KVPY Sample Paper KVPY Stream-SX Model Paper-8

An electron of mass ?m? and charge ?e? initially at rest gets accelerated by a constant electric fields E. the rate of change of de-Broglie wavelength of this electron at time t, ignoring relativistic effects is:

A) \[\frac{-h}{eE{{t}^{2}}}\]

B) \[\frac{-eht}{E}\]

C) \[\frac{-mh}{eE{{t}^{2}}}\]

D) \[\frac{-h}{eE}\]

Correct Answer: A

Solution :

Acceleration, \[a=\frac{Ee}{m}\]

Velocity of electron, \[v=at\,=\frac{Eet}{m}\]

Wavelength,\[\lambda =\frac{h}{mv}=\frac{h}{Eet}\]

Now \[\frac{d\lambda }{dt}=-\frac{h}{eE{{t}^{2}}}\]