JEE PYQ: Atomic Physics Question 45
Question 45 - 2020 (09 Jan Shift 2)
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:
(1) $\frac{h}{|e|E\sqrt{t}}$
(2) $\frac{|e|Et}{h}$
(3) $\frac{h}{|e|Et}$
(4) $\frac{-h}{|e|Et^2}$
Show Answer
Answer: (4)
Solution
Acceleration of electron in electric field, $a = \frac{eE}{m}$. $v = 0 + \frac{eE}{m}t = \frac{eEt}{m}$. $\lambda = \frac{h}{mv} = \frac{h}{m \cdot \frac{eEt}{m}} = \frac{h}{eEt}$. Differentiating w.r.t. $t$: $\frac{d\lambda}{dt} = \frac{-h}{eEt^2}$.
BETA
