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

Answer: (A)

$3:2$

Answer 2

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, $\frac{R_{1}}{R_{2}} =\left(\frac{A_{1}}{A_{2}}\right)^{1 / 3}$ $=\left(\frac{216}{64}\right)^{1 / 3}=\frac{6}{4}$ $\Rightarrow R_{1}: R_{2} =3: 2$