The magnetic moment of an electron due to its orbital motion is proportional to $(n =$ principal quantum number$)$

The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is

Using Bohr's atomic model, the orbital period of an electron in a hydrogen atom in the $n^{th}$ orbit is ($\epsilon_0$ = permittivity of free space, $h$ = Planck's constant, $m$ = mass of electron, $e$ = electronic charge).

According to Bohr's theory,the moment of momentum of an electron revolving in the $4^{\text{th}}$ orbit of a hydrogen atom is:

In a hydrogen-like ion,the energy difference between the $2^{\text{nd}}$ excitation state and the ground state is $108.8 \ eV$. The atomic number of the ion is:

$A$ muon is an unstable particle with a mass of $207 \, m_e$ and a charge of either $+e$ or $-e$. $A$ muon $(\mu^-)$ is captured by a hydrogen nucleus to form a muonic atom. If the proton captures the $\mu^-$, find the ionization energy of this atom in $keV$.