Binding Energy per Nucleon
Weizsäcker semi-empirical mass formula — peak at ⁵⁶Fe, labeled key nuclei.
Key Notes
Binding energy is the energy needed to disassemble a nucleus into its constituent protons and neutrons.
Equivalently, it is the ENERGY RELEASED when free nucleons assemble into a nucleus (mass-energy equivalence).
Mass defect: Δm = Zm_p + (A−Z)m_n − m_nucleus. The nucleus weighs LESS than its parts.
Binding energy: B = Δm · c². Often quoted in MeV using 1 u = 931.5 MeV/c².
Binding energy per nucleon B/A is the most useful quantity: nuclei with larger B/A are more stable.
B/A peaks at A ≈ 56 (Fe-56, Ni-62) with ~8.8 MeV/nucleon. Falls off for heavier and lighter nuclei.
Fission of heavy nuclei (A > 56) and fusion of light nuclei (A < 56) BOTH release energy because the products have higher B/A.
Iron-56 is the most stable nucleus per nucleon — endpoint of stellar nucleosynthesis.
Formulas
Mass defect
Always > 0 for bound nuclei.
Binding energy
Using 1 u = 931.5 MeV/c²: B [MeV] = Δm [u] × 931.5.
Binding energy per nucleon
Stability indicator; ~8.5 MeV for stable mid-mass nuclei.
Semi-empirical mass formula (Weizsäcker)
Volume, surface, Coulomb, asymmetry, pairing terms — fits B/A trend well.
Important Points
B/A vs A curve: rises steeply for light nuclei, plateaus around 8-9 MeV for A = 50-150, slowly falls for heavy nuclei. Peak at Fe-56.
Light nuclei (H, He, Li) have low B/A ⇒ FUSION releases energy.
Heavy nuclei (U, Pu) have B/A ~ 7.6 ⇒ FISSION into mid-mass products (B/A ~ 8.5) releases ~200 MeV per fission.
Stellar nucleosynthesis produces elements up to iron via fusion — beyond iron, fusion is endothermic.
Heavier elements (gold, uranium) are made in SUPERNOVAE and neutron-star mergers via r-process.
Binding energy explains why mass is NOT conserved in nuclear reactions: energy released = mass defect × c².
Binding Energy per Nucleon notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.