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 equal to

• A. $ 3:2 $
• B. $ 1:3 $
• C. $ 1:2 $
• D. $ 2:3 $

Answer 1

The Correct Option is A

Radius of nuclei having mass number $A$ is determined as $R =R_{0} A^{1 / 3} $ (where, $ R_{0}=$ constant) $=1.2 \times 10^{-15}$ This implies, $ \frac{R_{1}}{R_{2}} =\left(\frac{A_{1}}{A_{2}}\right)^{1 / 3}$ $=\left(\frac{216}{64}\right)^{1 / 3}=\frac{6}{4} $ $ \Rightarrow R_{1}: R_{2} =3: 2$