Every series of the hydrogen spectrum has an upper and lower limit in wavelength. The spectral series which has an upper limit of wavelength equal to $18752 \mathring{A}$ is:
(Rydberg constant $R = 1.097 \times 10^7 \ m^{-1}$)

The transition of an electron in a hydrogen atom that emits a photon whose wavelength lies in the ultraviolet region of the electromagnetic spectrum is

Ratio of the wavelengths of the first line of the Lyman series and the first line of the Balmer series is

For a hydrogen atom,$\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions $1$ and $2$ respectively,as shown in the figure. The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$. The value of $x$ 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.

If the series limit of the Lyman series for a Hydrogen atom is equal to the series limit of the Balmer series for a hydrogen-like atom,then the atomic number of this hydrogen-like atom will be: