An electron (mass m) with an initial velocity `v=v_(0)hat(i)(v_(0)gt0)` is in an electric field `E=-E_(0)hat(l)(E_(0)="constant"gt0)`. Its de-Broglie wavelength at time t is given by

Options

A. `lambda_(0)t`
B. `lambda_(0)(1 + (eE_(0))/(mVf_(0)t))`
C. `(lambda_(0))/((1 + (eE_(0))/(mV_(0))t))`
D. `lambda_(0)`

Answer

C

Explanation

`rarr v_(0)hat(i)`
`underset(v_(0) i)larr`
`rArr v = v_(0) + (e E_(0))/(m)t`
`rArr lambda = (h)/(m(v_(0) + (e E_(0))/(m)t)) = (h)/((mv_(0) + e E_(0) t)) = (lambda_(0))/((l+(e E_(2))/(m v_(0))t))`