An atom has $x$ energy levels,then the total number of spectral lines in its emission spectrum is given by:

The emission spectrum of hydrogen is found to satisfy the expression for the energy change $\Delta E$ (in joules) such that $\Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \, J$ where $n_1 = 1, 2, 3 \dots$ and $n_2 = 2, 3, 4 \dots$. The spectral lines correspond to the Paschen series when:

The frequency of radiation absorbed or emitted when transition occurs between two stationary states with energies $E_1$ (lower) and $E_2$ (higher) is given by

The light of wavelength $242 \, nm$ is required to remove an electron from a $Na$ atom. What is the ionization energy of the sodium atom in $kJ \, mol^{-1}$?

What is the energy (in $J$ atom$^{-1}$) required for the following process?
$Li^{2+}(g) \to Li^{3+}(g) + e^-$
(Take the ionization energy for the $H$ atom in the ground state as $2.18 \times 10^{-18}$ $J$ atom$^{-1}$)

The radius of the second Bohr orbit for hydrogen atom is .......... $\mathring{A}$.
(Planck's constant $h = 6.626 \times 10^{-34} \, Js$; mass of electron $= 9.1091 \times 10^{-31} \, kg$; charge of electron $e = 1.60210 \times 10^{-19} \, C$; permittivity of vacuum $\epsilon_0 = 8.854185 \times 10^{-12} \, C^2 N^{-1} m^{-2}$)