The frequency corresponding to transition n = 1 to n = 2 in hydrogen atom is

$$\begin{gathered} \mathrm{\nu } =\mathrm{C}\overline{\mathrm{\nu }} ={\mathrm{CRZ}}^2\left[\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right] \\ {\mathrm{\nu }}_{2\to 4}\left({\mathrm{He}}^{+}\right) =\mathrm{CR}\left(4\right)\left[\frac{1}{4}-\frac{1}{16}\right] =\mathrm{CR}\left(\frac{3}{4}\right) \\ \mathrm{Given} , {\mathrm{\nu }}_{2\to 4}\left({\mathrm{He}}^{+}\right) ={\mathrm{\nu }}_{{\mathrm{n}}_2\to {\mathrm{n}}_1}\left(\mathrm{H}\right) \\ \mathrm{CR}\left(\frac{3}{4}\right) = \mathrm{CR}\left[\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right] \\ \frac{3}{4} = \left[\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right] \\ \mathrm{From} \mathrm{options} , {\mathrm{n}}_1=1 \mathrm{and} {\mathrm{n}}_2=2 \\ \mathrm{i}.\mathrm{e} \mathrm{n}=2 \mathrm{to} \mathrm{n}=1 \mathrm{transition} \end{gathered}$$