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  4. An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

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Q. An electron of mass m and magnitude of charge $|e|$ initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

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Solution:

$a = \frac{eE}{m}$
$v = u+at =\left(\frac{eE}{m}\right)t$
$\lambda = \frac{h}{mv}$
$\frac{d\lambda}{dt} = \frac{-\left(hm\right). \frac{dv}{dt}}{\left(mv\right)^{2}} = -\frac{ah}{mv^{2}} = -\frac{h}{\left|e\right|Et^{2}}$