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:
B
$$\dfrac {-h}{|e| Et^2}$$
D
$$-\dfrac {h}{|e| Et \sqrt t}$$
Correct option is A. $$\dfrac {-h}{|e| Et^2}$$
$$P=\dfrac{h}{\lambda_D}$$
$$\lambda_D=\dfrac{h}{p}=\dfrac{h}{mv}$$
$$\because \dfrac{v}{t}=a\Rightarrow v=at$$
$$v=at$$
$$\because F=qE$$
$$ma=qE$$
$$\boxed{a=\dfrac{qE}{m}=\dfrac{eE}{m}}$$
So, $$v=\dfrac{|e|E}{m}t$$
$$\therefore \lambda_D=\dfrac{h}{m\left(\dfrac{|e|E}{m}\right)t}=\dfrac{h}{|e|Et}$$
Rate of change of de-Broglie wavelength is given by differentiating the wavelength w.r.t. time.
$$\boxed{\dfrac{d\lambda_D}{dt}=-\dfrac{h}{|e|Et^2}}$$