The limiting line in the Balmer series of the $H$ spectrum has a frequency of ....... $(R_\infty = 3.29 \times 10^{15} \, cycles/s)$

The frequency of one of the lines in the Paschen series of a hydrogen atom is $2.340 \times 10^{11} \ Hz$. The quantum number $n_2$ which produces this transition is

The energy (in $eV$) associated with the electron in the $1^{st}$ orbit of $Li^{2+}$ is

$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

The ratio of the velocity of an electron in the ground state of a hydrogen atom to its velocity in the second excited state of a $He^{+}$ ion is:

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions $(i)$ $n=4$ to $n=2$ and $(ii)$ $n=3$ to $n=1$ are $\lambda_1$ and $\lambda_2$ $\mathring{A}$ respectively. The value of $(\lambda_1-\lambda_2)$ (in cm) is ($R_H$ = Rydberg constant)