Nuclear binding energy

Weigh a nucleus carefully and compare it with the sum of the masses of its individual protons and neutrons measured separately, and the nucleus always comes up slightly lighter. This missing mass — the mass defect — is not lost; by mass-energy equivalence, E = mc², it has been converted into the energy that holds the nucleus together, called the binding energy. Equivalently, the binding energy is exactly the amount of energy that would need to be supplied to pull the nucleus apart into its separate, free nucleons — a tightly bound nucleus therefore has both a large binding energy and a correspondingly large mass deficit relative to its separated parts.

Dividing binding energy by the number of nucleons gives binding energy per nucleon, a measure of how tightly, on average, each nucleon is held. Plotted against atomic mass number, this quantity rises steeply for the lightest nuclei, peaks around iron and nickel (mass numbers near 56-62), and then declines slowly for heavier nuclei. This single curve is the key to understanding both major forms of nuclear energy release. Fusing light nuclei together — hydrogen into helium, for instance — moves the product further up the rising part of the curve, so the product nucleus has more binding energy per nucleon than the reactants; the difference is released as energy, which is why fusion powers stars. Splitting a heavy nucleus into two medium-mass fragments moves both fragments up toward the peak from the declining side of the curve, again increasing total binding energy per nucleon and releasing the difference; this is why fission of heavy nuclei such as uranium also releases energy. Nuclei already near the peak, such as iron, release no net energy from either fusing further or splitting apart — which is exactly why iron is the endpoint of energy-releasing fusion inside stars, and why nuclei near the peak of the curve are typically the most stable nuclei found in nature.