Answer:
Option C
Explanation:
The wave number ($\bar{v}$) of the radiation = $\frac{1}{\lambda}$
= $R_{\infty}\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
Now for case (I) n1= 3, n2= 2
$\frac{1}{\lambda_{1}}=R_{\infty}\left[\frac{1}{9}-\frac{1}{4}\right]$
R∞ = Rydberg constant
$\frac{1}{\lambda_{1}}=R_{\infty}\left[\frac{4-9}{36}\right]$
$=\left[\frac{-5R_{\infty}}{36}\right]$
$\lambda_{1}=\left[\frac{-36}{5R_{\infty}}\right]$
$\frac{1}{\lambda_{2}}=R_{\infty}\left[\frac{1}{4}-\frac{1}{1}\right]$
= $\left[\frac{-3R_{\infty}}{4}\right]$
$\lambda_{2}=\left[\frac{-4}{3R_{\infty}}\right]$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{-36}{5R_{\infty}}\times\frac{3R_{\infty}}{-4}$
$\frac{\lambda_{1}}{\lambda_{2}}$ = $\frac{27}{5}$