Nuclear Binding Energy Confusion

[Greatness]

I read that nuclear binding energy is the energy required to separate a nucleus into its comprising nucleons.

Why then is mass defect calculated from this?
How is the nuclear binding energy graph used to calculate energy released from fusion?

Please explain in layman's terms, if you could explain some vocabulary involving your explanation, that would be great.

Thanks.

 

[dauto]

The nuclear binding energy tells the energy required to separate a nucleus into its comprising nucleons , as you said.
If in any reaction (not just nuclear fusion) you compare the total (add all the binding energy for different reactants/products) binding energy for before and after the reaction, you will see that there might be a difference between them. If you have an energy deficit, that energy must be provided for the reaction to occur and the reaction is considered endothermic. If you have a surplus, the extra energy is released by the reaction and the reaction is exothermic.

 

[Greatness]

The nuclear binding energy tells the energy required to separate a nucleus into its comprising nucleons , as you said.
If in any reaction (not just nuclear fusion) you compare the total (add all the binding energy for different reactants/products) binding energy for before and after the reaction, you will see that there might be a difference between them. If you have an energy deficit, that energy must be provided for the reaction to occur and the reaction is considered endothermic. If you have a surplus, the extra energy is released by the reaction and the reaction is exothermic.

So, the energy released by fusion is due to the mass defect...
When there is less mass associated to the energy of the nucleus or atom, as per E=mc^2, then the extra energy is released...
Am I correct?

 

[dauto]

So then why is energy released when two nuclei fuse for light elements, it is not because extra energy is present when this occurs...

The fused nuclei have more binding energy than the unfused ones(for light elements). The excess is released by the reaction

In fusion, energy is required for the new nuclei to form but energy is still released as per the mass defect.

Energy is required to overcome the repulsion between positively charge nuclei, but more is produced at the end.

Note that none of that is different than what happens in chemical reactions. Paper doesn't burn expontaneously either. It requires some heat. But more heat is released by the reaction.

Binding energy, Mass defect - Potato, Potahto.

 

[Greatness]

The fused nuclei have more binding energy than the unfused ones(for light elements). The excess is released by the reaction
Energy is required to overcome the repulsion between positively charge nuclei, but more is produced at the end.

Note that none of that is different than what happens in chemical reactions. Paper doesn't burn expontaneously either. It requires some heat. But more heat is released by the reaction.

Binding energy, Mass defect - Potato, Potahto.

Alright, but unfortunately I'm still confused with the use of "binding energy". When you say that the fused nuclei have more binding energy, does this mean that they require more energy to be separated into their nucleons? It seems very counterintuitive to me.
Are the energies of the first element + the energies of the second =, greater, or less than the energy of the newly formed nuclei resulting from fission? Is this energy binding energy or...I'm quite confused.
How are binding energy and mass defect related then?

 

[mfb]

Alright, but unfortunately I'm still confused with the use of "binding energy". When you say that the fused nuclei have more binding energy, does this mean that they require more energy to be separated into their nucleons? It seems very counterintuitive to me.

It is a bit counterintuitive, indeed - the more binding energy a nucleus has, the less energy it has (relative to a collection of unbound protons and neutrons).

Are the energies of the first element + the energies of the second =, greater, or less than the energy of the newly formed nuclei resulting from fission?

If fission releases energy, the new nucleus has a smaller rest energy than the sum of the original nuclei. The new nucleus has a larger binding energy, therefore the fission reaction can release energy.

 

[Greatness]

It is a bit counterintuitive, indeed - the more binding energy a nucleus has, the less energy it has (relative to a collection of unbound protons and neutrons).

If fission releases energy, the new nucleus has a smaller rest energy than the sum of the original nuclei. The new nucleus has a larger binding energy, therefore the fission reaction can release energy.

Alright, thanks, I forgot about that.

Why does the new nucleus have a smaller rest energy, is it due to the mass defect? Why does the mass defect occur, do we even know?

 

[dauto]

The mass defect and the binding energy are the same thing. Related by Einsteins formula E=mc^2. It happens because nucleons interact with each other through the strong nuclear interaction. None of that should be very mysterious since it is completely analogous to what happens for instance in chemistry. When a Carbon atom binds to two oxygen atoms the binding energy gets released due to the electric interaction between the atoms. That binding energy is related to the mass defect through the Formula E=mc^2. The mass defect due to chemical interactions is much smaller than the ones due to Nuclear interactions but it exists nonetheless. Lavoisier principle is only approximately true.