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 `lambda_(0)` is its de - Broglie wavelength initially, then its de - Broglie wavelength at time `t` is

Options

A. `lambda_(0)t`
B. `lambda_(0)`
C. `lambda(1+(eE_(0))/(mv_(0))t)`
D. `(lambda_(0))/((1+(eE_(0))/(mv_(0))t))`

Answer

D

Explanation

Initial de-Broglie wavelength, `lambda_(0)=h/(mv_(0))`,
Wavelength at time `t, lambda=h/(mv)`
where, `v=v_(0)+(eE_(0))/m t`
Now, `(lambda)/(lambda_(0))=(v_(0))/v=(v_(0))/(v_(0)(1+(eE_(0))/(mv_(0))t))`
or `lambda=(lambda_(0))/(1+(eE_(0))/(mv_(0))t)`