# Mass defect-bound energy

## Main Question or Discussion Point

Simple question:

We have defect of mass delta(m) in some nucleus. This simply means that sum of all protons and neutrons is larger than the measured mass of the nucleus.

When I break this bound energy, that mass defect that is turned into bound energy, I have fission? Assuming that I do this with a neutron(most easily approaches nucleus). Energy will be released equal to this bound energy?

Shouldn't then those protons and neutrons, that were scattered, be "defected"?

## Answers and Replies

Related Atomic and Condensed Matter News on Phys.org
SpectraCat
Science Advisor
Simple question:

We have defect of mass delta(m) in some nucleus. This simply means that sum of all protons and neutrons is larger than the measured mass of the nucleus.

When I break this bound energy, that mass defect that is turned into bound energy, I have fission? Assuming that I do this with a neutron(most easily approaches nucleus). Energy will be released equal to this bound energy?
No .. you have that backwards .. in order to split off a nucleon, you would need to put in excitation equal to at least the binding energy. The mass defect reflects binding energy that was *dissipated* when the nucleus was formed ... therefore you need to put it back in in order to reverse the process.

No .. you have that backwards .. in order to split off a nucleon, you would need to put in excitation equal to at least the binding energy. The mass defect reflects binding energy that was *dissipated* when the nucleus was formed ... therefore you need to put it back in in order to reverse the process.
So... When I invest energy into reaction, e.g. sending neutron towards some nucleus, It will have to be at least the energy of the binding. Well, when the nucleus was formed, if I invested energy, why does mass defect show up? How does this work exactly?

Can you clear these misunderstandings I have?

Thanks

SpectraCat
Science Advisor
So... When I invest energy into reaction, e.g. sending neutron towards some nucleus, It will have to be at least the energy of the binding. Well, when the nucleus was formed, if I invested energy, why does mass defect show up? How does this work exactly?

Can you clear these misunderstandings I have?

Thanks
The mass defect shows up because a certain amount of mass was converted into energy when the nucleus was formed. This energy is radiated away (typically as gammas). Basically it is nothing more complicated than E=mc2 ... it's just that the energy involved from binding of nucleons due to the strong force is so large that it makes sense to measure it as mass.

Note that there is nothing special about this ... there is a mass defect associated with the binding of electrons to atoms as well. It's just very very small compared to the mass defects due to nucleons in the nucleus. However it can still be measured .. I don't have a reference handy but I believe that this mass defect for electron binding has been measured by very high-precision mass spectrometry.

I am beginning to form a slight picture. If I want to expel one nucleon from the core, I have to hit it with at least binding energy. When hit it, energy is released? What happens then? What happens to that defect of mass, that binding energy?

SpectraCat
Science Advisor
I am beginning to form a slight picture. If I want to expel one nucleon from the core, I have to hit it with at least binding energy. When hit it, energy is released? What happens then? What happens to that defect of mass, that binding energy?
No .. energy is released on *binding*. If you want to *break* the binding, you have to put energy back in. There is no energy released by the breaking of the bond.

Ahaaaaaaaaaaaaaaaaaaaaaaaaa :D I had it confused with a fission, nuclear explosion etc.

SpectraCat
Science Advisor
Ahaaaaaaaaaaaaaaaaaaaaaaaaa :D I had it confused with a fission, nuclear explosion etc.
Fission is different .. in such a case, a nucleus with a *lower* binding energy per nucleon splits, resulting in two daughter nuclei with *higher* binding energy per nucleon. So the overall process releases energy. However, fission often (always?) has an activation energy associated with it, so you need to put a little energy in (e.g. with a neutron collision) so that you can get a LOT of energy out.

That last point may have been what was confusing you ... yes, you do have to do something to start the process, which then releases energy. It's similar to lighting a fire with a match .. you put in a little energy to start the combustion process, but the overall process releases far more energy that you put in initially.

Last edited:
Thank you for your help Cat <3