Question

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

• A. $\frac{1}{4}$
• B. $\frac{4}{9}$
• C. $\frac{9}{4}$
• D. $4$

Answer 1

The correct option is C $\frac{9}{4}$

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