According to Bohr's atomic model,the angular momentum of an electron in the $5^{th}$ orbit of an $H$-atom is:

In Bohr's atomic model,the electron is assumed to revolve in a circular orbit of radius $0.5 \times 10^{-10} \; m$. If the speed of the electron is $2.2 \times 10^{6} \; m/s$,then the current associated with the electron will be $.... \times 10^{-2} \; mA$. [Take $\pi$ as $\frac{22}{7}$]

Show that the first few frequencies of light that is emitted when electrons fall to the $n^{\text{th}}$ level from levels higher than $n$,are approximate harmonics (i.e.,in the ratio $1:2:3...$) when $n >> 1$.

The electron in a hydrogen atom makes a transition from the $M$ shell to the $L$ shell. The ratio of the magnitudes of the initial to the final centripetal acceleration of the electron is:

A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980 \ \text{\AA}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be (given $hc = 12500 \ \text{eV-\AA}$). (in $a_0$)

Magnetic field at the centre of a hydrogen-like atom (atomic number $= Z$) due to the motion of an electron in the $n^{th}$ orbit is proportional to