Exploring the Relationship Between Binding Energy and Distance in Nuclei

In summary, the weight of protons and neutrons forming a nucleus is less than the weight of them as standalone particles due to the "mass defect" which is the binding energy holding the nucleus together. When nucleons are separated, the strength of the strong force between them decreases, similar to the electric force. However, the scaling with distance is different for the strong force. When measuring the strong force at a fixed distance from a proton, it will always be the same, but as more particles are brought together, the total field strength increases.
  • #1
artis
1,481
976
I always read that the weight of the protons and neutrons forming a nucleus is less than the weight of them if counted as standalone particles, the difference being the "mass defect" which goes into the binding energy to hold the nucleus together.

So I have two questions.

1) The elementary particle for the strong interaction being the gluon is responsible for the strong force, the strong force is coming from each nucleon within a nucleus, so if I say separate these nucleons far apart, do they still "exert" the same amount of strong force? Analogous to how a charged particle has the same strength E field around it whether being alone or close to other particles?
2) Now if there is a "mass defect" between individual protons and neutrons and the same amount of protons and neutrons in a nucleus then how does this mass defect change with distance, in other words at which point or how far do the nucleons need to be separated in order for them to change their mass as the result of less binding energy, how does this weight vs binding energy scale with distance? Does it happen gradually or is there a sharp boundary in terms of distance after which each nucleon "gets back" it's full weight?3) if composite particles like protons and neutrons have the strong force always "with them" then are the gluons always emitted from them and if so do they compare to virtual photons of a static charge in the EM field or actual photons of a changing EM field? Can a particle like a proton lose energy by this strong force field if being standalone?
 
Physics news on Phys.org
  • #2
Have you read the Wikipedia page on the strong interaction? It seems to answer a lot of your questions on nuclear forces.
 
  • #3
On question 2: the mass of individual particles does not change, but when particles are bound together the mass of the bound system is less that the sum of the particles. The mass defect is the binding energy and not a mysterious physical change in the particle themselves.
 
  • Like
Likes artis and vanhees71
  • #4
artis said:
1) The elementary particle for the strong interaction being the gluon is responsible for the strong force, the strong force is coming from each nucleon within a nucleus, so if I say separate these nucleons far apart, do they still "exert" the same amount of strong force? Analogous to how a charged particle has the same strength E field around it whether being alone or close to other particles?
If you separate the nucleons the force between them decreases. This is analogous to the electric interaction where the force decreases with increasing distance, too. For the strong force the scaling with distance is different, however, the force drops faster.
 
  • Like
Likes artis and vanhees71
  • #5
hmm , thanks @PeroK it wasn't that obvious to me before that as you say
PeroK said:
the mass of individual particles does not change, but when particles are bound together the mass of the bound system is less that the sum of the particles.
Usually this is stated the other way around that "mass of nucleus is less than that of individual nucleons counted together". But I like the way you said better.
ps. yes I have read the wiki article.

Now as also @mfb said that separating the nucleons apart decreases the strength of the field much like with electric charge.
But electric charge always has the same strength irrespective of the distance between any such two charges, the strengh of the charge itself if measured a fixed distance from the say charged particle would be the same only the total E field strength would increase if many such charges were brought together, does the same rule apply to the strong force and measuring it a fixed distance from a proton for example, where the strong force is always the same a fixed distance from a proton or a neutron just that once together the total field strength increases because of the increase in particle count?
 
  • #6
artis said:
hmm , thanks @PeroK it wasn't that obvious to me before that as you say

Usually this is stated the other way around that "mass of nucleus is less than that of individual nucleons counted together". But I like the way you said better.
ps. yes I have read the wiki article.

Now as also @mfb said that separating the nucleons apart decreases the strength of the field much like with electric charge.
But electric charge always has the same strength irrespective of the distance between any such two charges, the strengh of the charge itself if measured a fixed distance from the say charged particle would be the same only the total E field strength would increase if many such charges were brought together, does the same rule apply to the strong force and measuring it a fixed distance from a proton for example, where the strong force is always the same a fixed distance from a proton or a neutron just that once together the total field strength increases because of the increase in particle count?

You seem slightly confused about the concept of electrostatic potential. Let's look at three examples:

1) A proton (positive charge) and an electron (negative charge). These attract each other and in QM they form a bound system (called a hydrogen atom), releasing energy in the form of a photon as they do. The mass of the hydrogen atom is the mass of a proton + mass of the electron - the released binding energy.

This forms a stable system because you need to input at least the binding energy to separate the two particles (this is called ionisation).

2) Two protons repel each other. They cannot form a bound system electrostatically. If you did hold them together, then they would separate naturally as soon as you release them.

3) Protons and neutrons are also subject to the strong force, which is attractive. A nucleus generally needs neutrons to help hold it together and counteract the electrostatic repulsion between the protons. The strong force is short range. As the nucleus grows, each proton is effectively repelled by all the other protons, but only attracted (strongly) by the nearest neutrons and protons. Eventually, if it gets too big, the nucleus becomes unstable as the short range strong force cannot overcome the long range electrostatic repulsion of all the protons.
 
  • #7
@PeroK I think you misunderstood my misunderstanding,

I do get that two like charges repel, maybe I should have pointed in my example that if they would be kept together somehow they would form a total E field which would be greater in magnitude than if there was just a single charge. An example I guess would be an electron potential well , where if the electrons are more and closer together they have a stronger field if measured some distance away from the well, than if they were less and further apart.
If this is correct which I think it is, then does the strong force act in a similar fashion where if not accounted for the electrostatic repulsion between protons, eventually more protons/neutrons together would have a stronger strong force field if measured a certain distance from the nucleus, than if there were fewer such particles?ps. in your examples , in example 1 when you say mass of proton + mass of electron - the binding energy I assume you are referring to the electrostatic binding energy, because as far as I know the electron has no strong force as it is an elementary particle, so the proton's strong force has nothing to bind to?
 
