The ratio of the radii of the second and third orbits of an $H$-atom is . . . . . . .

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,show that this frequency equals the classical frequency of revolution of the electron in the orbit.

$A$ 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 Bohr's model of the hydrogen atom,which of the following pairs of quantities are quantized?

Consider a hydrogen-like atom whose energy in the $n^{th}$ excited state is given by $E_n = - \frac{13.6 Z^2}{n^2}$. When this excited atom makes a transition from an excited state to the ground state, the most energetic photons have energy $E_{max} = 52.224 \ eV$ and the least energetic photons have energy $E_{min} = 1.224 \ eV$. The atomic number of the atom is:

When an electron in a hydrogen atom is excited from its $4^{th}$ to $5^{th}$ stationary orbit,the change in angular momentum of the electron is (Planck's constant: $h = 6.6 \times 10^{-34} \ J \cdot s$)