The difference in the binding energy per nucleon

[Avalon_18]

if binding energy per nucleon is proportional to the number of nucleons in the range of the nuclear force. then why is the binding energy for carbon 12 higher than nitrogen 14

 

[Nugatory]

We calculate the binding energy per nucleon from the known total binding energy, not the other way around. The binding energies of the two nuclei are observational facts; then we divide one by 12 and the other by 14 to get the binding energy per nucleon.

 

[Avalon_18]

We calculate the binding energy per nucleon from the known total binding energy, not the other way around. The binding energies of
the two nuclei are observational facts; then we divide one by 12 and the other by 14 to get the binding energy per nucleon.

but then the question would become if carbon has less nucleon than nitrogen why is the binding energy larger for carbon. neither of the nuclei is large enough that the nuclear forces from one nucleon wouldn't affect the other nucleons.

 

[Nugatory]

but then the question would become if carbon has less nucleon than nitrogen why is the binding energy larger for carbon. neither of the nuclei is large enough that the nuclear forces from one nucleon wouldn't affect the other nucleons.

There's a lot more to nuclear binding energies than just the number of nucleons and the size of the nucleus. If you consider only those factors you can explain some broad-brush phenomena such as the way that the binding energy curve bottoms out at iron and climbs in both directions from there; but look more closely at nearby nuclei anywhere along the curve and it will be clear that there is more going on than that.

I do not know of any decent B-level explanation of these subtleties... perhaps some other posters here do.