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:
Answer & explanation
Correct answer: option 1
Here, u = 0, $a=\frac{eE}{m}$
$∴ v=u+at=0+\frac{eE}{m}t$
de – Broglie wavelength, $λ=\frac{h}{mv}=\frac{h}{m(eEt/m)}=\frac{h}{eEt}$
Rate of change of de-Broglie wavelength $\frac{dλ}{dt}=\frac{h}{eE}(-\frac{1}{t^2})=\frac{-h}{rEt^2}$