An electron (mass $m$) with initial velocity $\vec{v} = v_0 \hat{i} + v_0 \hat{j}$ is in an electric field $\vec{E} = -E_0 \hat{k}$. If $\lambda_0$ is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time $t$ is given by: