Question

The ratio of the radii of ${}_{13}{\text{Al}}^{27}$ and ${}_{52}{\text{Te}}^{125}$ nuclei is

• A. $5:3$
• B. $9:25$
• C. $3:5$
• D. $25:9$

Answer 1

The correct option is C $3:5$

Given:

Mass number, $A_{\text{Al}}=27$ ; $A_{\text{Te}}=125$

As we know that

$R=R_0{\left(A\right)}^{1/3}$

$\therefore R\propto A^{1/3}$

$\Rightarrow \frac{R_{\text{Al}}}{R_{\text{Te}}}={\left[\frac{A_{\text{Al}}}{A_{\text{Te}}}\right]}^{1/3}={\left[\frac{27}{125}\right]}^{1/3}$

$\Rightarrow \frac{R_{\text{Al}}}{R_{\text{Te}}}=\frac{3}{5}$

$\begin{array}{c}{R}_{Al}:R_{Te}=3:5\end{array}$

Hence, option $\left(\text{C}\right)$ is correct.