The surface areas of two nuclei are in the ra | vedclass

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(A) The surface area $S$ of a nucleus is given by $S = 4\pi R^2$,where $R$ is the radius of the nucleus.Given the ratio of surface areas: $\frac{S_1}{

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$27: 125$

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(A) The surface area $S$ of a nucleus is given by $S = 4\pi R^2$,where $R$ is the radius of the nucleus.Given the ratio of surface areas: $\frac{S_1}{S_2} = \frac{4\pi R_1^2}{4\pi R_2^2} = \frac{R_1^2}{R_2^2} = \frac{9}{25}$.Taking the square root,we get the ratio of radii: $\frac{R_1}{R_2} = \sqrt{\frac{9}{25}} = \frac{3}{5}$.The radius $R$ of a nucleus is related to its mass number $A$ by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant.Therefore,$\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3}$.Cubing both sides,we get $\frac{A_1}{A_2} = \left(\frac{R_1}{R_2}\right)^3$.Substituting the ratio of radii: $\frac{A_1}{A_2} = \left(\frac{3}{5}\right)^3 = \frac{27}{125}$.Thus,the ratio of the mass numbers is $27: 125$.

The surface areas of two nuclei are in the ratio $9: 25$. The mass numbers of the nuclei are in the ratio

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