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What is the mass number of nucleus having radius equal to $\frac{1}{3}$ of that of ${ }^{189}$ Os?
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The correct answer is:
7
$\begin{aligned} & \mathrm{R}=\mathrm{R}_0 \mathrm{~A}^{1 / 3} \\ & \Rightarrow \frac{1}{3} \mathrm{R}_0(189)^{1 / 3}=\mathrm{R}_0 \mathrm{~A}^{1 / 3} \\ & \Rightarrow \frac{1}{3} \times(189)^{1 / 3}=\mathrm{A}^{1 / 3} \\ & \Rightarrow \frac{1}{27} \times 189=\mathrm{A} \\ & \Rightarrow \mathrm{A}=7\end{aligned}$
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