JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Modern Physics

An electron of mass

m

and magnitude of charge

∣ e ∣

initially at rest gets accelerated by a constant electric field E . The rate of change of de-Broglie wavelength of this electron at time

t

ignoring relativistic effects is

(A) $\frac{∣ e ∣ E t}{h}$
(B) $- \frac{h}{∣ e ∣ Et}$
(C) $- \frac{h}{∣ e ∣ E t}$
(D) $- \frac{h}{e ∣ Et ^{2}}$ ✓ Correct

Answer: (D)

Solution

The de Broglie wavelength is

λ = \frac{h}{m v}

. Starting from rest in a constant field, the electron's speed grows as

v = a t = \frac{∣ e ∣ E}{m} t

, so

λ = \frac{h}{m} \cdot \frac{m}{∣ e ∣ E t} = \frac{h}{∣ e ∣ E t}

. Differentiating with respect to time gives

\frac{d λ}{d t} = - \frac{h}{∣ e ∣ E t ^{2}}

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option

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