The stopping potential for the photoelectrons emitted from a metal surface of work function $1.7 \ eV$ is $10.4 \ V$. Identify the energy levels corresponding to the transitions in a hydrogen atom which will result in the emission of a wavelength equal to that of the incident radiation for the above photoelectric effect.

In an $H$-like atom,when an electron transits from energy state $n=5$ to $n=2$,a photon of wavelength $434 \, nm$ is emitted. What will be the wavelength of the photon emitted when the transition occurs from energy state $n=4$ to $n=2$?

$A$ $12.5\,eV$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

In the hydrogen atom spectrum, ($R$ is Rydberg's constant):
$A$. The maximum wavelength of the radiation of the Lyman series is $\frac{4}{3R}$.
$B$. The Balmer series lies in the visible region of the spectrum.
$C$. The minimum wavelength of the radiation of the Paschen series is $\frac{9}{R}$.
$D$. The minimum wavelength of the Lyman series is $\frac{5}{4R}$.
Choose the correct answer from the options given below:

The wavelength of the second Balmer line in the hydrogen spectrum is $600 \ nm$. The wavelength for its third line in the Lyman series is:

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