a
Here, \(\vec{E}=-E_{0} \hat{i} ;\) initial velocity \(\vec{v}=v_{0} \hat{i}\) Force action on electron due to electric field

\(\bar{F}=(-e)\left(-E_{0} \hat{i}\right)=e E_{0} \hat{i}\)

Acceleration produced in the electron, \(\vec{a}=\frac{\vec{F}}{m}=\frac{e E_{0}}{m} \hat{i}\)

Now, velocity of electron after time \(t\) 

\(\vec{v}_{t}=\vec{v}+\vec{a} t=\left(v_{0}+\frac{e E_{0} t}{m}\right) \hat{i}\)

or \(\left|\vec{v}_{t}\right|=v_{0}+\frac{e E_{0} t}{m}\)

Now, \(\lambda_{t}=\frac{h}{m v_{t}}=\frac{h}{m\left(v_{0}+\frac{e E_{0} t}{m}\right)}=\frac{h}{m v_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)}\)

\(=\frac{\lambda_{0}}{\left(1+\frac{e E_{0} t}{m v_{0}}\right)} \quad \quad \quad\left(\because \lambda_{0}=\frac{h}{m v_{0}}\right)\)