Question

The ratio of the radii of the nuclei of mass numbers 27 and 64 is:

• A. 3 : 4
• B. 4 : 3
• C. 9 : 16
• D. 16 : 9

Hint:

Nuclear radius scales as $R \propto A^{1/3}$. The ratio of radii is the cube root of the ratio of mass numbers.

Answer 1

The Correct Option is A

The radius of a nucleus is given by $R = R_0 A^{1/3}$, where $A$ is the mass number and $R_0$ is a constant.
For $A_1 = 27$, $R_1 = R_0 (27)^{1/3} = R_0 \times 3$.
For $A_2 = 64$, $R_2 = R_0 (64)^{1/3} = R_0 \times 4$.
Ratio $R_1 : R_2 = 3 : 4$.