$A$ bulb of $40 \ W$ is producing light of wavelength $620 \ nm$ with $80 \%$ efficiency. The number of photons emitted by the bulb in $20 \ s$ is $(1 \ eV = 1.6 \times 10^{-19} \ J, hc = 12400 \ eV \ \mathring{A})$

The value of Rydberg constant $\left(R_H\right)$ is $2.18 \times 10^{-18} \ J$. The velocity of an electron having mass $9.1 \times 10^{-31} \ kg$ in Bohr's first orbit of a hydrogen atom $= \dots \dots \dots \times 10^5 \ ms^{-1}$ (nearest integer).

The work function for a caesium atom is $1.9 \, eV$. Calculate $(a)$ the threshold wavelength and $(b)$ the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength of $500 \, nm$,calculate the kinetic energy and the velocity of the ejected photoelectron.

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 $2$.

If the wavelength of an electromagnetic radiation is $2000 \ \text{Å}$, what is its energy in ergs?

First and second excitation potentials of hydrogen atom (in $eV$) would be respectively