Question

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:

• A. 24
• B. 32
• C. 40
• D. 20

Answer 1

Answer: (A)

24

Answer 2

The radius $R$ of a nucleus is proportional to the cube root of its mass number $A$:

$R \propto A^{1/3}.$

Let $R_1$ and $R_2$ be the radii of two nuclei with mass numbers $A_1$ and $A_2$, respectively. Given:

$R_1 = \frac{1}{2} R_2 \quad \text{and} \quad A_2 = 192.$

Using the proportionality,

$\frac{R_1}{R_2} = \left( \frac{A_1}{A_2} \right)^{1/3}.$

Substitute $R_1 = \frac{1}{2} R_2$:

$\frac{1}{2} = \left( \frac{A_1}{192} \right)^{1/3}.$

Cubing both sides:

$\frac{1}{8} = \frac{A_1}{192}.$

Solving for $A_1$:

$A_1 = 192 \times \frac{1}{8} = 24.$

Thus, the answer is:

24\.