The ratio of the energies of the hydrogen atom in its first to second excited state is :

1/4 4/9 9/4 4

9/4

First excited state i.e. second orbit (n = 2) Second excited state i.e. third orbit (n = 3) $∵ E=-\frac{13.6}{n^2} \Rightarrow \frac{E_2}{E_3}=\left(\frac{3}{2}\right)^2=\frac{9}{4}$