual particles?

18. Sep 12, 2017

### jbriggs444

Because that is the way that "mass" or, more specifically, "invariant mass" is defined. It is the norm of the energy-momentum four-vector.

In more common terms, it is the total energy of the system as measured in frame of reference where the system is at rest. Divided by $c^2$ according to the formula: $E=mc^2$ if using a system of units in which c is different from 1. If you reduce the energy of the system while keeping it motionless, you reduce its mass.

Edit: "Binding energy" is negative. It is a deduction from the total system energy. But it is not tied to any particular nucleon. So the masses of the individual nucleons are reckoned without the deduction.

19. Sep 12, 2017

### Mister T

The mass of the nucleus is smaller, but the mass of the nucleons is the same. So think of pulling those nucleons apart; the energy you put into the process is called the binding energy, and it equals the increase in mass that you measure. Assembling the nucleus is the reverse of this process. There's no conversion of mass to energy, just a change in what you're calling something; the thing you once called mass is now a thing you call energy.

The same process happens when you pull a neutral hydrogen atom apart by removing the electron. It's just that the amount of energy is so small compared to the separate masses of the proton and the electron that you don't notice the change. That allows you to pretend that the mass of the atom is equal to the sum of the mass of a proton and the mass of an electron, and that the energy that binds them together is something separate from the mass. That pretense would be exposed, though, if you were able to measure that tiny change in mass.

20. Sep 12, 2017

### Mister T

The notion that the mass of a composite body equals the sum of the masses of its constituents is part of the newtonian approximation. It's an illusion, a pretense. Einstein's discovery of rest energy, and its equivalence to mass, has taught us this lesson.