What is the angular momentum of an electron when it revolves in orbits?

The energy difference of two stable orbits of Hydrogen is $214.68 \ kJ \ mol^{-1}$. If the transition of an electron takes place,find the emitted frequency. (Note: $v = \Delta E/h$ and $h = 6.626 \times 10^{-34} \ J \ s$)

In a mixture of $H$ and $He^{+}$ gases,all $H$ atoms and $He^{+}$ ions are excited to their first excited states. Subsequently,on de-excitation in $H$ atoms,energy is transferred to the excited $He^{+}$ ion. The quantum number $n$ of the $He^{+}$ ion after the energy is transferred is:

Supposing the energy of the fourth shell for a hydrogen atom is $-25 \, a.u.$ (arbitrary unit). What would be its potential energy in the ground state?

The electron in the $n^{th}$ orbit of $Li^{2+}$ is excited to $(n+1)$ orbit using the radiation of energy $1.47 \times 10^{-17} \ J$. The value of $n$ is $....$. Given $R_H = 2.18 \times 10^{-18} \ J$.

Quantum theory was postulated by :