Question

If the radii of nuclei of ${}_{13}A{l}^{27}$ and ${}_{30}Z{n}^{64}$ are $R_1$ and $R_2$ respectively, then $\frac{R_1}{R_2}$ is equal to

• A. $\frac{27}{64}$
• B. $\frac{64}{27}$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Here, $A_1=27,A_2=64$
The volume of the nucleus is directly proportional mass number.
So, $\frac{3}{4}\pi R^3\propto A$
or $R\propto A^{1/3}$
$=\frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}$
$\Rightarrow \frac{R_1}{R_2}={\left(\frac{27}{64}\right)}^{1/3}=\frac{3}{4}$