An electron of mass m and magnitude of charge e at rest, gets accelerated by a constant electric field E .…

An electron of mass m and magnitude of charge e at rest, gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at a time t is (ignore relativistic effects)
  1. dλdt=-heEt
  2. dλdt=-2heEt
  3. dλdt=-2heEt2
  4. dλdt=-heEt2

Solution

The acceleration of the electron is

a=eEm

The velocity of the electron as a function of time is

v=at=eEmt

The de-Broglie wavelength is

λ=hmv

λ=hmeEmt

λ=heEt
dλdt=-heEt2

Asked in: JEE Main 2020 (09 Jan Shift 2)

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