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) $\frac{- h}{eEt^{2}}$
B) $\frac{- e\ Et}{E}$
C) $\frac{- mh}{e\ Et^{2}}$
D) $\frac{- h}{e\ E}$
Explanation
(a) Here, $u = 0;a = \frac{eE}{m};v = ?;t = t$
$\therefore\ \ v = u + at = 0 + \frac{eE}{m}t$
de-Broglie wavelength,
$\lambda = \frac{h}{mv} = \frac{h}{m(eEt/m)} = \frac{h}{eEt}$
Rate of change of de-Broglie wavelength
$\frac{d\lambda}{dt} = \frac{h}{eE}\left( - \frac{1}{t^{2}} \right) = \frac{- h}{eEt^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.