# Binding energy vs Mass number Plot and Pairing effect for higher nuclei region

I have two doubts.

1. In every text or literature, one always see the graph of binding energy per nucleon vs mass number and not binding energy vs mass number. Is it like we don't interpret any useful information from the graph between binding energy vs mass number or is there something else.

2. The second doubt is why we have some kinks only for lighter nuclei region and not for heavy nuclei region. I have read something about it, and it has to do with pairing effect and magic numbers. But that leads me to doubt then why don't we see those kinks for magic number 50, 82 and 126?

$$1.$$

I think you can get useful information from the graphs of neuclear binding energy vs mass number. But that would only be the information that we would also pull from neuclear binding energycper nucleus vs mass number.

The difference is what information you take directly from it at first glance. With "neuclear binding energy per nucleon vs mass number" we see directly that the generalized binding energy also increases with an increasing number of nucleons in the nucleus. On the other hand, with "neuclear binding energy vs mass number" we see directly that more nucleons do not necessarily require as much more energy as the fewer nucleons:

(see here: data form wolfram alpha)

$$2.$$

I don't know the answer here. But if I may spread my guess: These spikes mean that the amount of binding energy that the nuclide needs to absorb or not absorb this one nucleon is less than the previous binding energy of the nuclide per nucleon. This amount of difference is also divided by the number of nucleons. So if this difference does not increase with an increasing number of nucleons, this peak should become smaller and smaller. So we should be able to find those ticks there, too, but they're just so tiny. (just a guess)

Example: The binding energy of C-$$13$$ per nucleon $$\approx 7.5 ~\mathrm{MeV}$$ (total: $$\approx 97 ~\mathrm{MeV}$$) and C-$$12$$ per nucleon $$\approx 7.7 ~\mathrm{MeV}$$ (total: $$\approx 92 ~\mathrm{MeV}$$) aka this one nucleon that came along brought only $$\approx 5 ~\mathrm{MeV}$$ binding energy to that aka less then the other nucleons (we see a big spike). But if we do the same comparison with uranium-$$235$$ and $$236$$ (total for U-$$235$$ is $$\approx 1784 ~\mathrm{MeV}$$ and for $$236$$ is $$\approx 1790 ~\mathrm{MeV}$$, so new nucleon has $$\approx 6.6 ~\mathrm{MeV}$$), we see a " Difference" of about $$1 ~\mathrm{MeV}$$, which is large but not visually noticeable due to the high number of nucleons in the graph.