If Rydberg's constant is $R$,the longest wavelength of radiation in Paschen series will be $\frac{\alpha}{7 R}$,where $\alpha=$ . . . . . .

$A$ $12.5\,eV$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

$X$ different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number $n = 6$. The value of $X$ is ..... .

Find the ratio of the wavelength of the first line of the Lyman series for a doubly ionized lithium atom $(Li^{2+})$ to the wavelength of the first line of the Lyman series for deuterium $(D)$.

The first member of the Balmer series of a hydrogen atom has a wavelength of $6561 \; \mathring{A}$. The wavelength of the second member of the Balmer series (in $nm$) is

What is the maximum wavelength of the $H_{\alpha}$ line in the Balmer series of the hydrogen atom (in $nm$)?