Question

If $r_1$, and $r_2$ are the radii of the atomic nuclei of mass numbers $64$ and $125$ respectively, then the ratio ($r_1/r_2$) is

• A. $\frac{64}{125}$
• B. $\sqrt{\frac{64}{125}}$
• C. $\frac{5}{4}$
• D. $\frac{4}{5}$

Answer 1

Answer: (D)

$\frac{4}{5}$

Answer 2

The radius of the atomic nuclei $(r)$ is directly proportional to cube root of Mass number (Z)
$\begin{array}{l} \Rightarrow r \propto Z ^{\frac{1}{3}} \\\ \Rightarrow \frac{ r _{1}}{ r _{2}}=\left(\frac{64}{125}\right)^{\frac{1}{3}}=\frac{4}{5} \end{array}$