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