If the velocity of an electron in the $n^{th}$ orbit of a hydrogen atom is $0.0109 \times 10^{10} \, cm \, s^{-1}$,what is the value of $n$?

Match List-$I$ with List-$II$.

List-$I$ (Spectral Series for Hydrogen)	List-$II$ (Spectral Region)
$A$. Lyman	$I$. Infrared region
$B$. Balmer	$II$. $UV$ region
$C$. Paschen	$III$. Infrared region
$D$. Pfund	$IV$. Visible region

Choose the correct answer from the options given below:

Calculate the wavelength of the emitted radiation when an electron transitions from $n = 3$ to $n = 2$ in a hydrogen atom. To which region does this radiation belong?

Calculate the wave number of a photon emitted during the transition from the orbit $n = 2$ to $n = 1$ in a hydrogen atom $(R_{H} = 109677 \ cm^{-1})$. (in $cm^{-1}$)

An electron in a hydrogen atom in its ground state absorbs $2$ times as much energy as the minimum required for it to escape from the atom. The kinetic energy of the emitted electron is ............ $eV$.

If the maximum kinetic energy of photoelectrons ejected from a metal surface when it is irradiated with a radiation of frequency $4 \times 10^{14} \ s^{-1}$ is $6.63 \times 10^{-20} \ J$,then the threshold frequency of the metal is