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JEE Advanced2017PhysicsDual Nature of MatterActual

A photoelectric material having work-function ϕ 0 is illuminated with a light of wavelength λ λ < h c ϕ 0 . The fastest photoelectron has a de Broglie wavelength λ d . A change in wavelength of the incident light by Δ λ results in a change Δ λ d in λ d . The ratio Δ λ d Δ λ is proportional to

Options

  1. Aλ d 3 λ 2
  2. Bλ d 3 λ
  3. Cλ d 2 λ 2
  4. Dλ d λ

Correct answer

A. λ d 3 λ 2

Step-by-step solution

According to the equation of photoelectric effect, K E m a x = h c &#955; - &#160; &#981; 0 Kinetic energy in terms of momentum is given as K E = p 2 2 m p 2 2 m = h c &#955; - &#981; 0 h &#955; d 2 2 m = h c &#955; - &#981; 0 Assuming small changes, differentiating both sides, h 2 2 m - 2 d &#955; d &#955; d 3 = &#160; - h c &#955; 2 &#160; d &#955; d &#955; d d &#955; &#160; &#8733; &#955; d 3 &#955; 2

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