Use the nuclear radius relation

The radius of a nucleus is given by $R = R_0 A^{1/3}$ where:

• $R$ = nuclear radius
• $R_0$ = constant
• $A$ = mass number

Given condition

Let the required nucleus have mass number $A$.

The nucleus with mass number $192$ has radius $R_{192} = R_0 (192)^{1/3}$

The required nucleus has radius equal to half of this: $R = \frac{1}{2} R_{192}$

Apply the formula

$R_0 A^{1/3} = \frac{1}{2} R_0 (192)^{1/3}$

Cancel $R_0$: $A^{1/3} = \frac{1}{2}(192)^{1/3}$

Cube both sides

$A = \left(\frac{1}{2}\right)^3 \times 192$

$A = \frac{1}{8} \times 192 = 24$

Match with options

The correct option is: $\boxed{24}$

So, Option B is correct.