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

The Correct Option is A

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:

\[ 24. \]