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

Options

A. `(-h)/(eEt^2)`
B. `(-eht)/(E )`
C. `(-mh)/(eEt^2)`
D. `(-h)/(eE)`

Answer

A

Explanation

Here `u = 0 , a = (eE)/(m), v = ? , t= ? `
`therefore v = u + at = 0 + (eE)/(m) t`
de-broglie wavelength `lamda = (h)/(mv) = (h)/(m(eEt//m)) = (h)/(eEt)`
Rate of change of de-broglie wavelength
`(dlamda)/(dt) = (h)/(eE) = (- (1)/(t^2) ) = (-h)/(eEt^2)`