Question

The wavelength of $H_{\alpha }$ line of the Paschen series is $6912\stackrel{o}{A}$. The wavelength of the $H_{\beta }$ line of Paschen series is (in $\stackrel{o}{A}$) :

Answer 1

$H_{\alpha }$ line of Paschen series is produced due to the transition from $n=4$ to $n=3$
$H_{\beta }$ line of Paschen series is produced due to the transition from $n=5$ to $n=3$
Therefore,
$\frac{1}{{\lambda }_{\alpha }}=R_H[\frac{1}{3^2}-\frac{1}{4^2}]$ ...(1)
$\frac{1}{{\lambda }_{\beta }}=R_H[\frac{1}{3^2}-\frac{1}{5^2}]$ ...(2)
Where $R_H$ is the Rydberg constant.
From the equation (1) and (2) we get,
$\frac{{\lambda }_{\beta }}{{\lambda }_{\alpha }}=\frac{7\times 225}{144\times 16}$
${\lambda }_{\beta }=\frac{7\times 225}{144\times 16}\times 6912\stackrel{o}{A}$
$\Rightarrow {\lambda }_{\beta }=4725\stackrel{o}{A}$