The correct answer is a) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$
The wave associated with moving particle is called matter wave or de-Broglie wave and it propagates in the form of wave packets with group velocity.
An electron (mass m ) with an initial velocity$ v=v_{0} \hat{i} \quad \text { is in an electric field } \quad E=-E_{0} \hat{i} $ It’s de Broglie wavelength at time t is given bya) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$ b) $\lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)$ c) $\Lambda_{0}$ d) $\lambda_{0} t$
An electron (mass m ) with an initial velocity$ v=v_{0} \hat{i} \quad \text { is in an electric field } \quad E=-E_{0} \hat{i} $ It’s de Broglie wavelength at time t is given bya) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$ b) $\lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)$ c) $\Lambda_{0}$ d) $\lambda_{0} t$