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The binding energy per nucleon is calculated as BE/A = (Δm × 931.5 MeV/u) / A, where A is the mass number (total number of nucleons). For helium-4 (A = 4) with a binding energy of 28.3 MeV, BE/A = 28.3 / 4 ≈ 7.07 MeV/nucleon. For iron-56 (A = 56) with a binding energy of approximately 492.3 MeV, BE/A ≈ 8.79 MeV/nucleon. Nuclei lighter than iron-56 can increase their BE/A by fusing together, while nuclei heavier than iron-56 can increase their BE/A by splitting apart — this is the fundamental thermodynamic driver of nuclear reactions.
The shape of the BE/A curve reflects several competing nuclear forces. At very low mass numbers (hydrogen-1 through helium-3), BE/A rises steeply because each new nucleon added contributes significant strong-force binding with relatively few neighbors. In the middle of the chart (carbon through nickel), BE/A plateaus near its maximum because the short-range strong force saturates — each nucleon only interacts with its immediate neighbors. For nuclei heavier than nickel, the long-range electrostatic repulsion between protons causes BE/A to gradually decline, making these nuclei progressively less stable.
The BE/A curve has profound astrophysical implications. Stars generate energy by fusing light elements in their cores, progressing from hydrogen fusion to helium, carbon, oxygen, and eventually silicon and sulfur fusion, ending at iron-peak elements. Once a stellar core is composed primarily of iron-56 and nickel-56, fusion can no longer release energy, and the core collapses, potentially triggering a supernova explosion. Elements heavier than iron are produced by neutron capture processes during supernovae and neutron star mergers. The BE/A concept also underpins the design of nuclear fission reactors, where uranium-235 and plutonium-239 are preferred fuels because their fission products have significantly higher BE/A values, releasing approximately 200 MeV per fission event.
Isotopes, atomic mass, mass number, neutrons, and nuclear binding energy
Explore CategoryIron-56 has the highest binding energy per nucleon at approximately 8.79 MeV/nucleon, making it the most thermodynamically stable nucleus. Nickel-62 is very close and is sometimes cited as slightly higher in total binding energy.
The peak at iron-56 results from the balance between the attractive short-range strong nuclear force (which dominates for light nuclei) and the repulsive long-range Coulomb force between protons (which increases faster in heavy nuclei). At iron-56, these forces produce the most stable configuration.
Fusion increases BE/A only when the product nucleus is closer to iron-56 than the reactants. For nuclei lighter than iron, fusion moves them up the BE/A curve toward higher stability, releasing energy. For nuclei heavier than iron, fusion would move them away from the peak, requiring energy input.
Hydrogen-1 (a single proton with no neutrons) has a binding energy per nucleon of exactly 0 MeV/nucleon because there are no nuclear bonds to account for. Deuterium (hydrogen-2) has BE/A ≈ 1.11 MeV/nucleon, the lowest non-zero value.
Reactor engineers use BE/A values to calculate the energy released per fission event and to select fuel materials. Uranium-235 and plutonium-239 are efficient fission fuels because their fission products lie much higher on the BE/A curve, converting that mass difference into approximately 200 MeV of usable energy.