The wavelength of the first line of the Balmer series is $6563 \; Å$. The Rydberg constant for hydrogen is about

The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is

The ratio of the longest to shortest wavelengths in the Brackett series of hydrogen spectra is

In the hydrogen spectrum,the wavelengths of light emitted in a series of spectral lines is given by the equation,$\frac{1}{\lambda}=R\left(\frac{1}{4^{2}}-\frac{1}{n^{2}}\right)$,where $n=5, 6, 7, \ldots$ and $R$ is Rydberg's constant. Identify the series and wavelength region.

The shortest wavelength in the Balmer series of the hydrogen atom spectrum is approximately equal to (use $R_{H} = 1.097 \times 10^7 \ \text{m}^{-1}$) (in $\text{Å}$)

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 $..........$