Q. An electron of mass m with an initial velocity $\vec{V} = V_0\hat{i}$ ($V_0 > 0$) enters an electric field $\vec{E} = -E_0\hat{i}$ ($E_0$ = constant > 0) at t = 0. If $\lambda_0$ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is
A) $\lambda_0 t$
B) $\lambda_0\left(1 + \frac{eE_0}{mV_0}t\right)$
C) $\frac{\lambda_0}{\left(1 + \frac{eE_0}{mV_0}t\right)}$
D) $\lambda_0$
Explanation
[Solution] Force on the electron is $+eE_0\hat{i}$, so $v = V_0 + \frac{eE_0}{m}t$ and $\lambda = \frac{h}{mv} = \frac{\lambda_0}{1 + \frac{eE_0}{mV_0}t}$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.