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An electron (mass m ) with an initial velocity v → = v 0 i ^ v 0 > 0 is moving in an electric field E → = - E 0 i ^ E 0 > 0 where E 0 is constant. If at t = 0 , de-Broglie wavelength is λ 0 = h m v 0 , then its de-Broglie wavelength after time t is given by

Options

  1. Aλ 0
  2. Bλ 0 1 + e E 0 t m v 0
  3. Cλ 0 t
  4. Dλ 0 1 + e E 0 t m v 0

Correct answer

D. λ 0 1 + e E 0 t m v 0

Step-by-step solution

Initial de-Broglie wavelength of electron, λ 0 = h m v 0 ....(i) Force on electron in electric field, F = - e E = - e - E 0 i ^ = e E 0 i ^ Acceleration of electron, a = F m = e E 0 i ^ m Velocity of electron after time t , v = v 0 i ^ + e E 0 i ^ m t = v 0 + e E 0 m t i ^ = v 0 1 + e E 0 m v 0 t i ^ de-Broglie wavelength associated with electron at time t is λ = h m v ⇒ λ = h m v 0 1 + e E 0 m v 0 t = λ 0 1 + e E 0 m v 0 t

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