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(D) 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.For the first nucleus,

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$0.5$

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(D) 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.For the first nucleus, $R_{\alpha} = R_{0}\alpha^{1/3}$.For the second nucleus, $R_{\beta} = R_{0}\beta^{1/3}$.Taking the ratio, we get $\frac{R_{\alpha}}{R_{\beta}} = \left(\frac{\alpha}{\beta}\right)^{1/3}$.Given that $\beta = 8\alpha$, we substitute this into the ratio:$\frac{R_{\alpha}}{R_{\beta}} = \left(\frac{\alpha}{8\alpha}\right)^{1/3} = \left(\frac{1}{8}\right)^{1/3} = \frac{1}{2} = 0.5$.

$A$ nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$. If $\beta = 8\alpha$, then $R_{\alpha}/R_{\beta}$ is:

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