Find the ratio of the first wavelengths of the Lyman series and the Balmer series.

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

The second line of the Balmer series has a wavelength of $4861 Å$. The wavelength of the first line of the Balmer series is: (in $Å$)

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen spectrum (in $\text{ nm}$)? (Take $hc = 1240 \text{ eV nm}$)

If an electron in a hydrogen atom jumps from the $3^{rd}$ orbit to the $2^{nd}$ orbit,it emits a photon of wavelength $\lambda$. When it jumps from the $4^{th}$ orbit to the $3^{rd}$ orbit,the corresponding wavelength of the photon will be

In hydrogen atom spectra,if the ratio of wavelengths corresponding to the first line of the Lyman series and the first line of the Balmer series is $9 \alpha$,the value of $\alpha$ is