State whether the following statements are true or false:
$(i)$ The $Bohr$ model cannot explain how atoms form molecules.
$(ii)$ The $Bohr$ model is accepted as the planetary model.
$(iii)$ Electrons in an atom do not absorb or emit energy while moving in a stationary orbit.
$(iv)$ The spectral lines of the $Brackett$ series are found in the ultraviolet region.

Calculate the ionization energy of $H$,$He^{+}$,and $Li^{2+}$ in $kJ \, mol^{-1}$.

In the hydrogen spectrum,if $n = 4$,what is the ratio of the number of lines in the emission spectrum in the ultraviolet and visible regions?

When an electron drops from a higher energy level to a lower energy level,then

When an electric discharge is passed through hydrogen gas,the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
$\bar{v} = 109677 \left[ \frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}} \right] \ cm^{-1}$
What points of Bohr's model of an atom can be used to arrive at this formula? Based on these points,derive the above formula,giving a description of each step and each term.

For $Li^{2+}$,the ratio of radii $r_2 : r_5$ is: