Q.

A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and λ2 .  If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material is (h = Planck's constant, c = speed of light)

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a

2hcλ

b

hc3λ

c

hc2λ

d

hcλ

answer is C.

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Detailed Solution

Let ϕ0  be the work function of the surface of the material. Then, According to Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectrons in the first case isKmax1=hcλ-ϕ0and that in the second case isKmax2=hcλ2-ϕ0=2hcλ-ϕ0 But Kmax2=3Kmax1( given )∴  2hcλ-ϕ0=3hcλ-ϕ02hcλ-ϕ0=3hcλ-3ϕ03ϕ0-ϕ0=3hcλ-2hcλ2ϕ0=hcλ   or   ϕ0=hc2λ
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A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and λ2 .  If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material is (h = Planck's constant, c = speed of light)