The wavelengths of the photons emitted in transitions in the hydrogen spectrum are given by the Rydberg equation
$\begin{align*}\frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2} \right)\end{align*}$
Therefore, the desired ratio is
$\begin{align*}\frac{\lambda_{L \alpha}}{\lambda_{B \alpha}} = \frac{\displaystyle\frac{1}{2^2} - \frac{1}{3^2}}{\displaystyle...$
Therefore, answer (E) is correct.

Solution to 2001 Problem 21