# Conceptual question about binding energy, from OCR paper

• bonbon22
In summary: The mass defect or the "binding energy released" is equal to the binding energy which holds the nucleons together.
bonbon22
Homework Statement
Stars produce energy by nuclear fusion.
One particular fusion reaction between two protons (1
1H) is shown below.
1H1 + 1H1 ----> 2H1 + electron + neutrino
In this reaction 2.2MeV of energy is released.
(a) Only one of the particles shown in the reaction has binding energy.
Determine the binding energy per nucleon of this particle. Explain your answer
Relevant Equations
no equations
https://www.ocr.org.uk/Images/471908-question-paper-unit-h556-02-exploring-physics.pdf
24 A right near the end
there is energy relased in this reaction of nuclear fusion but they want the binding energy per nucleon
does that mean the binding energy released, as a gamma photon, per nucleon of the hydrogen atom and not the binding energy which holds the 2 H hydrogen atom together per nucleon ? Essentially what I am asking is , is the mass defect or the " binding energy released" EQUAL to the binding energy which holds the nucleons together as this question phrases it. And does this apply to all decays essentially , i can see the contrast with fission reactions where it releases less energy.. just want to confirm if my train of thought is correct also ... cheers

final question is lepton number conserved in this reaction as we have a lepton number of two on the left but on the right its one for the electron in the 2H1 atom , then 1 for the electron released , so in that case including the neutrino there is three on the right, why is a neutrino released also ? Charge doesn't seem to be conserved either as 0 charge on the left but on the right 1 electron 1 proton from the hydrogen atom and -1 from extra electron, am i missing something??

bonbon22 said:
Problem Statement: Stars produce energy by nuclear fusion.
One particular fusion reaction between two protons (1
1H) is shown below.
1H1 + 1H1 ----> 2H1 + electron + neutrino
In this reaction 2.2MeV of energy is released.
(a) Only one of the particles shown in the reaction has binding energy.
Determine the binding energy per nucleon of this particle. Explain your answer
Relevant Equations: no equations

https://www.ocr.org.uk/Images/471908-question-paper-unit-h556-02-exploring-physics.pdf
24 A right near the end
there is energy relased in this reaction of nuclear fusion but they want the binding energy per nucleon
does that mean the binding energy released, as a gamma photon, per nucleon of the hydrogen atom and not the binding energy which holds the 2 H hydrogen atom together per nucleon ? Essentially what I am asking is , is the mass defect or the " binding energy released" EQUAL to the binding energy which holds the nucleons together as this question phrases it. And does this apply to all decays essentially , i can see the contrast with fission reactions where it releases less energy.. just want to confirm if my train of thought is correct also ... cheers

final question is lepton number conserved in this reaction as we have a lepton number of two on the left but on the right its one for the electron in the 2H1 atom , then 1 for the electron released , so in that case including the neutrino there is three on the right, why is a neutrino released also ? Charge doesn't seem to be conserved either as 0 charge on the left but on the right 1 electron 1 proton from the hydrogen atom and -1 from extra electron, am i missing something??
Isn't it showing a positron, not an elctron?
According to https://en.m.wikipedia.org/wiki/Proton–proton_chain_reaction, the deuterium product is negatively charged, which puzzles me, but does restore the charge balance.

haruspex said:
Isn't it showing a positron, not an elctron?
According to https://en.m.wikipedia.org/wiki/Proton–proton_chain_reaction, the deuterium product is negatively charged, which puzzles me, but does restore the charge balance.
If you ask me, this might be a mistake in the Wikipedia article.

For reference, the original reaction in the original attachment (problem 24 in PDF file) is

$^1_1 \rm{H} \ + \ ^1_1 \rm{H} \ \rightarrow \ ^2_1 \rm{H} \ + \ ^{\ \ \ 0}_{+1} \rm{e} + \nu.$

Although not explicitly shown, I think it's assumed that all the hydrogen nuclei (including the deuterium nucleus) are +1 ionized. I mean we're talking about hot plasma here. Very, very hot plasma. We're not going to have electrons bound to nuclei in the sun's core, particularly during a fusion reaction. (At least that's my guess.)

