Question

An electron of mass m and 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 ______.

Options

• ${\displaystyle \frac{-\text{h}}{{\text{eEt}}^2}}$

• ${\displaystyle \frac{-\text{eht}}{\text{E}}}$

• ${\displaystyle \frac{-\text{mh}}{{\text{eEt}}^2}}$

• ${\displaystyle \frac{-\text{h}}{\text{eE}}}$

Answer 1

An electron of mass m and 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 ${\displaystyle \underline{\frac{-\text{h}}{{\text{eEt}}^2}}}$.

Explanation:

Here, u = 0; a = ${\displaystyle \frac{\text{eE}}{\text{m}}}$; v = ?; t = t

∴ v = u + at = 0 + ${\displaystyle \frac{\text{eE}}{\text{m}}\text{t}}$

de-Broglie wavelength,

λ = ${\displaystyle \frac{\text{h}}{\text{mv}}=\frac{\text{h}}{\text{m}(\text{eEt}/\text{m})}=\frac{\text{h}}{\text{eEt}}}$

Rate of change of de-Broglie wavelength

${\displaystyle \frac{\text{d}\lambda }{\text{dt}}=\frac{\text{h}}{\text{eE}}(-\frac{1}{{\text{t}}^2})=-\frac{\text{h}}{{\text{eEt}}^2}}$