A photon of wavelength 4 × 10-7 m strikes on metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron (1 eV= 1.6020 × 10-19 J).

A photon of wavelength 4 × 10^-7 m strikes on metal surface, the work function of the   metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy  of the emission, and (iii) the velocity of the photoelectron (1 eV= 1.6020 × 10^-19 J).
Answer
(i) Energy (E) of a photon = hν

Where,
h = Planck’s constant = 6.626 × 10^-34 Js
c = velocity of light in vacuum = 3 × 10⁸ m/s
λ = wavelength of photon = 4 × 10^-7 m
Substituting the values in the given expression of E:

Hence, the energy of the photon is 4.97 × 10^-19 J.
(ii) The kinetic energy of emission E_k is given by

= (3.1020 - 2.13) eV
= 0.9720 eV
Hence, the kinetic energy of emission is 0.97 eV.
(iii) The velocity of a photoelectron (ν) can be calculated by the expression,
the kinetic energy of emission in Joules and ‘m’ is the mass of the
photoelectron. Substituting the values in the given expression of v: