Question:
A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If the relation between the mass numbers is \(A_2 = 3 A_1\), find \(\frac{V_1}{V_2}\).
A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If the relation between the mass numbers is \(A_2 = 3 A_1\), find \(\frac{V_1}{V_2}\).
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For nuclei, \(V \propto A\) since \(V \propto R^3\) and \(R \propto A^{1/3}\). Volume ratios follow mass number ratios.
Updated On: Jul 18, 2026
- \(\frac{1}{3^3}\)
- \(\left(\frac{1}{3}\right)^3\)
- \(\frac{1}{3}\)
- \(\frac{1}{\sqrt{3}}\)
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The Correct Option is C
Solution and Explanation
Step 1: Recall relation between mass number and volume of nucleus.
\[ V \propto A \]
Volume of nucleus is proportional to its mass number since radius \(R \propto A^{1/3}\) and \(V \propto R^3\).
Step 2: Express volumes in terms of mass numbers.
\[ V_1 \propto A_1, \quad V_2 \propto A_2 \]
Step 3: Form the ratio.
\[ \frac{V_1}{V_2} = \frac{A_1}{A_2} \]
Step 4: Substitute given relation.
\[ A_2 = 3 A_1 \implies \frac{V_1}{V_2} = \frac{A_1}{3 A_1} = \frac{1}{3} \]
Step 5: Verify reasoning.
Volume ratio proportional to mass number ratio, correct by definition.
Step 6: Final conclusion.
\[ \boxed{\frac{V_1}{V_2} = \frac{1}{3}} \]
\[ V \propto A \]
Volume of nucleus is proportional to its mass number since radius \(R \propto A^{1/3}\) and \(V \propto R^3\).
Step 2: Express volumes in terms of mass numbers.
\[ V_1 \propto A_1, \quad V_2 \propto A_2 \]
Step 3: Form the ratio.
\[ \frac{V_1}{V_2} = \frac{A_1}{A_2} \]
Step 4: Substitute given relation.
\[ A_2 = 3 A_1 \implies \frac{V_1}{V_2} = \frac{A_1}{3 A_1} = \frac{1}{3} \]
Step 5: Verify reasoning.
Volume ratio proportional to mass number ratio, correct by definition.
Step 6: Final conclusion.
\[ \boxed{\frac{V_1}{V_2} = \frac{1}{3}} \]
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