Question

Why do electrons have wave properties?

Answer 1

Dual nature of electron:

Let us go through some key factors that lead us to the conclusion that electrons have a dual nature.

• Louis De Broglie, a French physicist, proposed in 1924 that if light contains an electron, it acts as both a material particle and a wave.
• This results in the development of a new wave mechanical theory of matter.
• When minuscule particles like electrons are in motion, they have wave qualities, according to this hypothesis.
• De-Broglie defined the wavelength associated with a moving electron of mass m and velocity v as $\mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{mv}}$, where, h is the Planck’s constant.
• It was also verified experimentally by Davisson and Germer experiment by observing diffraction by electron beam.
• In this experiment we accelerated an electron by a potential V, then the kinetic energy of electron is

$\Rightarrow \mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{\mathrm{p}}=\sqrt{\frac{\mathrm{h}}{2\mathrm{eVm}}}$

• De-Broglie application is applicable to all material objects but the significance is only in the case of microscopic particles. It has no significance in our daily life.
• Thus, this explains the dual nature of electron.