The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by:

$A$ 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 : $h=6.63 \times 10^{-34} \ Js, m_{e}=9.0 \times 10^{-31} \ kg$]

In which transition is one quantum of energy emitted?

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is = ....... (Bohr radius $a_0$)

Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying $0.5\, V$ when the radiation of $250\, nm$ is used. The work function of the metal is ................ $eV$

The ratio of the maximum wavelengths of the Lyman and Balmer series is ....