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Q.

An electron of mass m and magnitude of charge $|e|$ initially at rest 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:

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a

$- \frac{h}{|e| E \sqrt{t}}$

b

$- \frac{h}{|e| E t}$

c

$- \frac{|e| E t}{h}$

d

$\frac{- h}{|e| E t^{2}}$

answer is D.

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Detailed Solution

$\begin{array}{l} F o r c e o n e l e c t r o n = F = E q \\ \Rightarrow M a = E . e \\ \Rightarrow a = \frac{E e}{m} \\ U \sin g E q u a t i o n o f K i n e m a t i c s, \\ v = u + a t \\ \Rightarrow v = 0 + \frac{E e}{m} t \\ A l s o, d e B r o g l i e w a v e l e n g t h = λ = \frac{h}{m v} = \frac{h}{m . \frac{E e}{m} t} \\ \Rightarrow \frac{d λ}{d t} = \frac{- h}{E e t^{2}} [∵ \frac{d}{d t} (\frac{1}{t}) = \frac{- 1}{t^{2}}] \end{array}$

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An electron of mass m and magnitude of charge e initially at rest 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: