What will be the ratio of radii of two nuclei having their mass numbers in the ratio of 64 : 125?

4 : 5

The correct answer is Option (2) → 4 : 5

Radius of a nucleus: $R = R_0 A^{1/3}$, where A is the mass number

Let the mass numbers of the two nuclei be $A_1 : A_2 = 64 : 125$

Then, the ratio of radii:

$\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} = \left(\frac{64}{125}\right)^{1/3}$

$\frac{R_1}{R_2} = \frac{4}{5}$

∴ Ratio of radii = 4 : 5