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

$(i)$ Energy $(E)$ of a photon $= \frac{hc}{\lambda}$
$E = \frac{(6.626 \times 10^{-34} \, Js)(3 \times 10^{8} \, ms^{-1})}{4 \times 10^{-7} \, m} = 4.9695 \times 10^{-19} \, J$
Converting to $eV$: $E = \frac{4.9695 \times 10^{-19} \, J}{1.6020 \times 10^{-19} \, J/eV} = 3.1020 \, eV$
$(ii)$ Kinetic energy $(E_k) = E - \Phi = 3.1020 \, eV - 2.13 \, eV = 0.9720 \, eV$
$(iii)$ Velocity $(v)$ is given by $E_k = \frac{1}{2}mv^2$
$v = \sqrt{\frac{2E_k}{m}} = \sqrt{\frac{2 \times 0.9720 \times 1.6020 \times 10^{-19} \, J}{9.10939 \times 10^{-31} \, kg}}$
$v = \sqrt{0.3418 \times 10^{12} \, m^2s^{-2}} = 5.846 \times 10^{5} \, ms^{-1}$