Physics - Modern Physics Question with Solution | TestHub

Rydberg's relation is given by $\frac{1}{\lambda }={\mathrm{R}}_{\mathrm{H}}{\mathrm{Z}}^2\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$ For hydrogen, $\mathrm{Z}=1$. Given, for $3^{\text{rd }}$ to $2^{\text{nd }}$ orbit transition
And for $4^{\text{th }}$ to $3^{\text{rd }}$ orbit transition
Taking ratio of eqn (1) \& (2) $\begin{array}{rl}& \frac{{\lambda }_n}{\lambda }=\frac{5}{36}\times \frac{(16\times 9)}{7}=\frac{20}{7}\\ & \Rightarrow {\lambda }_n=\frac{20}{7}\lambda \end{array}$