A photoelectric material having work-function φ₀ is illuminated with light of wavelength λ (λ<hc/φ₀). The fastest photoelectron has a de Broglie wavelength λd. A change in wavelength of the incident light by Δλ results in a change Δλd in λd. Then the ratio Δλd/Δλ is proportional to
λdλ
λ²dλ²
λ³dλ²
λ³dλ
Solution:
The correct option is A λ³dλ² According to photoelectric equation,hc/λ - φ = 1/2mv² = p²/2m = h²/2mλd² Differentiating with respect to λ, -hc/λ²dλ = -h²/mλd³dλd Δλd/Δλ ∝ λ³dλ²