If the ionisation energy for the hydrogen atom is $13.6 \ eV$,then the energy required to excite it from the ground state to the next higher state is nearly: (in $eV$)

The number of spectral lines emitted by atomic hydrogen that is in the $4^{\text{th}}$ energy level is

The energy levels of a hydrogen atom are shown below. The transition corresponding to the emission of the shortest wavelength is

The energy levels with transitions for an atom are shown in the figure. The transitions corresponding to the emission of radiation of maximum and minimum wavelength are respectively:

An electron in a hydrogen atom first jumps from the third excited state to the second excited state and then from the second excited state to the first excited state. The ratio of the wavelengths $\lambda_1 : \lambda_2$ emitted in the two cases is

The ratio of the energies of the electron in the hydrogen atom in the first and second excited states is