In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is

$A$ hydrogen atom in an excited state transitions to the ground state by emitting a photon of wavelength $\lambda$. The value of the principal quantum number $n$ of the excited state is:
($R$: Rydberg constant)

In the Bohr model of the hydrogen atom,the angular velocity $\omega_n$ of the electron depends on the principal quantum number $n$ as:

Write the theoretical value and experimental value of the Rydberg constant,including the unit.

The difference between the $n^{th}$ and $(n+1)^{th}$ Bohr radius of an $H$ atom is equal to its $(n-1)^{th}$ Bohr radius. The value of $n$ is:

In the Bohr model,an electron of mass $m$ moves in a circular orbit around the proton. Considering the orbiting electron as a circular current loop,find the magnetic moment of the hydrogen atom when the electron is in the $n$th orbit. (Assume $h$ is Planck's constant)