Q. An electron of mass $m$ with an initial velocity $\vec v=v_0\hat i\ (v_0>0)$ enters an electric field $\vec E=-E_0\hat k$. If the initial de Broglie wavelength is $\lambda_0$, the value after time $t$ would be
A) $\frac{\lambda_0}{\sqrt{1+\frac{e^2E_0^2t^2}{m^2v_0^2}}}$
B) $\lambda_0\sqrt{1+\frac{e^2E_0^2t^2}{m^2v_0^2}}$
C) $\frac{\lambda_0}{\sqrt{1-\frac{e^2E_0^2t^2}{m^2v_0^2}}}$
D) $\lambda_0$
Explanation
[Solution by Dr. Abubacker] The force on the electron is $eE_0$ along $z$, so $p_z=eE_0t$ while $p_x=mv_0$. $p=\sqrt{m^2v_0^2+e^2E_0^2t^2}$ and $\lambda=\frac hp=\frac{\lambda_0}{\sqrt{1+\frac{e^2E_0^2t^2}{m^2v_0^2}}}$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.