The shortest wavelength in the Paschen series of the Hydrogen spectrum is (Rydberg constant of hydrogen $R_H = 1.097 \times 10^7 \ m^{-1}$). (in $nm$)

The shortest wavelength in the Balmer series of the hydrogen atom spectrum is approximately equal to (use $R_{H} = 1.097 \times 10^7 \ \text{m}^{-1}$) (in $\text{Å}$)

The ionization energy of the electron in the hydrogen atom in its ground state is $13.6 \text{ eV}$. The atoms are excited to higher energy levels to emit radiations of $6$ wavelengths. The maximum wavelength of the emitted radiation corresponds to the transition between:

The difference between the frequencies of the first and second Lyman lines of the hydrogen atom is (where $R$ is the Rydberg constant and $c$ is the speed of light in vacuum).

The ratio of the longest to shortest wavelengths in the Brackett series of hydrogen spectra is

In terms of Rydberg's constant $R,$ the wave number of the first Balmer line is