Mass-Energy Equivalence and Binding Energy

Weigh a helium-4 nucleus and compare it to two free protons and two free neutrons added up separately. The nucleus is lighter. That missing mass, called the mass defect, didn't vanish. It became the energy released when the nucleons bound together, and by Einstein's E=mc² that energy corresponds to a specific mass. Flip it around: to rip the nucleus apart into separate nucleons, you'd have to put that same energy back in. That energy is the binding energy, and it's the real measure of how tightly a nucleus holds itself together.

Because c² is such a huge number, a tiny mass defect translates into a huge amount of energy. In nuclear physics it's convenient to measure mass in atomic mass units (amu) and use the conversion 1 amu of mass corresponds to 931.5 MeV of energy. So binding energy equals the mass defect in amu times 931.5 MeV. This is why nuclear reactions release far more energy than chemical ones: chemical bonds involve electron rearrangements with immeasurably small mass changes, while nuclear bonds involve mass changes you can actually weigh.

Dividing binding energy by the number of nucleons gives binding energy per nucleon, a measure of nuclear stability. Plotted against mass number, this curve rises steeply for light nuclei, peaks near iron-56, and declines slowly for heavier nuclei. That peak explains both fusion and fission: light nuclei fusing toward iron, or heavy nuclei splitting toward iron, both move toward more binding energy per nucleon and release energy. This connects directly to the next idea, radioactive decay, where unstable nuclei shed mass-energy to move toward more stable configurations.