Question 18

For a nucleus $$^A_Z X$$ having mass number A and atomic number Z
A. The surface energy per nucleon $$(b_s) = -a_1 A^{2/3}$$.
B. The Coulomb contribution to the binding energy $$b_c = -a_2 \dfrac{Z(Z-1)}{A^{1/3}}$$.
C. The volume energy $$b_v = a_3 A$$
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:

$$E_v = a_3 A$$

$$E_s = -a_1 A^{2/3}$$

$$E_c = -a_2 \frac{Z(Z-1)}{A^{1/3}}$$

$$\text{Statement A is wrong: } b_s \text{ is total surface energy } (\propto A^{2/3})\text{, not per nucleon.}$$

$$\text{Statement B is correct: } b_c = -a_2 \frac{Z(Z-1)}{A^{1/3}}$$

$$\text{Statement C is correct: } b_v = a_3 A$$

$$\text{Statement D is correct: } E_s \propto \text{surface area } (4\pi R^2 \propto A^{2/3})$$

$$\text{Statement E is wrong: Surface nucleons interact with fewer neighbors than interior ones.}$$

Create a FREE account and get:

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions