Question

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 $t,$ is (ignore the relativistic effects)

• A. $\frac{-h}{eE{t}^2}$
• B. $\frac{-eht}{E}$
• C. $\frac{mh}{eE{t}^2}$
• D. $\frac{h}{eE}$

Answer 1

The correct option is A $\frac{-h}{eE{t}^2}$

Acceleration due to the electric field $\left(E\right)$ is,

$a=\frac{eE}{m}$

Given, initially electron is at rest,

$v=u+at=\frac{eEt}{m}$

The de-broglie wavelength associated with the electron is,

$\lambda =\frac{h}{mv}=\frac{h}{eEt}$

Now, $\frac{d\lambda }{dt}=-\frac{h}{eE{t}^2}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.