# A level physics nuclear physics - need help understanding binding energy

Hi, i've learnt about binding energy and mass defect, but it just doesn't make sense to me, so i'm hoping someone can explain it to me here.

From my understanding, the mass of the individual protons and neutrons is always more than the mass of the wholoe nuclei. This is because that missing mass has been converted into binding energy. In other words, this missing mass has been converted into energy that is needed by the strong nuclear force and that is the amount of energy we need to put in to the atom to seperate it back to it's constituant parts. What I don't understand is if the energy from the mass defect is used to hold the nuclei together, how is that the same amount of energy that the nuclei release.

This is because I've read that the energy from the mass defect is also the amount of energy that is released by the nuclei.

Please let me know if I've misunderstood something or i've said something that is incorrect.
Your question makes perfect sense: the confusion arises due to the fact that it is the difference in mass defects between the nuclei which fission (split to form lighter elements) or fuse (join to form heavier ones) which produces the net energy change of that nuclear reaction. This can be explained by looking at the nuclear binding energy curve.

Elements on the left of the curve (lighter than iron) may fuse to form elements which have a lower net mass defect, and therefore release energy. Elements on the right of the curve (heavier than iron) may fission to form elements which also have a lower net mass defect, and therefore release energy.

Another confusing thing is that the process is often described as "transforming" mass into energy, whereas in fact they are the same thing (mass-energy). The sum of the masses of the nuclei and the mass of the binding energy (expressed as E/c^2) is constant - there is no "missing mass". Probably safest to stick to the standard "transformation" description at A level though, despite it being potentially confusing.
(edited 1 year ago)
Original post by lordaxil
Your question makes perfect sense: the confusion arises due to the fact that it is the difference in mass defects between the nuclei which fission (split to form lighter elements) or fuse (join to form heavier ones) which produces the net energy change of that nuclear reaction. This can be explained by looking at the nuclear binding energy curve.

Elements on the left of the curve (lighter than iron) may fuse to form elements which have a lower net mass defect, and therefore release energy. Elements on the right of the curve (heavier than iron) may fission to form elements which also have a lower net mass defect, and therefore release energy.

Another confusing thing is that the process is often described as "transforming" mass into energy, whereas in fact they are the same thing (mass-energy). The sum of the masses of the nuclei and the mass of the binding energy (expressed as E/c^2) is constant - there is no "missing mass". Probably safest to stick to the standard "transformation" description at A level though, despite it being potentially confusing.

I'm sorry, I tried to understand that, but I just can't wrap my head around it.
No problem. Let's try it a different way, with a concrete example.

Let's say that you have an unstable 235U nucleus which gets hit by a neutron and splits into two smaller nuclei (for example, 141Ba and 92Kr) plus a couple of free neutrons. Reading off the binding energy curve above, 235U has about 7.5 MeV/nucleon, whereas 141Ba and 92Kr have about 8.25 MeV/nucleon and 8.7 MeV/nucleon, respectively (i.e. they are more stable than 235U). This means that some energy will be released during the fission reaction, and you can calculate roughly how much by multiplying the atomic masses of the reactants and products by their average binding energies:

$(141 \times 8.25 + 92 \times 8.7) - 235 \times 7.5 = +201$ MeV

This energy is coming from the difference in the "mass defects" of U, Ba and Kr - in other words, the fact that nucleons are more stable in Ba and Kr than they are in U, on average. Nevertheless, they are ALL more stable than free protons and neutrons (so they all have a positive mass defect).

Hope that helps.