# What is the reason for mass defect in a nuclide?

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1. Feb 14, 2016

### Anonymous Vegetable

I may be misguided here but to my understanding, separate nucleons have a higher mass altogether than the combined nucleus as the potential energy gained from being separated (in the field of the strong force) is being manifested in more mass. If this is true, and if it's not I'd like to know the reason, why would the nucleons retain this greater mass outside of the range of the strong force?

2. Feb 14, 2016

### CrazyNinja

How are the individual nucleons gaining mass? The difference in mass manifests itself in the form of kinetic energy.

3. Feb 14, 2016

### Anonymous Vegetable

Vibrational or of what 'form' of kinetic energy?

4. Feb 14, 2016

### CrazyNinja

Well, vibrational energy is nothing but a combination of potential and kinetic energies. But no, the nuclides do not vibrate, they fly off. THAT form of kinetic energy. This is the principle used in nuclear reactors where fission occurs. This kinetic energy is transferred to water → converts to steam → runs turbines → electricity is generated.

5. Feb 14, 2016

### Anonymous Vegetable

So by that logic, if you hypothetically brought those nucleons to a rest and weighed them, their mass would be no greater?

6. Feb 14, 2016

### CrazyNinja

No greater when compared to what? Do you want to compare :
1. The sum of their masses with the mass of the decayed nuclide; or
2. Their "moving" mass with "rest" mass?

7. Feb 14, 2016

### Anonymous Vegetable

I think you may be misreading my question. The mass of a nucleus is less than the mass of its nucleons added together separately (I assume these are rest masses). So how can that extra mass be kinetic energy?

8. Feb 14, 2016

### CrazyNinja

Okay I'm sorry. I was thinking in terms of decay because your question said "nuclides". My bad.

Yes, THAT mass defect turns into potential energy. So according to your question, if the nucleons did not retain this extra mass, where would it go?

EDIT: What other alternative do you suggest?

9. Feb 14, 2016

### Anonymous Vegetable

Oh so are you saying this potential energy is present when part of a nucleus?

10. Feb 14, 2016

### Staff: Mentor

No. The difference in mass comes about because of the work you have to do on the system in order to separate its components. If you could somehow "grab onto" the individual nucleons in a nucleus and pull them apart slowly, you would have to do work on them as you pull. When the nucleons are far enough apart that the binding forces are negligible, you stop. The mass of the system (the sum of the masses of the separated (and now stationary!) nucleons) is now greater than the mass of the original nucleus. The difference (the mass defect of the nucleus) equals the mass-equivalent (via E = mc2) of the work that you did.

[added: ah, I see you corrected yourself while I was typing.]

To AV: the increase in mass comes from the work done by whatever separated the nucleons.

11. Feb 14, 2016

### CrazyNinja

@jtbell ... Yup, you are right. I read the question wrong. My bad.
@Anonymous Vegetable ... yes, it is only present when it is part of the nucleus. jtbell's explanation will help you out.

12. Feb 14, 2016

### Anonymous Vegetable

I may just be an idiot but I still can't normalise the fact that pulling them apart gives them more mass.

13. Feb 14, 2016

### Staff: Mentor

The individual nucleons actually don't change their masses. The key thing here is that generally, the mass of a system of particles does not equal the sum of the masses of the particles. The mass of a system of particles includes (a) the masses of the component particles, (b) the mass-equivalent of the system's potential energy, and (c) the mass-equivalent of the kinetic energies that the component particles have when the system as a whole is stationary.

14. Feb 14, 2016

### Anonymous Vegetable

But in this case the system of particles (the nucleus) actually has less mass than the separate pieces added together?

15. Feb 14, 2016

### Staff: Mentor

Yes. Note that the potential energy of a bound system is negative. So the total energy of a bound system is less than the total energy of the unbound system (the separated components). Therefore the mass of the bound system is less than the mass of the unbound system.

16. Feb 14, 2016

### Anonymous Vegetable

This may sound silly, if it helps I'm still in school, but the potential energy being negative in a bound system is kind of a revelation to me, I was completely unaware.

17. Feb 14, 2016

### CrazyNinja

No prob bro. How old are you? I am 17, and fairly speaking, it feels weird the first time too. Don't worry, you will get used to it.

18. Feb 14, 2016

### Anonymous Vegetable

And out of curiosity, can I ask you to elaborate on vibrational being a combination of kinetic and potential?

19. Feb 14, 2016

### CrazyNinja

It would be easier for me if you could tell me how old you are.

20. Feb 14, 2016

### Anonymous Vegetable

Similar in age to you. But UK so perhaps different syllabuses.