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Question:

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