Find the ratio of energies of photons produced due to the transition of an electron in a hydrogen atom from its $(i)$ second permitted energy level to the first level,and $(ii)$ the highest permitted energy level to the first permitted level.

What is the ratio of the total energy of an electron in a hydrogen atom in the first excited state to that in the third excited state?

The energy required to remove an electron from the first excited state of $Li^{++}$ is ......... $eV$.

What is the energy of the electron revolving in the third orbit expressed in $ eV $ (in $eV$)?

$A$ monochromatic light is incident on a hydrogen sample in the ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x \times 10^{15} \ Hz$. The value of $x$ is (Given $h = 4.25 \times 10^{-15} \ eVs$)

The ionization energy of the hydrogen atom is $13.6 \ eV$. The potential energy of the electron in $n=2$ state of the hydrogen atom is