An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$-\sigma$'. The rate of change of de-Broglie wavelength associated with the electron varies inversely as $\mathrm{n}^{\text{th}}$ power of time. The numerical value of $n$ is ______.

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Modern Physics

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '

- σ

'. The rate of change of de-Broglie wavelength associated with the electron varies inversely as

n^{th}

power of time. The numerical value of

n

is ______.

Answer: 2

Solution

The uniform sheet gives a constant field

E = \frac{σ}{2 ε _{0}}

and hence a constant acceleration

a = \frac{e E}{m}

, so starting from rest the speed is

v = a t

. The de-Broglie wavelength is

λ = \frac{h}{m v} = \frac{h}{ma t}

, and its time derivative

\frac{d λ}{d t} = - \frac{h}{ma t ^{2}}

varies as

\frac{1}{t ^{2}}

. The value of

n

2

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Integer answer

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