Find the value of wave number $(\bar{v})$ in terms of Rydberg's constant,when the transition of an electron takes place between two levels of $He^{+}$ ion whose sum is $4$ and difference is $2$.

According to Bohr's theory,
$E_{n} = \text{Total energy}, K_{n} = \text{Kinetic energy}, V_{n} = \text{Potential energy}, r_{n} = \text{Radius of } n^{\text{th}} \text{ orbit}$
Match the following:

Column $I$	Column $II$
$A$. $V_{n} / K_{n} = ?$	$P$. $0$
$B$. If radius of $n^{\text{th}}$ orbit $\propto E_{n}^{x}, x = ?$	$Q$. $-1$
$C$. Angular momentum in lowest orbital	$R$. $-2$
$D$. $1/r_{n} \propto Z^{y}, y = ?$	$S$. $1$

For a $Bohr$ atom,the angular momentum of an electron is given by $M(n = 1, 2, 3, .....)$ :

$A$ photon of wavelength $4 \times 10^{-7} \, m$ strikes on a metal surface. The work function of the metal is $2.13 \, eV$. Calculate:
$(i)$ The energy of the photon in $eV$.
$(ii)$ The kinetic energy of the emission in $eV$.
$(iii)$ The velocity of the photoelectron in $ms^{-1}$ ($1 \, eV = 1.6020 \times 10^{-19} \, J$,mass of electron $m = 9.10939 \times 10^{-31} \, kg$).

Calculate the energy and frequency of the radiation emitted when an electron jumps from $n = 3$ to $n = 2$ in a hydrogen atom.

Among the following,which transition in the hydrogen spectrum would have the same wavelength as the Balmer transition,$n=4$ to $n=2$ in the $He^{+}$ spectrum?