What is the mass number of a nucleus having a | vedclass

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(B) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.Let $R_1$ be the radius of

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$7$

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(B) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.Let $R_1$ be the radius of the nucleus with mass number $A_1 = 189$,so $R_1 = R_0 (189)^{1/3}$.Let $R_2$ be the radius of the target nucleus with mass number $A_2$,so $R_2 = R_0 (A_2)^{1/3}$.According to the problem,$R_2 = \frac{1}{3} R_1$.Substituting the expressions,we get $R_0 (A_2)^{1/3} = \frac{1}{3} R_0 (189)^{1/3}$.Canceling $R_0$ from both sides,we have $(A_2)^{1/3} = \frac{1}{3} (189)^{1/3}$.Raising both sides to the power of $3$,we get $A_2 = (\frac{1}{3})^3 	imes 189$.$A_2 = \frac{1}{27} 	imes 189 = 7$.Therefore,the mass number is $7$.

What is the mass number of a nucleus having a radius equal to $\frac{1}{3}$ of that of ${}^{189}\text{Os}$?

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