Which transition in the hydrogen atomic spectrum will have the same wavelength as the transition,$n = 4$ to $n = 2$ of $He^{+}$ spectrum?

Values of work function $(W_0)$ for a few metals are given below:

Metal	$Li$	$Na$	$K$	$Mg$	$Cu$	$Ag$
$W_0 / eV$	$2.42$	$2.3$	$2.25$	$3.7$	$4.8$	$4.3$

The number of metals which will show photoelectric effect when light of wavelength $400 \ nm$ falls on it is $........$.
Given: $h = 6.6 \times 10^{-34} \ J \ s$,$c = 3 \times 10^8 \ m \ s^{-1}$,$e = 1.6 \times 10^{-19} \ C$

When an electric discharge is passed through hydrogen gas,the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
$\bar{v} = 109677 \left[ \frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}} \right] \ cm^{-1}$
What points of Bohr's model of an atom can be used to arrive at this formula? Based on these points,derive the above formula,giving a description of each step and each term.

In the Bohr model of the atom,when an electron undergoes a transition from $n = 1$ to $n = 3$,the energy absorbed or emitted is ........

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):

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate $(a)$ threshold wavelength and $(b)$ Planck's constant.

$\lambda \ (nm)$	$500, 450, 400$
$v \times 10^{-5} \ (cm \ s^{-1})$	$2.55, 4.35, 5.35$