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 :

Engineering

Physics

de Broglie Hypothesis and Dual Nature

Question

$- \frac{h}{| e | Et}$

$- \frac{h}{| e | {Et}^{2}}$

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

$\frac{| e | Et}{h}$

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$λ_{D} = \frac{h}{mv}$

$∴$ v = at

$v = \frac{eE}{m} t (a = \frac{eE}{m})$

$λ_{D} = \frac{h}{m (\frac{eE}{m}) t}$

$λ_{D} = \frac{h}{eEt}$

$\frac{{dλ}_{D}}{dt} = \frac{h}{| e | {Et}^{2}}$