An electron (mass $m$) with an initial velocity $\overrightarrow{v} = v_{0} \hat{i} \left(v_{0} > 0\right)$ is moving in an electric field $\overrightarrow{E} = -E_{0} \hat{i} \left(E_{0} > 0\right)$ where $E_{0}$ is constant. If at $t = 0$ the de Broglie wavelength is $\lambda_{0} = \frac{h}{mv_{0}}$,then its de Broglie wavelength after time $t$ is given by:

• A
  $\lambda_{0}$
• B
  $\lambda_{0} \left(1 + \frac{e E_{0} t}{mv_{0}}\right)$
• C
  $\lambda_{0} t$
• D
  $\frac{\lambda_{0}}{\left(1 + \frac{e E_{0} t}{mv_{0}}\right)}$