Question

If $r_1$ and $r_2$ are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio $\frac{r_1}{r_2}$ is :

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

Answer 1

Answer: (D)

$\frac{4}{5}$

The radius of the atomic nuclei ($r$) is directly proportional to cube root of Mass number ($Z$)

$\Rightarrow r\propto Z^{\frac{1}{3}}$

$\Rightarrow \frac{r_1}{r_2}={\left(\frac{64}{125}\right)}^{\frac{1}{3}}=\frac{4}{5}$

Hence, option D is correct.