If the ionization energy of a hydrogen atom in the ground state is $13.6 \ eV$,find the ionization potential of the third orbit in $eV$.

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

$A$ sample of hydrogen atoms is in an excited state (all the atoms). The photons emitted from this sample are made to pass through a filter through which light having a wavelength greater than $800 \ nm$ can only pass. Only one type of photon is found to pass through the filter. The sample's initial excited state is: [Take $hc = 1240 \ eV \cdot nm$,ground state energy of hydrogen atom = $-13.6 \ eV$.]

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

$A$ photon is emitted in transition from $n = 4$ to $n = 1$ level in a hydrogen atom. The corresponding wavelength for this transition is $......... \, nm$ (given,$h = 4 \times 10^{-15} \, eV \cdot s$ and $c = 3 \times 10^8 \, m/s$):

The first excited state of a hydrogen atom is $10.2 \ eV$ above the ground state. What temperature is needed to excite a hydrogen atom to its first excited state?