${r_n} = {n^2}{a_0} \Rightarrow \left\{ \begin{gathered} 1/25 = n_U^2 \times 0/05 \Rightarrow {n_U} = 5 \hfill \cr 0/2 = n_L^2 \times 0/05 \Rightarrow {n_L} = 2 \hfill \cr \end{gathered} \right.$
$\begin{equation} \left.\begin{aligned} {{E_n} = - {E_R}\frac{1}{{{n^2}}}}\\ {\Delta E = {E_U} - {E_L} = hf} \end{aligned} \right\} \end{equation} \Rightarrow - 13/6 \times \frac{1}{{{5^2}}} - ( - 13/6 \times 1\frac{1}{{{2^2}}}) = 4/2 \times {10^{ - 15}} \times f$
$ \Rightarrow 13/6 \times (\frac{1}{4} - \frac{1}{{25}}) = 4/2 \times {10^{ - 15}}f$
$ \Rightarrow 13/6 \times \frac{{21}}{{100}} = 4/2 \times {10^{ - 15}}f \Rightarrow f = 6/8 \times {10^{14}}Hz$