What is the work function of the metal if the light of wavelength 4000 A o generates photoelectrons of velocity 6 × 10 5   ms - 1 from it? (Mass of electron = 9 × 10 - 31 kg , velocity of light = 3 × 10 8 ms - 1 , Planck's constant = 6 .626 × 10 - 34 Js , Charge of electron = 6 .626 × 10 - 34 Js )

Step-by-step solution

hc λ = hc λ 0 + 1 2 mv 2 hc λ 0 = hc λ - 1 2 mv 2 = 6.626 × 10 - 34 × 3 × 10 8 4000 × 10 - 10 - 1 2 9.1 × 10 - 31 × 6 × 10 5 2 = 6.626 × 3 × 10 - 19 4 - 9.1 × 6 × 6 2 × 10 - 21 = 4.97 × 10 - 19 - 1.64 × 10 - 19 = 3.33 × 10 - 19 Joule Work function hc λ 0 = 3 .33 × 10 - 19 1 .6 × 10 - 19 = 2 .08 ≈ 2 .1   eV