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:

λd/λ
λ/λd
λ²/λd²
λd²/λ²

Correct answer: λd²/λ²

Solution

The ratio Δλd/Δλ is related to the de Broglie wavelength λd and the incident light wavelength λ, and can be derived from the equations governing the photoelectric effect and the de Broglie wavelength of the electron.

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