KCET · Physics · Nuclear Physics
The ratio of the nuclear radii of elements with mass numbers 216 and 125 is
- A \(216: 125\)
- B \(\sqrt{216}: \sqrt{125}\)
- C \(6: 5\)
- D None of these
Answer & Solution
Correct Answer
(C) \(6: 5\)
Step-by-step Solution
Detailed explanation
Nuclear radius is proportional to \(\mathrm{A}^{1 / 3}\), where is the mass number of nucleus.
\[
\begin{aligned}
\mathrm{R} &=\mathrm{R}_{0} \mathrm{~A}^{1 / 3} \\
\mathrm{R}_{0} &=1.2 \mathrm{fm} \\
\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}} &=\frac{\mathrm{R}_{0}(216)^{1 / 3}}{\mathrm{R}_{0}(125)^{1 / 3}}=\frac{6}{5}
\end{aligned}
\]
\[
\begin{aligned}
\mathrm{R} &=\mathrm{R}_{0} \mathrm{~A}^{1 / 3} \\
\mathrm{R}_{0} &=1.2 \mathrm{fm} \\
\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}} &=\frac{\mathrm{R}_{0}(216)^{1 / 3}}{\mathrm{R}_{0}(125)^{1 / 3}}=\frac{6}{5}
\end{aligned}
\]
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