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JEE Main 20209 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2020 · 9 January · Evening Shift · Physics · Dual Nature of Matter

An electron of mass m and magnitude of charge e at rest, gets...

An electron of mass mm and magnitude of charge ee at rest, gets accelerated by a constant electric field EE. The rate of change of de-Broglie wavelength of this electron at a time tt is (ignore relativistic effects)

Options

  1. Adλdt=−heEt\dfrac{d\lambda}{dt} = - \dfrac{h}{eEt}
  2. Bdλdt=−2heEt\dfrac{d\lambda}{dt} = - \dfrac{2h}{eEt}
  3. Cdλdt=−2heEt2\dfrac{d\lambda}{dt} = - \dfrac{2h}{eE{t}^{2}}
  4. Ddλdt=−heEt2\dfrac{d\lambda}{dt} = - \dfrac{h}{eE{t}^{2}}

Correct answer

D. dλdt=−heEt2\dfrac{d\lambda}{dt} = - \dfrac{h}{eE{t}^{2}}

Step-by-step solution

The acceleration of the electron is

a=eEma = \dfrac{eE}{m}

The velocity of the electron as a function of time is

v=at=eEmtv = at = \dfrac{eE}{m}t

The de-Broglie wavelength is

λ=hmv\lambda = \dfrac{h}{mv}

λ=hm(eEm)t\lambda = \dfrac{h}{m\left(\dfrac{eE}{m}\right)t}

λ=heEt\lambda = \dfrac{h}{eEt}
dλdt=−heEt2\dfrac{d\lambda}{dt} = - \dfrac{h}{eE{t}^{2}}

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