Q 12-11-181JEE MainJEE Main 2025 (2 Apr, Shift 2)Easy
An electron with mass $m$ with 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:
Answer: (D) $\lambda_0$
The magnetic force $q\vec v\times\vec B$ is always perpendicular to the velocity, so it does no work. The speed, and hence the magnitude of momentum, stays constant.
Since $\lambda = h/p$, the de Broglie wavelength stays $\lambda_0$.
Solution by Sreeraj P, M.Sc Physics