Two nuclei have mass numbers in the ratio 1 : 8. The ratio of their nuclear radii would be:

1 : 2

The correct answer is Option (1) → 1 : 2

The nuclear radius (R) is,

$R=R_0A^{1/3}$

$∴\frac{R_1}{R_2}=\frac{R_0{A_2}^{1/3}}{R_0{A_1}^{1/3}}=\left(\frac{A_1}{A_2}\right)^{1/3}$

$\frac{R_1}{R_2}=\left(\frac{A_1}{8A_1}\right)^{1/3}=\frac{1}{2}$