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.

The two lines A and B, shown in the graph of Fig. $20.18$, plot the de-Broglie wavelength $\left(\lambda \right)$ as a function of $\frac{1}{\sqrt{\mathrm{V}}} \left(\mathrm{V} \text{is the accelerating potential}\right)$ for two particles, having the same charge $q$. Which of the two represents particle of the heavier mass?

Draw a schematic diagram of the experimental arrangement used by Davisson and Germer to establish the wave nature of electrons. Explain briefly how the de-Broglie relation was experimentally verified in case of electrons.