An electron with mass ' \(m\) ' with an initial velocity \((\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}} \quad\left(\mathrm{v}_0 \gt 0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{j}\). If the initial de-Broglie wavelength at \(\mathrm{t}=0\) is \(\lambda_0\) then its value after time ' t ' would be :

1. A \(\frac{\lambda_0}{\sqrt{1-\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}\)
2. B \(\frac{\lambda_0}{\sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}\)
3. C \(\lambda_0 \sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}\)
4. D \(\lambda_0\)