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 $(D)$.

If the wavelength of the first line of the Balmer series of hydrogen is $6561 \; \mathring{A}$,the wavelength of the second line of the series should be........$\mathring{A}$

An electron jumps from the $4^{\text{th}}$ orbit to the $2^{\text{nd}}$ orbit of a hydrogen atom. Given Rydberg's constant $R_{H}=10^7 \ m^{-1}$,calculate the frequency in $Hz$ of the emitted radiation. (Take $c=3 \times 10^8 \ m/s$)

In the spectrum of hydrogen,the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

Name the different series obtained in the hydrogen spectrum and give the general formula for finding the wave number.

If $\Delta \lambda_L$ is the difference between the shortest and longest wavelengths of the Lyman series and $\Delta \lambda_B$ is the difference between the shortest and longest wavelengths of the Balmer series,then $\frac{\Delta \lambda_B}{\Delta \lambda_L} = $