If the series limit wavelength of the Lyman series for hydrogen atom is 912 $\stackrel{\text{0}}{\text{A}}$, then the series limit wavelength for the Balmer series for the hydrogen atom is

For Lyman series, the series limit wavelength is given by

$\frac{1}{\mathrm{\lambda }}=\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{{\mathrm{\infty }}^2}\right]=\mathrm{R}\mathrm{or}\mathrm{\lambda }=\frac{1}{\mathrm{R}}$

For Balmer series, the series limit wavelength is given by

$\begin{array}{l}\frac{1}{\mathrm{\lambda }\text{'}}=\mathrm{R}\left[\frac{1}{2^2}-\frac{1}{{\mathrm{\infty }}^2}\right]=\frac{\mathrm{R}}{4} \mathrm{or} \mathrm{\lambda }\text{'}=\frac{4}{\mathrm{R}}\\ \mathrm{Clearly}, \mathrm{\lambda }\text{'}=4\left[\frac{1}{\mathrm{R}}\right] \mathrm{or} \mathrm{\lambda }\text{'}=4\mathrm{\lambda }\end{array}$