For a nucleus ZAX having mass number A and atomic number Z A. The… | JEE Main 2023 (8 Apr, Shift 1)

Q15JEE Main 2023 · 8 APR · SHIFT 1Difficult

Mass Defect & Binding Energy

For a nucleus ${}_{\text{Z}}^{\text{A}}\text{X}$ having mass number $\text{A}$ and atomic number $\text{Z}$

A. The surface energy per nucleon $(b_{\text{s}}) = -a_1 A^{2/3}$ .

B. The Coulomb contribution to the binding energy $\text{b}_{\text{c}} = -a_2 \frac{Z(Z-1)}{A^{4/3}}$

C. The volume energy $\text{b}_{\text{v}} = a_3 A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_1, a_2$ and $a_3$ are constants)

Choose the most appropriate answer from the options given below:

Show answer and solution

Answer: (a)

A: false. Total surface term is $-a_1A^{2/3}$ ; per nucleon it is $-a_1A^{-1/3}$ .
B: false. Coulomb term in the binding energy is $-a_2\dfrac{Z(Z-1)}{A^{1/3}}$ , not $A^{4/3}$ .
C: true. Volume energy $b_v = a_3A$ (each nucleon contributes equally).
D: true. Surface nucleons have fewer neighbours, so the loss of binding energy is proportional to surface area $\propto A^{2/3}$ .
E: false. No fixed number of 12 neighbours is assumed for the surface term.
So the answer is (a) C, D only.

Mass Defect & Binding Energy question from JEE Main 2023 (8 Apr, Shift 1)