Q 12-11-184JEE MainJEE Main 2025 (8 Apr, Shift 2)Hard
An electron is released from rest near an infinite non-conducting sheet of uniform charge density $-\sigma$. The rate of change of the de Broglie wavelength associated with the electron varies inversely as the $n^{\text{th}}$ power of time. The numerical value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 2
The sheet's field $\dfrac{\sigma}{2\varepsilon_0}$ is uniform, so the electron (repelled by the negative sheet) has constant acceleration $a = \dfrac{e\sigma}{2m\varepsilon_0}$, and starting from rest, $p = mat$.
$$\lambda = \frac hp = \frac{h}{mat} \Rightarrow \frac{d\lambda}{dt} = -\frac{h}{ma}\cdot\frac1{t^2}$$
So $\left|\dfrac{d\lambda}{dt}\right| \propto \dfrac1{t^2}$ and $n = 2$.
Solution by Sreeraj P, M.Sc Physics