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Question

A photoelectric material having work-function ϕ0 is illuminated with light of wavelength λ (λ<hcϕ0). 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

A
λ3dλ2
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B
λ2dλ2
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C
λdλ
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D
λ3dλ
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Solution

The correct option is D λ3dλ2
According to photoelectric equation, hcλϕ=12mv2=p22m=h22mλ2d
hcλ2×Δλ=h2mλ3d×Δλd
ΔλdΔλλ3dλ2


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