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K₁ and K₂ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength ₁ and ₂ , respectively. If ₁=2 ₂ then the work function of material is given by:

Options

  1. AK₂+2K₁
  2. B2K₂-K₁
  3. CK₁-2K₂
  4. DK₂-2K₁

Correct answer

D. K₂-2K₁

Step-by-step solution

Using Einstein's photoelectric equation: K₁ = hc ₁ - K₂ = hc ₂ - Given ₁ = 2 ₂ , the first equation becomes: K₁ = hc 2 ₂ - Multiplying by 2 : 2K₁ = hc ₂ - 2 Substituting hc ₂ = K₂ + from the second equation: 2K₁ = (K₂ + ) - 2 2K₁ = K₂ - = K₂ - 2K₁ Answer: K₂-2K₁

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