If light of wavelength λ1 is allowed to fall on a metal, then kinetic energy of photoelectrons emitted is K1. If wavelength of light changes to λ2, then kinetic energy of electron changes to K2. Then, work function of the metal is
A
K1K2(λ1−λ2)λ1λ2
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B
K1λ1−K2λ2(λ1−λ2)
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C
K1λ1−K2λ2(λ2−λ1)
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D
λ1λ2K1K2(λ2−λ1)
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Solution
The correct option is CK1λ1−K2λ2(λ2−λ1) We know the equation for kinetic energy in photoelectric effect as hcλ=K+ϕ
where K is the kinetic energy of the electron coming out, ϕ is the work function of the material and λ is the wavelength of the photon.
Now for first case hcλ1=K1+ϕ .....(i) hcλ2=K2+ϕ .....(ii)
eq(i)/eq(ii) λ2λ1=K1+ϕK2+ϕ λ2K2+λ2ϕ=λ1K1+λ1ϕ
On rearranging ϕ=K1λ1−K2λ2λ2−λ1