Nickela: Electrons Diffract 1927
Quantum Foundations arc, page 17 of 193. Back to The Pixelated Physics Universe
Who they are
Nickela raises her nickel-crystal shield, and a spray of electrons bounces off as a single bright beam at 50 degrees.
Nickela is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
At Bell Labs in 1927, Clinton Davisson and Lester Germer fired slow electrons at a single crystal of nickel and measured how many bounced off at each angle. At 54 eV they found a sharp peak at about 50°: a diffraction peak. Treating the surface rows of atoms, spaced 0.215 nm apart, as a grating gives a wavelength of 0.165 nm. De Broglie's formula at 54 eV gives 0.167 nm. Electrons behave as waves.
$$ \begin{gathered} d\sin\phi = \lambda, \quad d = 0.215\ \mathrm{nm} \ \Rightarrow\ \lambda = 0.165\ \mathrm{nm} \\ \lambda = \frac{h}{\sqrt{2mE}} = 0.167\ \mathrm{nm} \qquad (E = 54\ \mathrm{eV}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $d$ | spacing of the rows of atoms on the nickel surface | m |
| $\phi$ | angle of the diffraction peak (50°) | rad |
| $\lambda$ | electron wavelength | m |
| $h$ | Planck constant, 6.626 070 15 × 10⁻³⁴ J·s (exact) | J·s |
| $m$ | electron mass | kg |
| $E$ | electron kinetic energy | J |
Honest caveat: It was not the only proof: G. P. Thomson independently saw electron diffraction in 1927.
Sources
- Davisson & Germer (1927) Diffraction of Electrons by a Crystal of Nickel, Phys. Rev. 30, 705
- Davisson & Germer (1927) The Scattering of Electrons by a Single Crystal of Nickel, Nature 119, 558
Crossovers
Nickela meets Δ-X (Heisenberg Runner / Uncertainty Principle). Nickela fires electrons at her crystal and gets a sharp diffraction beam, because each electron has a definite de Broglie wavelength λ = h/p. Δ-X points out the cost: a momentum that sharp means the electron's position is spread across many atomic planes. That spread is exactly why the planes can act together as a grating.
Nickela meets Distalis (Fraunhofer Diffraction). Nickela's electrons and Distalis's far-field light obey the same rule: far from the scatterer, the pattern is set by the Fourier transform of the structure. Nickela's structure is a crystal lattice; Distalis's is an aperture.
Nickela meets Roentgenor (X Marks the Unknown). Roentgenor's X-rays were later shown to diffract from crystals. Nickela did the same with electrons in 1927, which confirmed that matter has waves too.
Wear the lore
- Nickela – Electrons Diffract 1927 Physics T-Shirt
- Related infographic poster: Bragg's Law: Salt Planes – Plate 056 Physics Poster
Concept keywords: Electrons Diffract 1927, Nickela, Quantum Foundations, physics lore, Pixelated Physics