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If $r_1$ and $r_2$ are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio $\left(r_1 / r_2\right)$ is
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The correct answer is:
$\frac{4}{5}$
$r=r_0(A)^{1 / 3}$
$\therefore \quad \frac{r_1}{r_2}=\left(\frac{A_1}{A_2}\right)^{1 / 3}=\left(\frac{64}{125}\right)^{1 / 3}$
$=\left[\left(\frac{4}{5}\right)^3\right]^{1 / 3}=\frac{4}{5}$
$\therefore \quad \frac{r_1}{r_2}=\left(\frac{A_1}{A_2}\right)^{1 / 3}=\left(\frac{64}{125}\right)^{1 / 3}$
$=\left[\left(\frac{4}{5}\right)^3\right]^{1 / 3}=\frac{4}{5}$
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