If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ , then for 1.5 p momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

Step-by-step solution

h ν - ϕ = K E h c λ i n c i d e n t = K E + ϕ Given ϕ < < K E h c λ i n c i d e n t ≈ K E h c λ i n c i d e n t = p 2 2 m ......(i) h c λ ' = 1.5 p 2 2 m …….(ii) Divide (i) and (ii) λ ' λ = p 2 2.25 p 2 λ ' = λ × 100 2.25 = 4 9 λ ' = 4 9 λ