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_0)/mt/v_0))`
B. `lamda_0(1+(eE_0t)/(mv_0))`
C. `lamda_0`
D. `lamda_0t`

Answer

A

Explanation

Initial de-Broglie wavelength of electron
`lamda_0=h/(mv_0) " "...(i)`
Force on electron in electric field,
`vecF=-evecE=-e[-E_0hati]=eE_0hati`
Acceleration of electron `a = (vecF)/(m) = (eE_0hati)/m`
Velocity of electron after time t ,
`vecv=v_0hati+((eE_0hati)/m)t=(v_0+(eE_0)/mt)hati`
`=v_0(1+(eE_0t)/(mv_0))hati`
de-Broglie wavelength associated with electron at time t is
`lamda=(h)/(mvecv)`
`impliesh/(m[v_0((1+eE_0)/(mv_0)t)])=(lamda_0)/([1+(eE_0)/(mv_0)t])[:. lamda_0=h/(mv_0)]`