The radius of an atomic nucleus of mass numbe | vedclass

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(D) The radius $R$ of an atomic nucleus is related to its mass number $A$ by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant.This implies that

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$125$

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(D) The radius $R$ of an atomic nucleus is related to its mass number $A$ by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant.This implies that $R \propto A^{1/3}$ or $A \propto R^3$.Given for the first nucleus: $A_1 = 64$ and $R_1 = 4.8 	ext{ fermi}$.For the second nucleus: $R_2 = 6 	ext{ fermi}$ and we need to find $A_2$.Using the ratio: $\frac{A_2}{A_1} = \left(\frac{R_2}{R_1}ight)^3$.Substituting the values: $\frac{A_2}{64} = \left(\frac{6}{4.8}ight)^3$.Simplifying the fraction: $\frac{6}{4.8} = \frac{60}{48} = \frac{5}{4} = 1.25$.Therefore,$A_2 = 64 	imes (1.25)^3 = 64 	imes \frac{125}{64} = 125$.

The radius of an atomic nucleus of mass number $64$ is $4.8 \text{ fermi}$. Then the mass number of another atomic nucleus of radius $6 \text{ fermi}$ is

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