Mass Defect and Binding Energy
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Direct answer
A helium nucleus weighs measurably less than the two protons and two neutrons that formed it — about 0.0304 atomic mass units — and the missing mass is the binding energy: BE = Δm c^2, with the mass defect Δm = Z m_p + (A - Z) m_n - M_nucleus and the working conversion 1 u = 931.5 MeV. Dividing by A gives the binding energy per nucleon; plotted against A, it is the master diagram: a rise to about 8.75 MeV per nucleon near A = 56 (the iron region), then a slow decline to roughly 7.6 MeV at uranium. That shape is the energy story: light nuclei fuse, heavy nuclei fission, both climbing toward the iron peak.
What you must remember
- Mass defect: Δm = Z m_p + (A - Z) m_n - M_nucleus; always positive for bound nuclei — the nucleus weighs less than its parts.
- Einstein conversion: BE = Δm c^2; 1 u = 931.5 MeV is the working exchange rate (with 1 u = 1.66 × 10^-27 kg and c^2 doing the rest).
- The BE/nucleon curve: rises steeply from deuterium's low value, peaks at about 8.75 MeV per nucleon around A = 56 (iron), and declines gently toward about 7.6 MeV for uranium.
- Stability reading: nuclei with the largest BE per nucleon are the most tightly bound; iron-region nuclei sit at the top, which is why stellar fusion stops there.
- Fusion and fission energetics: both climb toward the iron peak — light nuclei fuse (the sun's hydrogen-to-helium cycle), heavy nuclei fission (about 200 MeV released per uranium event).
- Helium anchor: Δm ≈ 0.0304 u for He-4 gives BE ≈ 28.3 MeV, about 7.1 MeV per nucleon — the single most quoted worked example.
Where students lose nucleons
The first slip is using atomic masses blindly: tabulated values include electrons, which cancel only when both sides carry them equally — nuclear masses, as used above, avoid the bookkeeping. The second slip is confusing binding energy with energy released: the BE of an existing nucleus is what was released forming it (or must be supplied to break it), while the energy of a reaction is the difference in total binding energies between final and initial nuclei — a fission question asking for energy is asking for that difference, not for uranium's total BE. Third, iron is the most tightly bound nucleus per nucleon, not the most massive stable one; heavier elements form in energy-absorbing supernova processes — a favourite assertion-reason point. Finally, units: 1 u corresponds to 931.5 MeV of energy; and the curve's y-axis is per nucleon — uranium's total BE is roughly 1785 MeV even though its per-nucleon value has fallen.
Frequently asked questions
What is mass defect of a nucleus?
The difference between the sum of the free masses of its constituent nucleons and the actual mass of the bound nucleus — the mass converted into binding energy.
How is binding energy calculated from mass defect?
Through BE = Δm c^2, with the practical conversion 1 u of mass defect corresponding to 931.5 MeV of energy.
Where does the binding energy per nucleon curve peak?
At about 8.75 MeV per nucleon near mass number 56, in the iron region — the most tightly bound nuclei, toward which both fusion and fission energetically climb.
Why does fusion of light nuclei release energy?
The product has a higher BE per nucleon than the light reactants; the difference in total binding energy is released.
How much energy is released in a typical uranium fission event?
Roughly 200 MeV per fissioning 235-uranium nucleus, from the fragments' climb from about 7.6 toward the mid-curve of the binding energy per nucleon plot.