Dual Nature of Matter

JEE Main level, single correct, medium

65 of 200

Question 65 of 200

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)

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Answer: (D) dλdt=−heEt2\dfrac{d\lambda }{dt}=-\dfrac{h}{eE{t}^{2}}

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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