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In researching the topic of nuclear fusion, I have a few doubts related to the mass defect, 'negative' potential energy and resultant energy released as a by-product of nuclear fusion.

  1. When two hydrogen nuclei (for instance) fuse to form a helium nucleus, the nucleons experience extra nuclear energy which in turn increases the binding energy between the nucleons. What is the origin of this extra energy? What is the cause of this energy? What accounts for this extra energy?

  2. I have heard that during the fusion, the hydrogen nuclei have negative potential energy which in turn causes a mass defect in the product nuclei. How is negative potential energy possible? I have also read that it is the differential between two states of mass. And if so, what exactly causes the 'negative' potential energy in the hydrogen nucleus. Is it due to the extra nuclear energy experienced by the nucleons of the helium nucleus and that they reduce their mass or something else? Why is energy released in fusion according to $m =E/c^2$ ?

Please answer a lot in detail with an example of a fusion specimen as it is difficult for me to understand just in mathematical terms....

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  • $\begingroup$ This barely answers anything, but about "How is negative potential energy possible?", potential energy can be positive, negative or zero depending on the convention you pick. By convention, I mean the state which you define as having zero potential energy. $\endgroup$
    – Sankalp
    May 16, 2022 at 14:02

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This answer and the accompanying discussion may be helpful to you https://physics.stackexchange.com/a/667132/313823

It is really no different from a chemical reaction like

$$H+OH \longrightarrow H_2O $$

Two nuclear species join to form a product that has lower chemical potential energy than the reactants, and the excess energy is released as kinetic energy of the products.

Similarly fission is a less stable (higher energy) reactant splitting into lower energy products, either spontaneously (via nuclear decay), or with a catalyst like being impacted by a neutron. This potential energy difference between reactants and products is carried away by the kinetic energy of the products.

The terms "mass defect" and "binding energy" are just terms used during book keeping of the various reaction energies. They don't have much of a physical meaning, and don't represent some "secret" form of energy that only exists in nuclear reactions.

Edit to address your comment: Regarding how two nuclei fusing can release energy. The chain of reactions that happens in the Sun is illustrated in the first figure here: https://en.m.wikipedia.org/wiki/Nuclear_fusion#Nuclear_fusion_in_stars

I am not too versed in nuclear physics, but it seems clear that the first reaction $$^1H+\, ^1H\longrightarrow \, ^2He+\beta+\nu$$

results in the two protons (one of which becomes a neutron) ending up much closer together, which drastically lowers the potential energy between them due to the attractive strong force. This potential energy is released in the form of kinetic energy of the products of that reaction, which we see macroscopically as producing light and heat (i.e. when those products collide with other things).

Potential energy between bodies in a force field (e.g. the Earth and Moon due to gravity, electron and proton due to electromagnetic forces, nucleons due to the strong force) and it's dependence on the distance between the bodies is a fundamental concept in physics, and that may be what you want to focus on gaining a better understanding of first, rather than nuclear reactions in particular.

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  • $\begingroup$ The mass defect is physically measurable, so does have physical meaning. $\endgroup$
    – Jon Custer
    May 16, 2022 at 14:47
  • $\begingroup$ Maybe that was too strong a statement. What I meant was "mass defect" is just a way of quantifying the energy difference between reactants and products. Technically chemical reactions have a mass defect as well, but it's typically so small as to be negligible. $\endgroup$
    – RC_23
    May 16, 2022 at 15:08
  • $\begingroup$ But exactly what I wanted to know was that WHY is there a difference in potential energy between the species....... $\endgroup$
    – Hardik
    May 16, 2022 at 15:25
  • $\begingroup$ The same reason there is a potential energy difference between a boulder at the top of a hill, and the boulder at the bottom of the hill. Chemical and nuclear species all have potential energies based on the configuration of charges, color charges, spins, and other quantum numbers. Each species settles into the available quantum state that minimizes its potential energy. H and OH have a higher potential energy than $H_2O$ because of the available electron orbitals in each. $\endgroup$
    – RC_23
    May 16, 2022 at 16:43
  • $\begingroup$ @RC_23 can you please surmise that why is energy released when two hydrogen nuclei bind into a helium nucleus including the 'negative' potential energy concept and binding energy for a better understanding? Thanking you. $\endgroup$
    – Hardik
    May 17, 2022 at 7:28
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. . . . . which in turn increases the binding energy between the nucleons. What is the origin of this extra energy? What is the cause of this energy?.

I think you have misunderstood the idea of binding energy.
When nucleons (protons ands neutrons) join together energy is released to form a nucleus. The energy released is equal to the binding energy of the resulting nucleus which is also the energy which needs to be supplied to split up nucleus into its constituent parts. If a nucleus has a higher binding energy it means that it more energy is required to split it into its constituent part or, put another way, more energy is released when the constituent parts come together to form the nucleus.

I have heard that during the fusion , the hydrogen nuclei have negative potential energy which in turn causes a mass defect in the product nuclei.

This statement is very confusing as is your second group of questions. If you consider the constituent parts of a nucleus when they are far away from one another you can say that they have potential energy. When those constituent parts come together with the release of energy their potential energy has decreased. If when the constituent parts are far apart you define the potential energy to be zero then when the nucleus is formed it will have a negative (lower than zero) potential energy.

It is found the the sum of the masses of the conspuent parts of a nucleus is greater than the mass of the resulting nucleus. Thus going from constituent parts to a nucleus results in a decrease in mass which is called the mass defect. The binding energy of a nucleus $E_{\rm binding}$ and the mass defect $\Delta m$ are linked, $E_{\rm binding} = \Delta m\, c^2$.

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  • $\begingroup$ But if energy is required to separate the constituents then what is the scientific reason that energy is released when they bind together if we don't consider the other equation...? $\endgroup$
    – Hardik
    May 16, 2022 at 15:27
  • $\begingroup$ Which other equation? $\endgroup$
    – Farcher
    May 16, 2022 at 16:22
  • $\begingroup$ If we consider that if energy is required to separate the constituents of a nucleus then why is eenrgy is released when they bind? $\endgroup$
    – Hardik
    May 17, 2022 at 7:25
  • $\begingroup$ Lust like in a chemical reaction when hydrogen and oxygen combine to form water with the release of energy so to split water into hydrogen and oxygen requires an input of energy, $\endgroup$
    – Farcher
    May 17, 2022 at 7:58
  • $\begingroup$ can you please surmise that why is energy released when two hydrogen nuclei bind into a helium nucleus including the 'negative' potential energy concept and binding energy for a better understanding? Thanking you. $\endgroup$
    – Hardik
    May 17, 2022 at 9:35

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