Physics · nuclei · NEET
| Meaning | Total energy to split nucleus into all nucleons | Total binding energy divided by number of nucleons |
| Formula | Eb = (mass defect) times c squared | Ebn = Eb / A |
| Trend with A | Keeps increasing with mass number | Rises, peaks near A = 56, then slowly falls |
| Use | Total energy content of the nucleus | True measure of nuclear stability |
Binding energy (Eb) is the total energy needed to break a nucleus into all its separate protons and neutrons. Binding energy per nucleon (Ebn) is that total divided by the number of nucleons A, so Ebn = Eb / A. Total binding energy keeps rising as the nucleus gets bigger, but binding energy per nucleon is the true measure of stability. A heavy uranium nucleus has a large total binding energy yet a smaller value per nucleon than iron, so iron is more stable per particle. Always read the graph as per nucleon, not total.
At A around 56, each nucleon is pulled by the maximum number of close neighbours through the short range nuclear force, and the proton to proton electric repulsion is still small enough. This gives the tightest packing per nucleon, about 8.75 MeV. For lighter nuclei there are too few neighbours, so BE/A is low. For heavier nuclei the electric repulsion between many protons grows and slowly pulls BE/A down. So the peak sits at the balance point, near iron.
The nuclear force is short ranged, so a nucleon only feels the pull of nearby nucleons. But the electric (Coulomb) repulsion acts between every pair of protons across the whole nucleus. As A grows large, the total repulsion adds up over many protons and starts to loosen the binding. So binding energy per nucleon slowly decreases from the peak, reaching about 7.6 MeV at A = 238 for uranium.
Energy is released whenever a process moves nuclei to a higher point on the BE/A curve (more tightly bound). Heavy nuclei (right side, lower BE/A) split into two middle mass nuclei (higher BE/A) in fission, so energy is released. Light nuclei (left side, low BE/A) join to form a heavier nucleus (higher BE/A) in fusion, so energy is released. Both move toward the iron peak, which is why iron cannot give energy by either process.
In this range binding energy per nucleon stays nearly constant at about 8 MeV. This is because the nuclear force is short ranged and saturates: a nucleon deep inside the nucleus only interacts with its immediate neighbours, and that number does not change as the nucleus grows. So each added nucleon contributes roughly the same binding, keeping the per nucleon value flat. This flatness is direct evidence of the saturation property of the nuclear force.
A nucleus with mass number 240 breaks into two fragments each of mass number 120. The binding energy per nucleon of the unfragmented nucleus is 7.6 MeV while that of each fragment is 8.5 MeV. The total gain in the binding energy in the process is:
The maximum is about 8.75 MeV and it occurs near mass number A = 56, which corresponds to iron (Fe-56). This peak marks the most stable region of nuclei.
For uranium-238 it is about 7.6 MeV per nucleon. This is lower than the iron peak, which is why heavy nuclei like uranium can release energy by splitting (fission).
A higher binding energy per nucleon means each nucleon is more tightly bound, so the nucleus is more stable and harder to break apart. Iron sits at the top of the curve and is the most stable.
No. Total binding energy keeps increasing with mass number, while binding energy per nucleon rises, peaks near iron, then slowly falls. For stability comparisons you must use the per nucleon curve.
Any change that moves nuclei higher on the curve (more binding energy per nucleon) releases energy. Heavy nuclei splitting and light nuclei joining both move toward the iron peak, so both release energy.
