# 17.5.3 De Broglie Wavelength

In 1924 Prince Louis de Broglie advanced (in his one-page doctoral thesis) a ludicrous hypothesis. He was convinced that the wave-particle paradox should not be confined to photons only. Instead, the chaos should be extended to all particles, including electrons and protons.

If light, which we assumed to be waves, can behave like particles with momentum $\displaystyle p=\frac{h}{\lambda }$ in some situations, then it is only fair that electrons, which we assume to be particles, should behave in some situations like waves with wavelength

$\displaystyle \lambda =\frac{h}{p}$

In 1927, G P Thomson designed an experiment to verify this claim. He knew of experiments where diffraction patterns are formed by shining x-ray through very thin gold foils[1]. He figured that he only had to replace the x-ray with a beam of mono-energetic electrons. He chose electrons with KE of 25 keV, which according to de Broglie’s formula, should behave like a wave of wavelength $\displaystyle 7.7\times {{10}^{{-12}}}\text{ m}$. This is to match the wavelength of the x-rays normally used in such experiments.

As it turned out, concentric rings were formed on the photographic plate! It is the exact same interference pattern (including the positions of the rings) as what would have been produced if x-ray of $\displaystyle 7.7\times {{10}^{{-12}}}\text{ m}$ were used instead of the electron beam. The diffraction of electrons served as the first evidence of the wave nature of electrons[1].

Demonstration

Electron Diffraction

Concept Test

3454

Comics

De Broglie’s Car Chase

[1] Davisson and Germer performed another experiment in which the diffraction pattern is formed by reflecting a low power electron beam on nickel crystal. They won the Nobel prize together with Thompson.

[1] The regular arrangement of the atoms of the gold crystal act as a natural three-dimensional diffraction grating.