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COMEDK2023Morning ShiftPhysicsDual Nature of MatterActual

Let K₁ be the maximum kinetic energy of photoelectrons emitted by light of wavelength ₁ and K₂ corresponding to wavelength ₂ . If ₁=2 ₂ , then

Options

  1. AK₁=2 K₂
  2. BK₁ < K₂ / 2
  3. C2 K₁=K₂
  4. DK₁>2 K₂

Correct answer

B. K₁ < K₂ / 2

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy K of emitted photoelectrons is given by K = hc - , where is the work function of the metal. For wavelength ₁ , K₁ = hc ₁ - . For wavelength ₂ , K₂ = hc ₂ - . Given ₁ = 2 ₂ , we substitute ₁ in the expression for K₁ : K₁ = hc 2 ₂ - . Since > 0 , we have hc 2 ₂ - Also, K₂ = hc ₂ - , which implies hc ₂ = K₂ + . Substituting this into the expression for K₁ : K₁ = K₂ + 2 - = K₂ 2 - 2 . Since > 0 , it follows that K₁ Answer: K₁ < K₂ / 2

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