JEE Physics 2023 Question with Solution

Given: A nucleus $^A_ZX$ has mass number $A$ and atomic number $Z$.

Find: Which listed statements are correct based on the binding energy equation.

The solution provides the binding energy relation:

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

From this equation:

• Volume term is $a_v A$
• Surface energy term is $-a_s A^{2/3}$
• Coulomb term is $-a_c \frac{Z(Z-1)}{A^{1/3}}$
• Asymmetry term is $-a_a \frac{(A-2Z)^2}{A}$
• Pairing term is $\delta(A, Z)$

The extracted solution explicitly states that C and D are directly supported by the equation.

Therefore, the correct option is D.

Given: The question concerns the semi-empirical mass formula for nuclear binding energy.

Find: Which combination of statements matches the equation.

The hint says that the binding energy equation is essential to understand nuclear stability. The provided explanation analyzes each term of

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

Then it matches the statements with the formula and concludes that only C and D are supported.

Since the options are:

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

The correct option is D.