$A$ hydrogen atom absorbs radiation of wavelength $975 \, \text{\AA}$ to transition from the ground state to an excited state. To which energy level will the atom transition?

An electron of a hydrogen-like atom,having $Z=4$,jumps from the $4^{\text{th}}$ energy state to the $2^{\text{nd}}$ energy state. The energy released in this process will be $......... \text{eV}$.
(Given $Rch = 13.6 \text{ eV}$)
Where $R =$ Rydberg constant,
$c =$ Speed of light in vacuum,
$h =$ Planck's constant.

The ratio of the kinetic energies of the electrons in the third and fourth excited states of the hydrogen atom is

An electron collides elastically with an $H$-like atom and excites it from the ground state to $n = 3$. Find the energy transferred to the $H$-like atom in $eV$.

If the electron in a hydrogen atom were in the energy level with $n = 3$,how much energy in joule would be required to ionise the atom? (Ionisation energy of $H$-atom is $2.18 \times 10^{-18} \ J$):

$A$ difference of $2.3\; eV$ separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?