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Question

# The kinetic energy of most energetic electrons emitted from a metallic surface is doubled when the wavelength of the incident radiation is changed from 400nm to 310nm the work-function of the metal is :

A
0.9eV
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B
1.7eV
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C
2.2eV
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D
3.1eV
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Solution

## The correct option is D 2.2eVGiven,λ1=400 nmand λ2=310 nmwhere (K.E)max for λ1=E1and (K.E)max for λ2=E2From given:E2=2E1Since from photo-electric effect,(K.E)max=Egnc−ϕ0where ϕ0= work-function of the metal surfaceHence From Given:- E1=hc400 nm−ϕ0−−−(1)E2=hc310 nm−ϕ0−−−(2)From (A) and (2)2E1=hc310 nm−ϕ0⇒ E1=hc620 nm−ϕ02−−−(3)From (1) and (3)E1=hc620 nm−ϕ02=hc400 nm−ϕ0⇒ hc620 nm−ϕ02=hc400 nm−ϕ0hc≡1240 eV−nmHence; 1240620−ϕ02=1240400−ϕ0⇒ 1240400−1240620=ϕ0−ϕ02⇒ 3.1−2 eV=ϕ02⇒ 1.1=ϕ02⇒ ϕ0=2.2 eV

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