An electron of mass $m$ with an initial velocity $\vec{V}=V_0\hat{i}$ ($V_0>0$) enters an electric field $\vec{E}=-E_0\hat{i}$ ($E_0=\text{constant}>0$) at $t=0$. If ${\lambda }_0$ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time $t$ is:

1. A
   ${\lambda }_{0}t$
2. B
   ${\lambda }_0\left(1+\frac{e{E}_{0}t}{m{V}_0}\right)$
3. C
   $\frac{{\lambda }_0}{\left(1+\frac{e{E}_{0}t}{m{V}_0}\right)}$
4. D
   ${\lambda }_0$