nuclear binding energy

Meaning: Nuclear binding energy is the energy needed to separate a nucleus into its individual protons and neutrons, and equally the energy released when they combine. A nucleus has less mass than its free nucleons; this mass defect corresponds to that energy by mass-energy equivalence. Binding energy per nucleon measures stability and peaks near iron-56.

Equation: E = Δm c², with Δm = (Z mp + N mn) − mnucleus. E is binding energy (J), Δm is mass defect (kg), Z and N are the numbers of protons and neutrons, mp, mn and mnucleus are masses (kg), and c = 3.00 × 10⁸ m/s.

On the MCAT: Expect to compute a mass defect from given masses and convert it to energy, or read a graph of binding energy per nucleon versus mass number. Fusion of light nuclei and fission of heavy nuclei both release energy because the products lie nearer the iron peak.

Common confusion: Stability is judged by binding energy per nucleon, not total, since larger nuclei have larger totals. Also, the nucleus does not hold extra energy to release; its mass is missing, and that energy must be supplied to pull it apart.