Question

Write de Broglie hypothesis. Obtain the formula for de Broglie wavelength of an electron which is accelerated from rest through a potential $V$ volt.

Answer 1

The de Broglie wavelength is the wavelength, $\lambda$, associated with a massive particle and is related to its momentum, $p$, through the Planck constant, h: $\lambda =\frac{h}{p}$

For an electron accelerated by potential V,

$qV=\frac{p^2}{2m}$

$⟹p=\sqrt{2mqV}$

Hence $\lambda =\frac{h}{\sqrt{2mqV}}$