The frequency of revolution of an electron revolving in the $n^{th}$ orbit of an $H$-atom is proportional to:

Assertion $(A)$: The magnetic moment $(\mu)$ of an electron revolving around the nucleus decreases with increasing principal quantum number $(n)$.
Reason $(R)$: Magnetic moment of the revolving electron,$\mu \propto n$.

Consider a hydrogen-like ionized atom with atomic number $Z$ with a single electron. In the emission spectrum of this atom,the photon emitted in the $n = 2$ to $n = 1$ transition has energy $74.8 \ eV$ higher than the photon emitted in the $n = 3$ to $n = 2$ transition. The ionization energy of the hydrogen atom is $13.6 \ eV$. The value of $Z$ is:

$A$ hydrogen-like atom has one electron revolving around a stationary nucleus. If the energy required to excite the electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is $47.2 \ eV$,find the atomic number of the given atom.

The gyromagnetic ratio of an electron in a hydrogen atom,according to the Bohr model,is

For an electron moving in the $n^{\text{th}}$ Bohr orbit,the de Broglie wavelength of the electron is: