What is the angular momentum of an electron in Bohr's hydrogen atom whose energy is $-3.4 \,eV$?

Using the formula for the radius of the $n^{th}$ orbit $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,derive an expression for the total energy of an electron in the $n^{th}$ Bohr orbit.

$A$ stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. The recoil speed of the atom is (where $R=$ Rydberg constant,$h=$ Planck's constant,and $m=$ mass of the hydrogen atom).

The maximum wavelength that a sample of hydrogen atoms can absorb is

According to the classical electromagnetic theory,calculate the initial frequency of the light emitted by the electron revolving around a proton in a hydrogen atom.

What is the ratio of the wavelengths emitted during the $2 \to 1$ transition in $Li^{++}$,$He^+$,and $H$?