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. `(lamda_(0))/((1+(eE_(o))/(m)(t)/(v_(0))))`
B. `lamda_(0)(1+(eE_(0)t)/(mv_(0)))`
C. `lamda_(0)`
D. `lamda_(0)t`

Explanation

Initial de-Broglie wavelength of electron,
`" "lamda_(0)=(h)/(mv_(0))`
Force on electron in electric field, `" "F=-eE=-e[-E_(0)hati]=eE_(0)hati`
Acceleration of electron `" "a=F/m=(eE_(0)hati)/(m)`
Vfelocity of electron after time t,
`" "v=v_(0)hati+((eE_(0)hati)/(m))t=(v_(0)+(eE_(0))/(m)t)hati`
`" "v_(0)(1+(eE_(0))/(mv_(0)))hati`
de-Broglie wavelength associated with electron at time t is
`" "lamda =(h)/(mv)`
`implies" "=(h)/(m[v_(0)(1+(eE_(0))/(mv_(0))t)])=(lamda_(0))/([1+(eE_(0))/(mv_(0))])" "[thereforelamda_(0)=(h)/(mv_(0))]`