
Initial de-Broglie wavelength of electron,
λ0=mv0h ....(i)
Force on electron in electric field,
F=−eE=−e[−E0i^]=eE0i^
Acceleration of electron, a=mF=meE0i^
Velocity of electron after time t,
v=v0i^+(meE0i^)t=(v0+meE0t)i^=v0(1+mv0eE0t)i^
de-Broglie wavelength associated with electron at time t is
λ=mvh
⇒λ=m[v0(1+mv0eE0t)]h=[1+mv0eE0t]λ0