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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: Nov 19, 2024
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Correct Answer: 4
Solution and Explanation
For a nucleus, the volume \( V \) is proportional to \( A \), the mass number, given by:
\[ V = \frac{4}{3}\pi R^3, \]where the radius \( R \) of a nucleus is proportional to the cube root of its mass number \( A \):
\[ R = R_0 A^{1/3}. \]Thus, the volume \( V \) of a nucleus can be expressed as:
\[ V \propto A. \]Since \( A_2 = 4A_1 \), the ratio of volumes is:
\[ \frac{V_2}{V_1} = \frac{A_2}{A_1} = 4. \]Was this answer helpful?
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