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The surface of certain metal is first illuminated with light of wavelength λ 1 = 350 n m and then, by a light of wavelength λ 2 = 540 n m . It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of 2 . The work function of the metal (in e V ) is close to (Energy of photon = 1240 λ i n n m e V )

Options

  1. A2.5
  2. B1.8
  3. C5.6
  4. D1.4

Correct answer

B. 1.8

Step-by-step solution

λ 1 = 350 n m , λ 2 = 540 n m , V 1 V 2 = 2 ⇒ V 1 = 2 V a n d V 2 = V h c λ 1 = ϕ + 1 2 m 2 V 2 h c λ 2 = ϕ + 1 2 m V 2 h c λ 1 - 4 h c λ 2 = ϕ - 4 ϕ h c 4 540 - 1 340 = 3 ϕ ϕ = 1.8 e V

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