AI Tutor
If you shoot tiny steel BBs at a metal plate with two narrow slits, you get two distinct stripes on the wall behind it. But what happens when you fire electronsβ€”which everyone assumed were just tiny charged particlesβ€”through a microscopic lattice?
In 1924, Louis de Broglie proposed that any moving particle with momentum pp has an associated matter wave with wavelength Ξ»=hp\lambda = \frac{h}{p}.
To observe diffractionβ€”the bending and interference of waves around obstaclesβ€”the spacing between obstacles must be comparable to the wave's wavelength. For an electron accelerated by typical lab voltages, this wavelength is roughly 0.1Β toΒ 0.2Β nanometers0.1\text{ to }0.2\text{ nanometers}, which is precisely the spacing between atoms in a crystalline solid.
How could experimental physicists definitively prove that electrons actually produce these wave interference patterns in a laboratory?

The Davisson-Germer Experiment

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired a beam of electrons at a heated nickel crystal inside a vacuum tube and measured the intensity of scattered electrons at various angles.
Because the nickel was annealed into a regular crystalline array, the atomic surface rows acted as a diffraction grating with atomic spacing D=0.215Β nmD = 0.215\text{ nm}.
When the accelerating voltage was tuned to exactly V=54Β VV = 54\text{ V}, a prominent intensity spike appeared at a scattering angle of Ο•=50∘\phi = 50^\circ.
For a surface grating, constructive wave interference occurs when the path difference between adjacent scattered rays equals an integer number of wavelengths: nΞ»=Dsin⁑ϕn\lambda = D \sin\phi.
Let's calculate whether de Broglie's theoretical formula matches this experimental observation.

Testing the Theory