A nucleus weighs less than the protons and neutrons that make it. That missing mass is the binding energy, the glue of the nucleus, and through E = mc² it powers both the stars and the reactor.
The mass defect Δm is the difference between the total mass of the separate nucleons and the smaller mass of the bound nucleus. By E = mc² this corresponds to the binding energy = Δm c²: the energy released when the nucleus forms, or needed to pull it apart. The binding energy per nucleon peaks near iron, so fusing light nuclei and splitting heavy nuclei both release energy.
Slide along the binding-energy-per-nucleon curve. It rises steeply for light nuclei, peaks near iron (A ≈ 56, the most stable nuclei), then falls gently. Energy is released whenever a change moves nucleons up the curve, which is why light nuclei fuse and heavy nuclei split.
A few definitions and one constant carry the whole topic.
Stability is measured by binding energy per nucleon, not total binding energy (uranium has the largest total but is far less stable than iron). For the energy released in a reaction, use E = c²Δm with Δm = (mass of reactants) − (mass of products); a positive value means energy is released. Always convert mass to the same units first (kg with c² in joules, or u with the 931 MeV shortcut).
Four quick checks on mass defect and binding energy. Each correct answer earns XP and lights this skill on your star map.
Compared with the total mass of its separated nucleons, the mass of a nucleus is:
The binding energy of a nucleus is equal to:
On the binding-energy-per-nucleon curve, the most stable nuclei are found:
Energy is released in both nuclear fusion and nuclear fission because the products have:
In a worked example, find the mass defect in kilograms (or u), then multiply by c² (or 931 MeV/u). A common slip is forgetting that the masses given are usually atomic masses; for binding-energy questions the electron masses cancel, but for decay-energy questions check whether the data are nuclear or atomic.
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