An electron with mass ' $m$ ' with an initial velocity $(\mathrm{t}=0)…

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. $\frac{\lambda_0}{\sqrt{1-\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}$
  2. $\frac{\lambda_0}{\sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}$
  3. $\lambda_0 \sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}$
  4. $\lambda_0$

Solution

Magnetic field does not work
$\therefore$ Speed will not charge, so De-Broglie wavelength remains same.

Asked in: JEE Main 2025 (02 Apr Shift 2)

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