Draw the energy level diagram for the electron in a hydrogen atom and show the different series of lines hydrogen atom can produce.

Calculate the wavelength of the first spectral line in the corresponding Lyman series of hydrogen $\left(\mathrm{H}\right)$ atom.

$\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{R}$}\right.=91.2 \mathrm{nm}\right)$

In a hydrogen atom, an electron undergoes transition from the $2^{\mathrm{nd}}$ excited state to the $1^{\mathrm{st}}$ excited state and then to the ground state. Identify the spectral series to which these transitions belong.

In a hydrogen atom, an electron undergoes transition from the second excited state to the first excited state and then to the ground state. Find out the ratio of the wavelengths of the emitted radiations in the two cases.