Question

The difference between the radii of 3^rd and 4^th orbits of ${\mathrm{Li}}^{2+}$ is ${\mathrm{\Delta R}}_1.$ The difference between the radii of 3^rd and 4^th orbits of ${\mathrm{He}}^{+}$ is ΔR₂. Ratio ${\mathrm{\Delta R}}_1:{\mathrm{\Delta R}}_2$is:

• A. 8:3
• B. 3:8
• C. 3:2
• D. 2:3

Answer 1

The correct option is D

2:3

Explanation of the correct option:

The correct answer is option D:

Calculating the difference between the radii,

$$\begin{gathered} {\left(R_4-R_3\right)}_{L{i}^{+2}}=\frac{0.529}{3}\left\{4^2-3^2\right\}=\Delta R_1 \\ {\left(R_4-R_3\right)}_{H{e}^{+2}}=\frac{0.529}{2}\left\{4^2-3^2\right\}=\Delta R_2 \end{gathered}$$

Now finding the ratio,

$$\begin{gathered} \frac{\Delta R_1}{\Delta R_2}=\frac{1/3}{1/2} \\ =\frac{2}{3} \end{gathered}$$

Hence, option D is correct, i.e., $2:3.$