The binding energy per nucleon s can be derived from the difference AM between the mass of a nuclide and the sum of its components and is an important model-independent parameter characterizing each isotope. When plotted as a function of atomic mass number A, s shows ahump-like shape, increasing from hydrogen to iron (and neighbouring elements at A ~ 60) and then smoothly decreasing towards the heaviest elements. This pattern yields important inferences on the origin, abundance and stability of the elements.

The synthesis of nuclei below the iron peak occurs with release of nuclear energy, whereas the production of heavier elements requires an energy input. For example, the synthesis of one helium nucleus from two protons and two neutrons releases 28 MeV (or 4.5 x 10-5 erg) of atomic energy, which exceeds the typical energy of chemical interactions by a factor ~106 (!). If synthesis occurs in some hypothetical thermo-isolated environment, extremely high temperatures can result, leading to further interaction of charged particles in nucleosynthetic processes.

The total binding energy depends on the numbers of protons and neutrons in the nuclei. Competition of the short-distance nuclear forces (tending to keep the nucleons together) and the Coulomb repulsion forces (tending to disunite them) leads to neutron-proton ratios > 1in heavy nuclei. In a plot of the number of protons versus the number of neutrons, the "stability valley" departs from the isoline after the doubly magic 40Ca, approaching a neutron-to-proton ratio of 1.5 for the heaviest isotopes.

Strongly bound elements with a high s value should be more abundant than fragile ones, and the most strongly bound, iron, is expected to be especially abundant. For isotopes with A > 60, s decreases steadily with increasing nuclear mass, so that their abundance is expected to decrease also. A limit for the mass of stable isotopes is expected because of the increasing Coulomb forces in the nucleus; the heaviest stable nuclide is 209Bi. The binding energy of some heavy nuclei is less than the binding energies of their constituents (e.g. the binding energy of 238U is less than the binding energies of 4He and 234Th), and this relationship predicts their nuclear decay and fission.

As elements with an even number of protons can have many stable isotopes and those with an odd number of protons generally only one, a sawtooth shape of the elemental abundance curve is predicted. Also, because only a single stable isotope exists in an odd-isobar family, this isotope comprises all precursor nuclides, whereas even-even isotopes have generally no precursors. Therefore the abundance curve for odd isobars is smoother than that for even isobars.

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