Question

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:

• A. $-\frac{h}{|e|E\sqrt{t}}$
• B. $\frac{|e|Et}{h}$
• C. $-\frac{h}{|e|Et}$
• D. $\frac{-h}{|e|E{t}^2}$

Answer 1

The correct option is D $\frac{-h}{|e|E{t}^2}$

Acceleration of electron in electric field is, $a=\frac{eE}{m}$

Using equation
$v=u+at$
$\Rightarrow v=0+\frac{eE}{m}t$
$\Rightarrow v=\frac{eEt}{m}....\left(i\right)$
de-Broglie wavelength $\lambda$ is given by
$\lambda =\frac{h}{mv}=\frac{h}{m\left(\frac{eEt}{m}\right)}\left[\text{using (i)}\right]$
$\Rightarrow \lambda =\frac{h}{eEt}$
Differentiating w.r.t. $t$
$\frac{d\lambda }{dt}=\frac{d}{dt}\left(\frac{h}{eEt}\right)=\frac{-h}{eE{t}^2}$

Hence, $\left(D\right)$ is the correct answer.