Question:medium
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 mass numbers is \(A_2 = 4A_1\), then \(\frac{V_2}{V_1} =\) _______.
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 mass numbers is \(A_2 = 4A_1\), then \(\frac{V_2}{V_1} =\) _______.
Updated On: Feb 2, 2026
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Correct Answer: 4
Solution and Explanation
Nucleus Volume Calculation:
Volume Formula: \[ V = \frac{4}{3} \pi R^3 \]
Radius Dependence on Mass Number (A):
\[ R = R_0 \left( A \right)^{1/3} \]
Volume Equation with Radius Substitution:
\[ V = \frac{4}{3} \pi \left( R_0 (A)^{1/3} \right)^3 \]
Volume Ratio Simplification:
\[ \Rightarrow \frac{V_2}{V_1} = \frac{A_2}{A_1} = 4 \]
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