Nuclear Binding EnergyJEE Advanced

Concept

A nucleus weighs less than its separate protons and neutrons — the missing mass ($\Delta m$) became the binding energy holding it together ($E = \Delta m c^2$). Plotting binding energy per nucleon against mass number gives the famous curve that peaks near iron (A ≈ 56) — the most tightly bound, most stable nuclei.

Key formula

Derivation

The semi-empirical mass formula models $B$ as a sum of effects: a bulk volume term ($+a_V A$), a surface correction ($-a_S A^{2/3}$), Coulomb repulsion of protons ($-a_C Z(Z-1)/A^{1/3}$), an asymmetry penalty for $N \neq Z$, and a pairing term.

The competition between the surface term (hurts light nuclei) and Coulomb term (hurts heavy nuclei) makes $B/A$ peak around iron at ≈ 8.8 MeV/nucleon.

Scenarios to explore

• Nuclear Binding Energy — Mass defect & the iron-peak stability curve.

Real-world applications

• Fusion of light nuclei (toward the peak) releases energy — powers stars.
• Fission of heavy nuclei (toward the peak) releases energy — nuclear reactors.
• Estimating nuclear masses and reaction Q-values.

JEE exam tips

• BE/A ≈ 8.8 MeV near iron, dropping to ~7.6 MeV for uranium and low for light nuclei.
• Energy released in a reaction = (BE of products) − (BE of reactants).

Common mistakes

• Thinking a higher total binding energy means more stable — it's binding energy per nucleon that matters.
• Using the wrong mass unit — convert mass defect in u to MeV with 931.5.
• Forgetting both fusion (light) and fission (heavy) move toward the iron peak.

Exam traps to avoid

• Both very light and very heavy nuclei are less stable (lower BE/A) than mid-mass nuclei.
• The mass defect is tiny in u but huge in energy because $c^2$ is enormous.