Two spherical nuclei have mass numbers 216 and 64 with their radii $R_1$ and $R_2$ respectively. The ratio $\dfrac{R_1}{R_2}$ is

The radius of a nucleus is related to its mass number $A$ by the empirical formula:

$R = R_0 A^{1/3}$

For the first nucleus with mass number $A_1 = 216$:

$R_1 = R_0 (216)^{1/3} = 6 R_0$

For the second nucleus with mass number $A_2 = 64$:

$R_2 = R_0 (64)^{1/3} = 4 R_0$

The ratio of their radii is:

$\dfrac{R_1}{R_2} = \dfrac{6 R_0}{4 R_0} = \dfrac{3}{2}$

Thus, the ratio is $3:2$.

Answer: $3:2$