Nuclear Binding Energy and Its Variation with Mass Number

The BINDING ENERGY of a nucleus, $BE$, is defined as the energy equivalent of its mass defect $\Delta m$ (Section 8.6), found using Einstein's relation:

Physically, the binding energy is the energy that would have to be supplied from outside to completely break the nucleus apart into its separate, free protons and neutrons; equivalently, it is the energy that would be RELEASED if those same free nucleons were instead brought together to form the nucleus. A larger binding energy therefore means a MORE STRONGLY BOUND, more stable nucleus.

Because larger nuclei naturally have a larger total binding energy simply on account of having more nucleons to bind, a fairer measure of HOW TIGHTLY a nucleus is bound, usable to compare nuclei of very different sizes, is the BINDING ENERGY PER NUCLEON,

obtained by dividing the total binding energy by the mass number. Plotting $BE/A$ against $A$ for every known stable nucleus produces one of the most important graphs in the whole of nuclear physics. The curve rises STEEPLY for the lightest nuclei, climbs to a broad maximum of about $8.7$-$8.8\ \text{MeV per nucleon}$ for nuclei in the neighbourhood of $A\approx 56$ (the iron-nickel region -- the most tightly bound, and hence the most stable, nuclei that exist), and then falls away slowly and gently for still heavier nuclei, down to around $7.6\ \text{MeV per nucleon}$ for a very heavy nucleus such as $^{238}_{92}\text{U}$. …