Question Bank MCQ • 2 Marks Section 9: Nuclear and Particle Physics Nuclear Properties & Nuclear Forces

QB_PH_SEC9_004: Nuclear Properties & Nuclear Forces

Question Statement

In the Bethe-Weizsäcker semi-empirical mass formula, the asymmetry energy term accounts for
(A) The reduction in binding energy caused by the Coulomb repulsion among protons
(B) The Pauli exclusion principle favoring equal numbers of protons and neutrons ($N = Z$)
(C) The decrease in binding energy for nucleons located near the nuclear surface
(D) The spin pairing tendency of identical nucleons
Correct Answer
B
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Step-by-Step Derivation & Verification: 1. **Semi-Empirical Mass Formula (SEMF)**: $B(A, Z) = a_v A - a_s A^{2/3} - a_c \frac{Z(Z-1)}{A^{1/3}} - a_{\text{asym}} \frac{(A - 2Z)^2}{A} + \delta(A, Z)$ 2. **Origin of Terms**: - $a_v A$: Volume energy (short-range saturated nuclear force). - $-a_s A^{2/3}$: Surface energy correction. - $-a_c \frac{Z(Z-1)}{A^{1/3}}$: Coulomb repulsion among protons. - $-a_{\text{asym}} \frac{(N - Z)^2}{A}$: Asymmetry energy. 3. **Physical Mechanism of Asymmetry**: - Protons and neutrons are fermions obeying the Pauli exclusion principle. - Because they occupy independent single-particle Fermi spheres, any difference $N - Z$ forces nucleons of the excess species into higher kinetic energy quantum states. - Maximum binding occurs when $N = Z$. 4. **Conclusion**: Option (B) is correct.
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