The nuclei have mass numbers in the ratio 1 : 27. The ratio of the their nucleus radii will be, respectively:

$\frac{1}{3}$

The correct answer is Option (4) → $\frac{1}{3}$

The radius (R) of a nucleus is given by -

$R=R_0A^{1/3}$

where,

A = Mass number

$\frac{R_1}{R_2}=\frac{R_0{A_1}^{1/3}}{R_0{A_2}^{1/3}}=\sqrt[3]{\frac{A_1}{A_2}}$

$=\sqrt[3]{\frac{1}{27}}=\frac{1}{3}$