Compute total binding energy, binding energy per nucleon and mass defect for any nucleus — with a BE/A stability curve.
Nuclear binding energy is the energy required to completely disassemble a nucleus into its individual protons and neutrons. Equivalently, it's the energy released when those nucleons come together to form the nucleus. The higher the binding energy, the more tightly the nucleons are held together, and the more stable the nucleus is.
The binding energy comes from the mass difference between the individual nucleons and the assembled nucleus. When protons and neutrons combine, a small amount of mass disappears — this is the mass defect. That missing mass is converted into energy via E = mc², and that energy is the binding energy holding the nucleus together.
The mass defect is calculated by comparing the total mass of the individual protons and neutrons to the actual measured mass of the nucleus:
Here, 1.007825 amu is the atomic mass of hydrogen (which accounts for the electron mass), and 1.008665 amu is the neutron mass. The factor 931.494 MeV/amu converts mass defect to energy.
The binding energy per nucleon (BE/A) is a much better indicator of stability than total binding energy. When you plot BE/A against mass number, you get the famous binding energy curve. It rises steeply for light nuclei, peaks around iron-56 and nickel-62 at roughly 8.8 MeV per nucleon, and then gradually decreases for heavier nuclei.
This curve explains both nuclear fusion and fission. Light nuclei below the peak can release energy by fusing together (moving up the curve). Heavy nuclei above the peak can release energy by splitting apart (also moving toward the peak). Iron and nickel sit at the top — they're the most tightly bound nuclei and represent the endpoint of energy-releasing nuclear reactions. This is why iron is so abundant in the cores of old, massive stars.
When the exact atomic mass isn't known, the binding energy can be estimated using the semi-empirical mass formula (also called the Bethe-Weizsäcker formula). This model treats the nucleus as a liquid drop and includes five terms: volume energy, surface energy, Coulomb repulsion, asymmetry energy, and a pairing term. It's remarkably accurate for most nuclei and is the standard tool for estimating binding energies across the nuclear chart.