Atoms question bank (Physics)

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 $x/32$. The value of $x$ is

For the wavelength of visible radiation of the Hydrogen spectrum, Balmer gave an equation as $\lambda = \frac{xm^2}{m^2 - 4}$, where $m$ is an integer value. The value of $x$ in terms of Rydberg's constant $R$ is