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An electron (mass m ) with initial velocity v → = v 0 i ^ + v 0 j ^ is in an electric filed E → = - E 0 k ^ . If λ 0 is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by:

Options

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

Correct answer

C. λ 0 1 + e 2 E 2 t 2 2 m 2 v 0 2

Step-by-step solution

Initial velocity of electron, v = v 0 i ^ + v 0 j ^ ⇒ u = v 0 2 + v 0 2 = v 0 2 Initial de Broglie wavelength associated with electron, λ 0 = h p = h m v 0 2 now, v = u + a t Velocity as a function of time = v 0 i ^ + v 0 j ^ + e E 0 m t k ^ so wavelength λ = h m 2 v 0 2 + e 2 E 0 2 m 2 t 2 λ = λ 0 1 + e 2 E 0 2 2 m 2 v 0 2 t 2

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