  • #8
@artis what don't you understand about the concept of a force working over a shorter range? The rest is largely irrelevant.
 
  • #9
As you were replying I was still writing see my last paragraph please.

Well I do understand that it works in a shorter range, I was just asking whether the total field adds up much like the electrostatic one if the number of particles is increased. I guess it does
 
  • #10
artis said:
As you were replying I was still writing see my last paragraph please.

Well I do understand that it works in a shorter range, I was just asking whether the total field adds up much like the electrostatic one if the number of particles is increased. I guess it does

I don't believe that the strong force admits a classical field theory - unlike the quantum electrostatic interaction. You can't talk about adding strong fields in that sense. Any calculations would have to be done on the basis of QCD.
 
  • #11
ok,so far we have come to the conclusion that the strong force if measured as a total a distance away from certain number of particles doesn't add up like the electrostatic field would if measured a certain distance away from given number of charged particles.

@PeroK you said in post #3
PeroK said:
the mass of individual particles does not change, but when particles are bound together the mass of the bound system is less that the sum of the particles.
So when the particles are in the bound system then each individual particle must weigh less because otherwise how come the total system weigh less ?
Or is it that each particle weighs the same also in the bound system just that the system together weighs less than it should if simply counted by the individual particle masses making up the system ?

If this is so then it seems like the individual particle masses within a bound system are in a sort of superposition if you will, where they weigh X if measured alone but X-Y if measured as part of the system?
 
  • #12
The total mass of the system is not the sum of masses of the individual particles in it.
artis said:
If this is so then it seems like the individual particle masses within a bound system are in a sort of superposition if you will, where they weigh X if measured alone but X-Y if measured as part of the system?
No.
 
  • #13
@artis the concept of mass is more complicated than simply adding particle masses. Binding energy is not a particle mass but it is relevant to the mass of a system.
 
  • #14
Ok I think I get the concept, the individual particle masses don't change, then when the particles make up a bound system the particles should not be considered anymore mass wise but now the whole atom should be looked at like one big "particle" having an emergent property which is that it's mass is not the same as that of is constituents.
And that I guess is because some amount of the mass/energy within the nucleus goes into keeping it together. Here I have two questions.

1) How would the mass ratio of the nucleus vs mass of it's individual particles combined change if each nucleon would be pulled so far apart that it would sit on the tail edge of the strong force, where separation can occur? What I'm asking is does the mass defect of the nucleus changes with nucleon distance from one another within the bound nucleus system or is it irrespective of that?2)This nucleus as a bound system mass defect is the same mass defect that is responsible for the mass into energy conversion during a nuclear reaction? For example fusion where the product of two fused lighter elements itself weighs less than the two atoms that made the heavier element before the reaction.

So say if I had protons and neutrons sitting around separated and then I somehow magically put them together so that all of them form say deuterium atoms at the same time this would then release a burst of energy similarly to how any other nuclear reaction releases energy whether fission or fusion ? By the principle of the mass to energy conversion?
 
  • #15
artis said:
1) How would the mass ratio of the nucleus vs mass of it's individual particles combined change if each nucleon would be pulled so far apart that it would sit on the tail edge of the strong force, where separation can occur?
You produce a really highly excited state or already independent nuclei. The ratio would get closer to 1. Where exactly depends on what exactly you do.
artis said:
This nucleus as a bound system mass defect is the same mass defect that is responsible for the mass into energy conversion during a nuclear reaction?
Sure.
artis said:
So say if I had protons and neutrons sitting around separated and then I somehow magically put them together so that all of them form say deuterium atoms at the same time this would then release a burst of energy similarly to how any other nuclear reaction releases energy whether fission or fusion ?
Sure. You just had fusion reactions.
 
  • #16
@mfb So if the nucleons would get pulled further apart the mass defect of the nucleus would start to disappear until at some point vanish completely?
 
  • #17
You can't really do this in a classical way where you could have "more separated" nucleons.
 
  • #18
@mfb I know ,I am just asking theoretically.

I guess you can't do that because the nucleons are either bound or not correct?
But in theory the amount of mass converted to binding energy for the bound system should depend on how "tightly" the particles are bound should it not ?
 

Related to Exploring the Relationship Between Binding Energy and Distance in Nuclei

1. What is binding energy?

Binding energy is the amount of energy required to hold together the nucleus of an atom. It is a measure of the strength of the attractive forces between the protons and neutrons in the nucleus.

2. How does binding energy change with distance?

Binding energy decreases as distance between particles in the nucleus increases. This is because the attractive nuclear force, which is responsible for binding the particles together, becomes weaker as the distance between particles increases.

3. What is the relationship between binding energy and nuclear stability?

The higher the binding energy, the more stable the nucleus is. This is because a higher binding energy means that the particles in the nucleus are more tightly bound together, making it more difficult for the nucleus to break apart.

4. How is binding energy calculated?

Binding energy is calculated by subtracting the total mass of the individual particles in the nucleus from the mass of the nucleus itself. This difference in mass is then converted into energy using Einstein's famous equation, E=mc^2.

5. Why is binding energy important in nuclear reactions?

Binding energy plays a crucial role in nuclear reactions as it determines the stability and energy release of the reaction. In nuclear fusion reactions, the combining of two nuclei releases energy due to the increase in binding energy, while in nuclear fission reactions, the splitting of a nucleus releases energy due to the decrease in binding energy.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
2
Views
797
  • High Energy, Nuclear, Particle Physics
Replies
28
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
5
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
3
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
12
Views
3K
  • High Energy, Nuclear, Particle Physics
Replies
3
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
474
Back
Top