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Question

A metal plate is exposed to light of wavelength λ. It is observed that electrons are ejected from the surface of the plate. When a retarding uniform electric field E is imposed, no electron can move away from the plate farther than a certain distance d. Then the threshold wavelength λ0 for the material of plate is (e is the electronic charge, h is Plank’s constant and c is the speed of light)

A
λ0=(1λhceEd)1
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B
λ0=(1λeEDhc)1
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C
λ0=λhceEd
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D
λ0=λeEdhc
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Solution

The correct option is B λ0=(1λeEDhc)1
We know the photoelectric equation as
hcλhcλ0=K.Emax
hcλhcλ0=qEd
where
q=charge of an electronE=eleectric field set up d=distance travelled by the electron
1λ0=1λeEdhc
λ0=(1λeEdhc)1

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