de-Brogile wavelength of electron,
$$
\lambda_0=\frac{\mathrm{h}}{\mathrm{mv}_0}
$$
Force on electron
$$
\Rightarrow \quad \mathrm{F}=-\mathrm{eE}=(-\mathrm{e})\left(-\mathrm{E}_0 \hat{\mathrm{i}}\right)=\mathrm{eE}_0 \hat{\mathrm{i}}
$$
Acceleration of electron
$$
\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}=\frac{\mathrm{eE}_0 \hat{\mathrm{i}}}{\mathrm{m}} \quad(\because \mathrm{F}=\mathrm{ma})
$$
Velocity of electron after time $t$, is $v=\left(v_0+\right.$ at $)$
$$
\begin{aligned}
&v=v_0 \hat{i}+\left(\frac{e E_0 \hat{i}}{m}\right) t=\left(v_0+\frac{e E_0}{m} t\right) \hat{i} \\
&v=v_0\left(1+\frac{e E_0}{m} t\right) \hat{i}
\end{aligned}
$$
Now for new de-Broglie wavelength associated with electron at time $t$ is
$$
\begin{aligned}
\lambda &=\frac{\mathrm{h}}{\mathrm{mv}} \\
\Rightarrow \lambda &=\frac{\mathrm{h}}{\mathrm{v}_0 \mathrm{~m}\left[\left(1+\frac{\mathrm{eE}_0 \mathrm{t}}{\mathrm{mv}_0}\right) \hat{\mathrm{i}}\right]}=\frac{\lambda_0}{\left[1+\frac{\mathrm{eE}_0}{\mathrm{mv}_0} \mathrm{t}\right]}
\end{aligned}
$$

$$
\left[\because \lambda_0=\frac{\mathrm{h}}{\mathrm{mv}_0}\right][\hat{\mathrm{i}}=1]
$$

$$
\lambda=\frac{\lambda_0}{\left[1+\left(\frac{e E_0}{\mathrm{mv}_0}\right) \mathrm{t}\right]}
$$