Is there a connection between mass defect and bound energy?

In summary, the conversation discusses the concept of mass defect in a nucleus and how it is related to binding energy. It is explained that in order to split off a nucleon from the nucleus, one would need to put in excitation energy equal to the binding energy. This energy was originally released when the nucleus was formed and is typically measured as mass. The conversation also touches on the process of fission and how it releases energy, but requires an initial input of energy to start the reaction.
  • #1
Bassalisk
947
2
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"?
 
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  • #2
Bassalisk said:
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.
 
  • #3
SpectraCat said:
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
 
  • #4
Bassalisk said:
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.
 
  • #5
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?
 
  • #6
Bassalisk said:
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.
 
  • #7
Ahaaaaaaaaaaaaaaaaaaaaaaaaa :D I had it confused with a fission, nuclear explosion etc.
 
  • #8
Bassalisk said:
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:
  • #9
Thank you for your help Cat <3
 

Related to Is there a connection between mass defect and bound energy?

What is mass defect-bound energy?

Mass defect-bound energy is the energy released when an atom's nucleus is formed from its individual protons and neutrons. It is the difference between the mass of the individual particles and the mass of the nucleus as a whole. This energy is responsible for holding the nucleus together and is a fundamental concept in nuclear physics.

How is mass defect-bound energy calculated?

Mass defect-bound energy is calculated using the famous equation E=mc^2, where E is the energy, m is the mass defect, and c is the speed of light. The mass defect is calculated by subtracting the mass of the individual particles (protons and neutrons) from the mass of the nucleus as a whole.

What is the significance of mass defect-bound energy?

The significance of mass defect-bound energy lies in its role in nuclear reactions and nuclear stability. It is the energy that holds the nucleus together and is responsible for the energy released in nuclear reactions such as fusion and fission. It also helps to explain the stability of certain nuclides compared to others.

What factors affect the value of mass defect-bound energy?

The value of mass defect-bound energy is affected by the number of nucleons (protons and neutrons) in the nucleus, as well as by the binding energy per nucleon. Nuclei with higher numbers of nucleons tend to have higher mass defect-bound energies, while nuclei with higher binding energies per nucleon tend to have lower mass defect-bound energies.

What is the relationship between mass defect-bound energy and nuclear binding energy?

Nuclear binding energy is another term for mass defect-bound energy. They both refer to the energy released when a nucleus is formed from its individual particles. However, nuclear binding energy is often used in the context of nuclear reactions and stability, while mass defect-bound energy is used in the context of nuclear physics and Einstein's famous equation.

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