Question

Two spherical nuclei have mass numbers 216 and 64 with their radii \(R_{1}\) and \(R_{2}\) respectively. The ratio \(\frac{R_{1}}{R_{2}}\) is

• A. \(1:2\)
• B. \(1:3\)
• C. \(2:3\)
• D. \(3:2\)

Hint:

Nuclear radius is proportional to the cube root of the mass number.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The radius of a nucleus is \(R=R_0A^{1/3}\), so \(R\propto A^{1/3}\).

Step 2: Calculation
\(\dfrac{R_1}{R_2}=\left(\dfrac{216}{64}\right)^{1/3}=\dfrac{6}{4}\), because \(6^{3}=216\) and \(4^{3}=64\).

Step 3: Simplify
\(\dfrac{R_1}{R_2}=\dfrac{3}{2}\), that is \(3:2\).

Final Answer:
The ratio \(R_1:R_2\) is \(3:2\). \[ \boxed{\text{(D) }3:2} \]