The ratio of the wavelengths of the spectral lines emitted due to transitions $3 \rightarrow 2$ and $2 \rightarrow 1$ orbits in the hydrogen atom is

The wavelength of radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom,the wavelength of the radiation emitted will be $\frac{20}{x} \lambda_0$. The value of $x$ is

The first three spectral lines of the $H$-atom in the Balmer series are given as $\lambda_{1}, \lambda_{2}, \lambda_{3}$. Considering the Bohr atomic model,the wavelengths of the first and third spectral lines $\left(\frac{\lambda_{1}}{\lambda_{3}}\right)$ are related by a factor of approximately '$x$' $\times 10^{-1}$. The value of $x$,to the nearest integer,is:

The lines in the Balmer series have their wavelengths lying between

In terms of Rydberg constant $R,$ the shortest wavelength in the Balmer series of the Hydrogen atom spectrum will be:

If the series limit frequency of the Balmer series is $\nu_{B}$,then the series limit frequency of the Brackett series is