Find out the distance between the $2^{nd}$ and $3^{rd}$ orbit of the $H^{-}$ ion.

What is the numerical value of angular momentum for an electron in the first orbit of a hydrogen atom? $(h = 6.626 \times 10^{-34} \ J \ s)$

An excited hydrogen atom emits light in the ultraviolet region at a frequency of $2.47 \times 10^{15} \ Hz$. Calculate the energy of a single photon. (Given: $h = 6.63 \times 10^{-34} \ J \cdot s$)

The work function for a caesium atom is $1.9 \, eV$. Calculate $(a)$ the threshold wavelength and $(b)$ the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength of $500 \, nm$,calculate the kinetic energy and the velocity of the ejected photoelectron.

The wave number of the spectral line in the emission spectrum of hydrogen will be equal to $\frac{8}{9}$ times the Rydberg's constant if the electron jumps from

Explain: "Rutherford's atomic model cannot explain the stability of an atom."