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Q.

A nucleus has mass number $A_{1} &$ volume $V_{1} .$ Another nucleus has mass number $A_{2}$ and volume $V_{2} .$ If the relation between the mass numbers $A_{2} = 3 A_{1},$ Then $\frac{v_{1}}{v_{2}} =$

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a

$3^{\frac{1}{3}}$

b

${(\frac{1}{3})}^{\frac{1}{3}}$

c

$\frac{1}{\sqrt{3}}$

d

$\frac{1}{3}$

answer is C.

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Detailed Solution

$\begin{array}{l} V = \frac{4}{3} π R^{3} \\ R = R_{0} A^{\frac{1}{3}} \\ V α A \\ \frac{V_{1}}{V_{2}} = \frac{A_{1}}{A_{2}} \\ \frac{V_{1}}{V_{2}} = \frac{A_{A}}{3 A_{1}} = \frac{1}{3} \end{array}$

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