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 de-Broglie wavelength initially, then its de-Broglie wavelength at time $t$ is

Initial de-Broglie wavelength $\lambda_0 = \frac{h}{mV_0}$. The acceleration of the electron is $a = \frac{eE_0}{m}$. Velocity after time $t$ is $V = V_0 + \frac{eE_0}{m}t$. The new wavelength $\lambda = \frac{h}{mV} = \frac{h}{m(V_0 + \frac{eE_0}{m}t)} = \frac{h}{mV_0(1 + \frac{eE_0}{mV_0}t)} = \frac{\lambda_0}{1 + \frac{eE_0}{mV_0}t}$.