Binding energy curve

Fig. 13.1 plots the binding energy per nucleon Ebn against the mass number A for many nuclei.

For middle-mass nuclei, 30 < A < 170, Ebn hardly changes with A. The curve peaks at about 8.75 MeV for A = 56 and falls to 7.6 MeV at A = 238.

Ebn is lower for light nuclei (A < 30) and for heavy nuclei (A > 170).

Conclusion (i): the force binding nucleons is attractive and strong enough to give a few MeV per nucleon.

Conclusion (ii): the flat middle means the force is short-ranged. A nucleon deep inside a big nucleus feels only the neighbours within range. If it can have at most p of them, its binding is about pk, k being a constant energy. Adding more nucleons far away does not change it, and most nucleons of a large nucleus are inside, not on the surface.

This is the saturation property of the nuclear force: each nucleon affects only nucleons close to it.

Conclusion (iii): a nucleus of A = 240 has lower Ebn than one of A = 120. If it splits into two A = 120 nuclei, the nucleons end up more tightly bound and energy is released: fission.

Conclusion (iv): two very light nuclei (A ≤ 10) joining into a heavier one also end up with higher Ebn, again releasing energy: fusion, the energy source of the sun.

The curve is smooth, but it shows peaks at nuclides such as ⁴He and ¹⁶O, which is taken as evidence of an atom-like shell structure in nuclei.