The nuclei have mass numbers in the ratio 1 : 27. The ratio of the their nucleus radii will be, respectively:
Answer & explanation
Correct answer: option 4
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
$\frac{R_1}{R_2}=\frac{R_0{A_1}^{1/3}}{R_0{A_2}^{1/3}}=\sqrt[3]{\frac{A_1}{A_2}}$
$=\sqrt[3]{\frac{1}{27}}=\frac{1}{3}$