The approximate ratio of the speed of light in vacuum to that of an electron in the first Bohr orbit of hydrogen atom is (in $: 1$)

The potential energy of an electron present in $He^{+}$ is:

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is

$A$ 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 $m = 9.10939 \times 10^{-31} \, kg$).

The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?

The energy of the electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. The energy of the electron in the first orbit of hydrogen would be