Question

# When monochromatic light of wavelength λ is incident on a metallic surface, the stopping potential for photoelectric current is 3V0. When same surface is illuminated with light of wavelength 2λ, the stopping potential is V0.The threshold wavelength for this surface when photoelectric effect takes place is

A
λ
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B
2λ
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C
3λ
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D
4λ
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Solution

## The correct option is D 4λKinetic energy of photoelectrons, K.E=hcλ−ϕ where work function, ϕ=hcλoAlso stopping potential (V) makes the photoelectrons to come to rest i.e K.E=eV⟹eV=hc(λo−λ)λoλ For incident wavelength =λ, stopping potential V=3Vo ∴ e(3Vo)=hc(λo−λ)λoλ ................(1)For incident wavelength =2λ, stopping potential V=Vo ∴ eVo=hc(λo−2λ)λo(2λ) ................(2)Dividing (2) from (1), we get 3=2(λo−λ)(λo−2λ)⟹λo=4λ

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