The wavelength of the second line of the Balmer series of a hydrogen atom is $\lambda \ nm$. What is the wavelength of the first line of the Lyman series of the $He^{+}$ ion (in $nm$)?

What is the energy associated with the first orbit of $Li^{2+}$ $(R_{H} = 2.18 \times 10^{-18} \ J)$?

How does the energy of an orbit change as we move away from the nucleus in a hydrogen-like atom?

The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by:

What is the number of photons of light with a wavelength of $4000 \ pm$ that provide $1 \ J$ of energy?

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.