Calculate the wavenumber of the photon emitted during transition from the orbit of $n=2$ to $n=1$ in a hydrogen atom. $[R_H = 109677 \ cm^{-1}]$ (in $cm^{-1}$)

If an electron in a hydrogen atom undergoes a transition from the $4^{th}$ stationary orbit and emits a line in the Lyman series,calculate the wavelength of the emitted radiation.

The radius of the first Bohr orbit for hydrogen is $0.53 \ \mathring{A}$. The radius of the third Bohr orbit would be .............. $\mathring{A}$.

In the Lyman series of hydrogen,which are the two maximum wavelengths? Why?

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.

Which energy level transition among the following will have the least wavelength?