Sol. $\_\_\_\_$ $\mathrm{n}=4$ $\_\_\_\_$ $\mathrm{n}=3$ $\_\_\_\_$ $\mathrm{n}=2$ $\_\_\_\_$ $\mathrm{n}=1$ Second excited state → first excited state $\mathrm{n}=3 \rightarrow \mathrm{n}=2$ $$ \frac{\mathrm{hc}}{\lambda_0}=13.6\left(\frac{1}{2^2}-\frac{1}{3^2}\right) $$ Third excited state → second orbit $\mathrm{n}=4 \rightarrow \mathrm{n}=2$ $$ \frac{\mathrm{hc}}{\left(20 \lambda_0 / \mathrm{x}\right)}=13.6\left(\frac{1}{2^2}-\frac{1}{4^2}\right) $$ (ii) ÷ (i) $$ \begin{aligned} & \frac{x}{20}=\frac{\frac{1}{2^2}-\frac{1}{4^2}}{\frac{1}{2^2}-\frac{1}{3^2}} \\ & x=27 \end{aligned} $$