Physics · nuclei · NEET
It is both numbers, and they are equal. When free protons and neutrons come together to form a nucleus, exactly Eb of energy is released. To do the reverse, that is to pull the same nucleus apart into free nucleons, you must supply the same Eb back. NEET usually states it as the energy REQUIRED to separate a nucleus into its individual nucleons, so remember it as an input energy that measures how tightly the nucleus is held.
When nucleons bind, the system loses energy (it becomes more stable). By Einstein's relation E = mc^2, losing energy means losing mass. So the bound nucleus weighs slightly less than the total of its free protons and neutrons. That missing mass is the mass defect Delta-M = (Z*mp + (A-Z)*mn) minus M(nucleus), and its energy equivalent is the binding energy.
Binding energy Eb is the TOTAL energy holding the whole nucleus together. Binding energy per nucleon Ebn = Eb divided by A (the mass number) is the AVERAGE energy per particle. Ebn is the better measure of stability: for most nuclei it is nearly constant at about 8 MeV per nucleon. A heavy nucleus can have huge total Eb yet a lower Ebn, so it can still be less stable.
Use the standard bridge 1 u = 931.5 MeV/c^2. So binding energy in MeV = (mass defect in u) x 931.5. For example, if Delta-M = 0.1371 u, then Eb = 0.1371 x 931.5 = 127.7 MeV. Always express the mass defect in u first, then multiply by 931.5 once.
Not directly. A large total binding energy alone can just mean the nucleus has many nucleons. Stability is decided by binding energy per nucleon Ebn. A nucleus with higher Ebn is more tightly bound and more stable. That is why iron region nuclei (peak Ebn about 8.7 MeV) are the most stable, not the very heavy ones.
Eb = Delta-M x c^2, where Delta-M = (Z*mp + (A-Z)*mn) - M(nucleus) is the mass defect. In exam units, Eb (MeV) = Delta-M (in u) x 931.5.
It is the energy equivalent of one atomic mass unit: 1 u = 931.5 MeV/c^2. Multiply the mass defect (in u) by 931.5 to get binding energy in MeV directly.
For nuclei in the mass range A = 30 to 170, the binding energy per nucleon is nearly constant, about 8 MeV per nucleon (peaking near 8.7 MeV for iron-region nuclei).
No. Mass defect Delta-M is the lost mass (in u or kg). Binding energy is that mass defect converted to energy using E = mc^2. They are linked but have different units.
It explains nuclear stability, and why fission of heavy nuclei and fusion of light nuclei both release energy. The per-nucleon curve is one of the most tested ideas in the Nuclei chapter.
