binding energy

Meaning: Binding energy is the energy needed to separate a nucleus into its individual protons and neutrons, and it is the energy released when they join. A bound nucleus has slightly less mass than its separated nucleons; this mass defect accounts for the energy. Higher binding energy per nucleon means a more stable nucleus. The per-nucleon value rises for light nuclei, peaks near iron-56, then declines slowly.

Equation: Eb = Δm c², with Δm = (Z mp + N mn) − mnucleus. Eb is binding energy (J), Δm is mass defect (kg), c = 3.00 × 10⁸ m/s, Z and N are the numbers of protons and neutrons, and the m terms are masses (kg). Also, 1 u corresponds to about 931 MeV.

On the MCAT: Given masses in u, find the mass defect and multiply by 931 MeV/u. Or read a graph of binding energy per nucleon versus mass number: fusion of light nuclei and fission of heavy nuclei both give products nearer the peak, so both release energy.

Common confusion: Students think the nucleus has more mass than its parts, or that binding energy is stored energy that gets used up. The bound nucleus has less mass; the difference left as released energy when it formed. Also, stability follows binding energy per nucleon, not the total.