Question:
The ratio of the radii of the nuclei \(^{64}_{29}X\) and \(^{216}_{84}Y\) is:
The ratio of the radii of the nuclei \(^{64}_{29}X\) and \(^{216}_{84}Y\) is:
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Nuclear radius depends only on mass number: \(R \propto A^{1/3}\).
Updated On: Jul 18, 2026
- \(\frac{2}{3}\)
- \(\frac{8}{15}\)
- \(\frac{8}{3}\)
- \(\frac{7}{8}\)
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The Correct Option is A
Solution and Explanation
Step 1: Nuclear radius relation.
Radius of nucleus is given by: \[ R = R_0 A^{1/3} \]
Step 2: Write ratio expression.
\[ \frac{R_X}{R_Y} = \left(\frac{64}{216}\right)^{1/3} \]
Step 3: Simplify mass numbers.
\[ \frac{64}{216} = \frac{2^6}{6^3} = \left(\frac{2}{3}\right)^3 \]
Step 4: Apply cube root.
\[ \left(\frac{2}{3}\right)^3^{1/3} = \frac{2}{3} \]
Step 5: Final ratio.
\[ \frac{R_X}{R_Y} = \frac{2}{3} \]
Final Answer:
\[ \boxed{\frac{2}{3}} \]
Radius of nucleus is given by: \[ R = R_0 A^{1/3} \]
Step 2: Write ratio expression.
\[ \frac{R_X}{R_Y} = \left(\frac{64}{216}\right)^{1/3} \]
Step 3: Simplify mass numbers.
\[ \frac{64}{216} = \frac{2^6}{6^3} = \left(\frac{2}{3}\right)^3 \]
Step 4: Apply cube root.
\[ \left(\frac{2}{3}\right)^3^{1/3} = \frac{2}{3} \]
Step 5: Final ratio.
\[ \frac{R_X}{R_Y} = \frac{2}{3} \]
Final Answer:
\[ \boxed{\frac{2}{3}} \]
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