Q. An electron of mass m and 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

(a) $ – \frac{h}{e E t^2}$

(b) $ – \frac{e h t}{E}$

(c) $ – \frac{m h}{e E t^2}$

(d) $ – \frac{h}{e E}$

**Ans: a **

Sol: v = u + at

$\large v = 0 + \frac{eE}{m} t $

$\large v = \frac{e E t}{m} $

Wavelength , $\large \lambda = \frac{h}{m v} $

$\large \lambda = \frac{h}{m (\frac{e E t}{m} )} $

$\large \lambda = \frac{h}{e E t} $

Differentiating with respect to t

$\large \frac{d\lambda}{dt} = \frac{h}{e E}(-\frac{1}{t^2}) $

$\large \frac{d\lambda}{dt} = – \frac{h}{e E t^2} $