$A$ metal surface is exposed to $500 \ nm$ radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 10^{14} \ Hz$. The velocity of the ejected electron is $....... \times 10^{5} \ ms^{-1}$ (Nearest integer).
[Use : $h=6.63 \times 10^{-34} \ Js, m_{e}=9.0 \times 10^{-31} \ kg$]

The threshold frequency $v_{0}$ for a metal is $7.0 \times 10^{14} \,s^{-1}.$ Calculate the kinetic energy of an electron emitted when radiation of frequency $v = 1.0 \times 10^{15} \,s^{-1}$ hits the metal.

If the first emission in the Lyman series of a hydrogen atom occurs at $121.5 \ nm$,what will be the energy difference between the first and second orbits in $kJ/mol$?

Consider one $He^{+}$ ion is in excited state $(n = 5)$. Which of the following observations hold true as per the Bohr's model?

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.

Based on equation $E = -2.178 \times 10^{-18} \ J \ \frac{Z^2}{n^2}$,certain conclusions are written. Which of them is not correct?