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Question

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(λ1λ2)λ1λ2
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B
K1λ1K2λ2(λ1λ2)
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C
K1λ1K2λ2(λ2λ1)
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D
λ1λ2K1K2(λ2λ1)
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Solution

The correct option is C K1λ1K2λ2(λ2λ1)
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=K1λ1K2λ2λ2λ1

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