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An electron (mass \( m \) ) with an initial velocity \( \mathbf{v}=v_{0} \hat{\mathbf{i}} \) is in an electric field \( \mathbf{E}=E_{0} \hat{\mathbf{j}} \). If \( \lambda_{0}=h / m v_{0} \), it's de Breoglie wavelength at
\( \mathrm{P} \) time \( t \) is given by

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(a) \( \lambda_{0} \)
(b) \( \lambda_{0} \sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}} \)
(c) \( \frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}} \)
(d) \( \frac{\lambda_{0}}{\left(1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}\right)} \)
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