An electron with mass $m$ and an initial velocity $(t=0)$ $\vec{v} = v_0 \hat{i}$ $(v_0 > 0)$ enters a magnetic field $\vec{B} = B_0 \hat{j}$. If the initial de Broglie wavelength at $t=0$ is $\lambda_0$,then its value after time $t$ would be:

• A
  $\frac{\lambda_0}{\sqrt{1-\frac{e^2 B_0^2 t^2}{m^2}}}$
• B
  $\frac{\lambda_0}{\sqrt{1+\frac{e^2 B_0^2 t^2}{m^2}}}$
• C
  $\lambda_0 \sqrt{1+\frac{e^2 B_0^2 t^2}{m^2}}$
• D
  $\lambda_0$