Question

An electron of mass $m$ and magnitude of charge $e$ at rest, gets accelerated by a constant electric field $E$ . The rate of change of de-Broglie wavelength of this electron at a time $t$ is (ignore relativistic effects)

• A. $\frac{d \lambda }{d t}=-\frac{h}{e E t}$
• B. $\frac{d \lambda }{d t}=-\frac{2 h}{e E t}$
• C. $\frac{d \lambda }{d t}=-\frac{2 h}{e E t^{2}}$
• D. $\frac{d \lambda }{d t}=-\frac{h}{e E t^{2}}$

Answer 1

Answer: (D)

The acceleration of the electron is
$a=\frac{e E}{m}$
The velocity of the electron as a function of time is
$v=at=\frac{e E}{m}t$
The de-Broglie wavelength is
$\lambda =\frac{h}{m v}$
$\lambda =\frac{h}{m \left(\frac{e E}{m}\right) t}$
$\lambda =\frac{h}{e E t}$
$\frac{d \lambda }{d t}=-\frac{h}{e E t^{2}}$