A nucleus has mass number A_1 and volume V_1. | vedclass

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(B) The volume of a nucleus is given by $V = \frac{4}{3} \pi R^3$.Since the radius of a nucleus is $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$

Vedclass · Accepted Answer

$4$

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(B) The volume of a nucleus is given by $V = \frac{4}{3} \pi R^3$.Since the radius of a nucleus is $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number,we substitute $R$ into the volume formula:$V = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$.This shows that the volume of a nucleus is directly proportional to its mass number,i.e.,$V \propto A$.Therefore,the ratio of the volumes is $\frac{V_2}{V_1} = \frac{A_2}{A_1}$.Given $A_2 = 4 A_1$,we have $\frac{V_2}{V_1} = \frac{4 A_1}{A_1} = 4$.

$A$ 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 $A_2 = 4 A_1$,then $\frac{V_2}{V_1} = $ . . . . . . .

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