Question

For a nucleus AAX having mass number A and atomic number Z
A. The surface energy per nucleon \((b_s)=−a_1A^{\frac{2}{3}} \)
B. The Coulomb contribution to the binding energy \(b_c=−a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}} \)
C. The volume energy b_v=a₃A
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. ( a₁,a₂ and a₃ are constants)
Choose the most appropriate answer from the options given below:

• A. A, B, C, D only
• B. B, C only
• C. C, D only
• D. B, C, E only

Hint:

The binding energy equation is essential in nuclear physics to understand stability

Answer 1

The Correct Option is C

Step 1: Analyze the terms in the binding energy equation.

$E_B = a_v A - a_s A^{2/3} - a_c \frac{Z(Z-1)}{A^{1/3}} - a_a \frac{(A-2Z)^2}{A} + \delta(A, Z)$.

- Volume term: $a_v A$

- Surface energy term: $-a_s A^{2/3}$

- Coulomb term: $-a_c \frac{Z(Z-1)}{A^{1/3}}$

- Asymmetry term: $-a_a \frac{(A-2Z)^2}{A}$

- Pairing term: $\delta(A, Z)$

Step 2: Match the options with the equation.

- C and D are directly supported by the equation.

Final Answer: The most appropriate choice is option (3).