Physics · nuclei · NEET
No. This is the most common mistake. Total binding energy keeps rising as the nucleus gets bigger (more nucleons means more total glue), but that does not mean the nucleus is more stable. Stability is decided by binding energy per nucleon (BE/A), which is total binding energy divided by mass number A. A uranium nucleus has a huge total binding energy but a lower BE/A (about 7.6 MeV) than iron (about 8.8 MeV), so iron is more stable. Always compare BE/A, not total BE.
BE/A is the average energy needed to pull out one nucleon from the nucleus. A high BE/A means each proton and neutron is held very tightly, so the nucleus is hard to break and is stable. A low BE/A means the nucleons are loosely bound, so the nucleus is less stable and more likely to change into a more stable form. Think of it as glue strength per particle, not total glue.
On the BE/A versus mass number graph, the curve rises for light nuclei, reaches a flat top around A = 56 (iron region, about 8.8 MeV per nucleon), and then slowly falls for heavy nuclei. The peak means iron nucleons are the most tightly bound. Any nucleus that moves toward this peak, whether by fusion of light nuclei or fission of heavy nuclei, releases energy and becomes more stable.
Both processes move nuclei toward the high BE/A middle of the graph. A very heavy nucleus (A around 240) has low BE/A. When it splits into two medium nuclei (A around 120) with higher BE/A, energy is released. A very light nucleus also has low BE/A; when two light nuclei fuse into a bigger one with higher BE/A, energy is released. In both cases the final BE/A is higher, so the products are more stable.
When BE/A increases, the nucleons fall into a lower energy, more bound state. Moving to a more tightly bound state releases the extra energy as kinetic energy of products or radiation. So going toward higher BE/A always gives out energy. Energy would have to be supplied only if you tried to move to a lower BE/A (a less stable state).
Higher binding energy per nucleon means a more stable nucleus. Always compare BE/A, which is total binding energy divided by mass number A.
About 8.8 MeV per nucleon, occurring near iron (Fe-56). For most medium nuclei between A = 30 and A = 170 the value stays nearly constant at about 8.0 MeV per nucleon.
Iron (Fe-56) is the most stable because it sits at the peak of the binding energy per nucleon curve, so its nucleons are the most tightly bound.
Between A = 30 and A = 170 the binding energy per nucleon is nearly constant, about 8 MeV. This is because the nuclear force is short range and saturates, so each nucleon interacts only with its nearest neighbours, not with every other nucleon.
Both fission of heavy nuclei and fusion of light nuclei move the products to a higher BE/A region. Since the final nucleons are more tightly bound, the difference in binding energy is released as energy.
