Question
The binding energy per nucleon curve peaks near at about . Use this curve to (a) explain why fusion of light nuclei releases energy, (b) explain why fission of heavy nuclei releases energy, and (c) estimate the energy released when a nucleus splits into two fragments of mass numbers and (plus 2 neutrons). Use BE/nucleon values: , , (all in MeV).
Solution — Step by Step
The binding energy per nucleon tells you how tightly each nucleon is held in the nucleus. Higher means more stable.
- For : is small — light nuclei are loosely bound.
- For (iron region): peaks at — most stable.
- For : slowly decreases due to Coulomb repulsion.
Combining two light nuclei produces a heavier one with higher . The total binding energy increases, and the difference is released as kinetic energy of products. Example: jumps from - to — huge gain per nucleon.
Splitting a heavy nucleus produces two medium-mass nuclei with higher . Same logic, opposite direction on the curve.
Total binding energy before:
Total binding energy after (ignoring 2 free neutrons, which have ):
Energy released:
Why This Works
Binding energy is the energy released when nucleons come together to form a nucleus from infinity. Equivalently, it’s the energy you’d need to break the nucleus apart. So total binding energy = (number of nucleons) × (BE per nucleon), and any reaction that increases this total releases energy.
The curve shape comes from the competition between the strong nuclear force (short-range, attractive, saturated near a nucleon) and Coulomb repulsion (long-range, builds up with ). Strong force dominates for light/medium nuclei; Coulomb dominates for heavy nuclei.
Alternative Method
You can compute fission energy from mass defects directly: . This requires looking up atomic masses to several decimal places and converting via . The binding-energy method is faster for back-of-envelope estimates and is what NEET/JEE typically expects.
The actual fission energy of is about — our estimate is in the right ballpark. Always sanity-check against this number in PYQs. Anything above or below for a single fission is a red flag.
Common Mistake
Students conflate “high BE per nucleon = high mass” with “stable = heavier”. Iron is stable because each nucleon is tightly bound, not because it’s heavy. Uranium has more total binding energy than iron, but the per-nucleon binding is lower — that’s why uranium can split and release energy.
The other slip is forgetting the neutrons in the fission products. While free neutrons have , the number of nucleons on each side must balance — here . If your nucleon count doesn’t match, your equation is wrong.
Final answer: Energy released per fission .