Wave number of series limit in Balmer series of Hydrogen atom is ‘x’. Wave number of series limit in Lyman series of Hydrogen atom is ‘y’. Ratio of ‘x’ to ‘y’ is

$$\begin{gathered} \overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H} }\left[\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\infty }^2}\right]; \\ {\mathrm{n}}_1=2 \mathrm{for} \mathrm{Balmer} \mathrm{series}; {\mathrm{n}}_2=\infty \mathrm{for} \mathrm{series} \mathrm{limit} \\ {\mathrm{n}}_1=1 \mathrm{for} \mathrm{Lyman} \mathrm{series}; {\mathrm{n}}_2=\infty \mathrm{for} \mathrm{series} \mathrm{limit} \\ {\overline{\mathrm{v}}}_{\mathrm{Balmer} }: {\overline{\mathrm{\nu }}}_{\mathrm{Lyman}} =\frac{1}{2^2} : \frac{1}{1^2} \\ {\overline{\mathrm{v}}}_{\mathrm{Balmer} }\left(\mathrm{x}\right) : {\overline{\mathrm{\nu }}}_{\mathrm{Lyman}}\left(\mathrm{y}\right) = 1 : 4 ; \end{gathered}$$