I'm guessing this can be re-written, specifying the charge on everything as

$^1_1 \rm{H}^+ \ + \ ^1_1 \rm{H}^+ \ \rightarrow \ ^2_1 \rm{H}^+ \ + \ ^{\ \ \ 0}_{+1} \rm{e}^+ + \nu.$

So when the Wikipedia article says,

$^1_1 \rm{H} \ + \ ^1_1 \rm{H} \ \rightarrow \ ^2_1 \rm{H}^- \ + \ \rm{e}^+ + \nu,$

it leads me to think that it got something wrong with the ionization. Perhaps the author of that equation didn't assume that the proton reactants were already ionized.

collinsmark said:
We're not going to have electrons bound to nuclei in the sun's core, particularly during a fusion reaction.
Yes, that’s what I thought, but I didn’t expect the ionisation charges to be omitted in the equations.
Also, further down the Wikipedia article, the Deuterium atom appears with no charge indicated. So the negative charge shown looks like a furphy.

collinsmark
bonbon22 said:
Essentially what I am asking is , is the mass defect or the " binding energy released" EQUAL to the binding energy which holds the nucleons together as this question phrases it.

The way I interpret the first question, the answer is "No," I think they are different things. By that I mean in the given reaction expression ($^1_1 \rm{H} + \ ^1_1\rm{H} \ \rightarrow \ ^2_1\rm{H} + \ ^{\ \ 0}_{+1}\rm{e} + \rm{\nu}$) there is a mass deficit (or mass defect) involved. But that's not what the question is asking for.

Rather (the way I intepret it), the first question is asking you to ignore all but one particle (at least for now). Then it asks you to find the binding energy of that particular particle alone, ignoring the entirety of the rest of the original reaction expression (at least for now).

I interpret the first question as asking this:
Only one particle has binding energy.
(a) Determine which particle that is.
(b) Determine the binding energy per nucleon of that particle.

Using this definition of Nuclear Binding Energy:
Nuclear binding energy is the minimum energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons.

By that definition, you do not need to worry about the "binding energy" of a neutron itself (into a proton, electron, antineutrino, etc.) But you do need to determine the mass defect of the particular particle with more than one nucleon into its constituent protons and neutrons [Edit: and then divide by the number of nucleons in the original particle].

At least that's how I interpret the first question.

[Edit: And at the risk of being redundant, once you find the particle in question (one of the particles in the original reaction formula), break that particle down into its protons and neutrons. You don't need to break it down beyond that. Then find the binding energy per neucleon.]

Last edited:

## What is binding energy?

Binding energy is the energy required to hold together the nucleons (protons and neutrons) in an atomic nucleus. It is also known as the energy of nuclear binding and is expressed in units of mass, typically in MeV (mega electron volts).

## How is binding energy calculated?

Binding energy is calculated using the famous equation E=mc², where E is the energy, m is the mass defect (difference between the mass of the nucleus and the sum of the masses of its individual nucleons), and c is the speed of light. The binding energy is the difference between the total mass of the individual nucleons and the mass of the nucleus itself.

## What is the significance of binding energy?

Binding energy is essential in understanding the stability of an atomic nucleus. The higher the binding energy, the more stable the nucleus is. This is because the energy required to break the nucleus into its individual nucleons is high, making it less likely to undergo nuclear reactions.

## How does binding energy affect nuclear reactions?

Binding energy plays a crucial role in nuclear reactions. In nuclear fusion, the process of combining two lighter nuclei to form a heavier one, the resulting nucleus has a higher binding energy than the initial nuclei. This increase in binding energy leads to the release of excess energy in the form of heat and light. In nuclear fission, the process of splitting a heavy nucleus into lighter ones, the resulting nuclei have lower binding energies, and the excess energy is released in the form of heat and radiation.

## What factors affect binding energy?

The main factor that affects binding energy is the number of nucleons in the nucleus. Generally, nuclei with intermediate numbers of nucleons (between 40 and 80) have the highest binding energies. Additionally, the arrangement of nucleons in the nucleus and the forces between them also play a role in determining the binding energy.

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