The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is proportional to ($e$ = electronic charge).

An electron in a hydrogen atom,after absorbing energy photons,can jump between energy states $n_1$ and $n_2$ $(n_2 > n_1)$. It then returns to the ground state,emitting six different wavelengths in the emission spectrum. The energy of the emitted photons can be equal to,less than,or greater than the absorbed photon energy. Determine $n_1$ and $n_2$.

The muon has the same charge as an electron but a mass that is $207$ times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy $E_{B\mu}$ of the muon in the ground state of a muonic hydrogen atom compare with the binding energy $E_{Be}$ of an electron in the ground state of a conventional hydrogen atom?

If the energy of an electron in the ground state is $-13.6 \text{ eV}$,find the speed of the electron in the fourth orbit of an $H$-atom.

The radius of the first (lowest) orbit of the hydrogen atom is $a_0$. The radius of the second (next higher) orbit will be (in $a_0$)

In a hydrogen atom,if $r_n$ is the radius of the $n^{th}$ orbit and $L_n$ is the orbital angular momentum,then which of the following relations is correct?