An electron (mass m ) with an initial velocity v → = v 0 i ^ v 0 > 0 is moving in an electric…

Initial de-Broglie wavelength of electron,

${\lambda }_0=\frac{h}{m{v}_0}$ ....(i)

Force on electron in electric field,

$\mathrm{F}=-e\mathrm{E}=-e\left[-E_0\hat{\mathrm{i}}\right]=e{E}_0\hat{\mathrm{i}}$

Acceleration of electron, $a=\frac{\mathrm{F}}{m}=\frac{e{E}_0\hat{\mathrm{i}}}{m}$
Velocity of electron after time $t$,

$v=v_0\hat{\mathrm{i}}+\left(\frac{e{E}_0\hat{\mathrm{i}}}{m}\right)t=\left(v_0+\frac{e{E}_0}{m}t\right)\hat{\mathrm{i}}=v_0\left(1+\frac{e{E}_0}{m{v}_0}t\right)\hat{\mathrm{i}}$

de-Broglie wavelength associated with electron at time $t$ is

$\lambda =\frac{h}{mv}$

$\Rightarrow \lambda =\frac{h}{m\left[v_0\left(1+\frac{e{E}_0}{m{v}_0}t\right)\right]}=\frac{{\lambda }_0}{\left[1+\frac{e{E}_0}{m{v}_0}t\right]}$