# B Binding energy question

1. Oct 10, 2016

### victorhugo

Go to 6:06

From what I've read, it appears that binding energy is the mass lost equally from each nucleon in a nucleus and it is used as some sort of 'glue' in the strong nuclear force to hold the nucleus together.
I'm guessing that is incorrect because, with that logic, 2mev + 10mev nuclei fusing to a nucleus that requires 28 mev looks like it would need energy. That also makes sense because larger nuclei have more electrostatic repulsion from protons and so would need more binding energy per nucleon to overcome that foce (or does that never change? is the binding energy per nucleon always the same, and what increases is the total binding energy due to more nucleons, so when an atom is unstable it is simply because the electrostatic repulsion have over come the strong nuclear force, instead of the strong nuclear force not being able to increase any more per nucleon?)

As such, it appears that binding energy is just how much energy 'needs to be lost' per nucleon. That way, the 28MEV in the video means that 28-10=18mev needs to be lost for the atom to hold itself together. Could someone please explain that further to me?

Thank you in advance.

2. Oct 10, 2016

### Staff: Mentor

Nuclear binding energy is simply the loss of energy from the nucleons that occurs whenever the nucleons fuse together. In other words, when the nucleons fuse together they release a certain amount of energy. The more energy lost from the nucleons, the higher the binding energy. If you were to pull those nucleons apart you would need to add energy equal to the binding energy. It is not a 'glue' that holds the nucleons together. That would be the strong nuclear force.

Let's look at deuterium and tritium. Deuterium has a binding energy of 2 MeV and tritium has a binding energy of 8 MeV. This means that if you were to pull deuterium apart into an unbound proton and neutron you would need to add 2 MeV of energy to do so. Splitting tritium up into one proton and two neutrons would require 8 MeV of energy.

Now, when deuterium and tritium fuse together they form helium-4. Helium-4 has a binding energy of 28 MeV. To split helium-4 up into 2 unbound protons and 2 unbound neutrons would require that amount of energy. Conversely, allowing those 4 particles to come together to form helium-4 would release 28 MeV into the environment. However, it is extremely rare for two free protons and two free neutrons to fuse together in this manner. The far more common method of creating helium-4 is through fusion of isotopes of hydrogen. So how much energy is released by the formation of helium-4 by the fusion of tritium and deuterium? The answer is that you simply take the binding energy of helium and subtract the binding energy of the fusing particles: 28 MeV - 8 MeV - 2 MeV = 18 MeV.

So, when tritium and deuterium fuse together to form helium-4, the reaction releases 18 MeV of energy into the environment.

The binding energy of a nucleus is the result of the strong force vs the electromagnetic force. The strong force is MUCH stronger than the EM force, but it is very short range. As nuclei grow larger, the strong force from one nucleon can only interact with the nucleons very close to it. However, the EM force has an infinite range and loses essentially no strength over the distance of an atomic nucleus. So as you add more nucleons the repulsive force from the EM force continues to build on every single proton, but the strong force does not. At a certain point, the EM force essentially "equalizes" with the strong force and adding more nucleons simply doesn't net you any binding energy. This is the case with Nickel-62.

3. Oct 10, 2016

### victorhugo

I understood all of your explanation clearly except for this part. There are some assumptions that aren't what I've learnt before.

Why do the nucleons lose mass to go into the binding energy? My teacher told me this went to the STRONG NUCLEAR force to hold the nucleons together.
You stated "The binding energy of a nucleus is the result of the strong force vs the electromagnetic force" & "it[the binding energy] is not a 'glue' that holds the nucleons together. That would be the strong nuclear force." so that confused me.
I think I don't know what the strong nuclear force is then.

4. Oct 10, 2016

### victorhugo

Also, what is the "ElectroMagnetic force" exactly? I know that protons repel each other due to the electrostatic force, and it makes sense that this is what pushes them apart. Is it then not just the ES force but an 'EM' force?

5. Oct 10, 2016

### Staff: Mentor

They lose mass become they lose energy. When they bind together a quantity of energy is released either as EM radiation (light, gamma rays, etc) or as other particles like neutrinos. Because of mass-energy equivalence (that thing that Einstein's equation e=mc2 refers to) the nucleus loses mass. No energy is given to the strong force. Energy isn't required for fundamental forces to work. Indeed it is the very opposite. Energy is the result of forces acting on objects and fields, not the other way around.

Note that the nucleons don't lose mass to go into the binding energy. Nothing goes into the binding energy. Binding energy just measures how much energy is given up when nucleons fuse together. A (bad) analogy is that binding energy is like pouring two bottles of soda into a big bowl and measuring how much splashed out. Except that you can always be really careful and not spill any soda, while energy is always released during fusion as long as the nuclei are below iron/nickel.

The strong nuclear force is one of the 4 fundamental forces of nature, the others being gravitation, weak force, and electromagnetism. All interactions between objects are the result of these 4 forces (another word for 'force' is 'interaction', so you could call them the 4 fundamental interactions).

The electrostatic force is just one manifestation of the EM force. Magnetic forces are also part of the electromagnetic force. Magnetic and electric forces are joined together because of how they are related. The exact reasons might be a bit beyond your level of knowledge at the moment, but if you'd like to know more feel free to make a thread on it.

6. Oct 10, 2016

### Staff: Mentor

The individual nucleons do not lose mass. The mass of a system of bound nucleons is less than the mass of a system of unbound nucleons, because of the (difference in) binding energy. Adding energy to a system (e.g. by doing work on a collection of nucleons in order to separate them) increases its mass, and removing energy from a system decreases its mass.

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