The potential energy of an electron in the hydrogen atom is $-6.8 \ eV$. Indicate in which excited state the electron is present.

The radius of the first excited state of a Helium ion $(He^+)$ is given by (where $a_0$ is the radius of the first stationary state of the hydrogen atom):

What will be the ratio of the wavelength of the third line of the Balmer series in the $He^{+}$ ion spectrum to the first line of the Balmer series in the $Li^{2+}$ ion spectrum?

$A$ certain metal has a work function of $\Phi = 2 \ eV$. It is irradiated first with $1 \ W$ of $400 \ nm$ light and later with $1 \ W$ of $800 \ nm$ light. Among the following,the correct statement is
[Given: Planck constant $(h) = 6.626 \times 10^{-34} \ J \ s$;
Speed of light $(c) = 3 \times 10^8 \ m \ s^{-1}$ ]

Heat treatment of muscular pain involves radiation of wavelength of about $900 \ nm$. Which spectral line of $H$ atom is suitable for this purpose?
$[R_H = 1.097 \times 10^7 \ m^{-1}, \ h = 6.626 \times 10^{-34} \ J \cdot s, \ c = 3 \times 10^8 \ m/s]$

$A$ certain electronic transition from an excited state to the ground state of the $H$ atom in one or more steps gives rise to four lines in the ultraviolet region of the spectrum. How many lines does this transition produce in the infrared region of the spectrum?