An electron of mass m with an initial velocity `vec(V) = V_(0)hat(i) (V_(0) gt 0)` enters an electric field `vec(E) = - E_(0)hat(i)` (`E_(0)` = constant `gt 0`) at t = 0. If `lamda_(0)` is its de Broglie wavelength initially, then its de Broglie wavelength at time t is

Options

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

Answer

C

Explanation

Initial de Broglie wavelength of the electron,
`lamda_(0) = (h)/(mV_(0))`
velocity of the electron after time t,
`V = u + at = V_(0) + (F)/(m) t = V_(0) + (eE_(0))/(m) t`
`= V_(0) [1 + (eE_(0))/(mV_(0))t]`
`:. lamda = (h)/(mV) = (h)/(mV_(0) [1 + (eE_(0))/(mV_(0)) t]) = (lamda_(0))/([1 + (eE_(0))/(mV_(0))t])`