State the uses of atomic spectra.

The binding energy of an $e^-$ in the ground state of a hydrogen atom is $13.6 \ eV$. The energy required to remove an electron from the ground state of a $He^+$ ion is:

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.

Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.

The wavelength of a spectral line emitted by a hydrogen atom in the Lyman series is $\frac{16}{15 R} \ cm$. What is the value of $n_2$? $(R = \text{Rydberg constant})$

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $n = 4$ to $n = 2$ of $He^+$ spectrum?