$A$ doubly ionised $Li$ atom is excited from its ground state $(n = 1)$ to $n = 3$ state. The wavelengths of the spectral lines are given by $\lambda_{32}, \lambda_{31}$ and $\lambda_{21}$. The ratios $\lambda_{32}/\lambda_{31}$ and $\lambda_{21}/\lambda_{31}$ are,respectively:

Which spectral series of the hydrogen atom is found in the ultraviolet region?

The shortest wavelength in the Lyman series is $91.2 \, nm$. The largest wavelength of the series is.....$nm$

In the line spectra of the hydrogen atom,the difference between the largest and the shortest wavelengths of the Lyman series is $304\,\mathring{A}$. The corresponding difference for the Paschen series in $\mathring{A}$ is:

Which of the following statement$(s)$ is(are) correct about the spectrum of hydrogen atom?
$(A)$ The ratio of the longest wavelength to the shortest wavelength in Balmer series is $9/5$.
$(B)$ There is an overlap between the wavelength ranges of Balmer and Paschen series.
$(C)$ The wavelengths of Lyman series are given by $\lambda = \frac{\lambda_0}{1 - 1/m^2}$,where $\lambda_0$ is the shortest wavelength of Lyman series and $m$ is an integer.
$(D)$ The wavelength ranges of Lyman and Balmer series do not overlap.

$v_{1}$ is the frequency of the series limit of the Lyman series,$v_{2}$ is the frequency of the first line of the Lyman series,and $v_{3}$ is the frequency of the series limit of the Balmer series. Then: