On this page
By 1912 physicists had two open questions. Were X-rays waves or particles? And were crystals really built from atoms in a regular three-dimensional grid? Max von Laue saw that one experiment could answer both. This post tells the story in his own words from his Nobel lecture, estimates the numbers that made him confident, and works through the diffraction condition for a row of atoms.
Who was Max von Laue?
The Nobel Prize facts page gives his birth on 9 October 1879 at Pfaffendorf, Germany, and his death in Berlin in April 1960. He received the unshared 1914 Nobel Prize in Physics "for his discovery of the diffraction of X-rays by crystals". His Nobel biography records that he studied under Max Planck in Berlin, took his doctorate in 1903 on interference in plane-parallel plates, and in 1909 began lecturing in Munich on optics, thermodynamics and relativity.
The biography adds two things worth knowing. He wrote eight papers on Einstein's relativity between 1907 and 1911. And under the Nazi government, when Einstein resigned from the Berlin Academy and its vice-president said this was no loss, Laue was the only member who protested.
Where did the idea come from?
In his Nobel lecture, Laue describes an evening in February 1912 when the young physicist Paul Ewald visited him for advice on his thesis about long light waves in a crystal lattice. Laue could not help with that, but the conversation raised another question: what happens to waves that are short compared with the lattice spacing? His "intuition for optics", he wrote, gave the answer at once: lattice spectra would have to appear.
He had two numbers. The spacing of atoms in a crystal was known to be of the order of 10⁻⁸ cm, from the density, the molecular weight and the mass of the hydrogen atom. Wilhelm Wien and Arnold Sommerfeld had estimated X-ray wavelengths at about 10⁻⁹ cm. The ratio was, in Laue's words, "extremely favourable".
How was the idea tested?
The lecture says that the leading physicists he consulted had doubts, and "a certain amount of diplomacy" was needed before Walter Friedrich and Paul Knipping could run the experiment. Their first crystal was copper sulphate, because large regular pieces were easy to get. The photographic plate behind it showed many deflected rays around the direct beam: the lattice spectra Laue had predicted.
On 8 June 1912 Sommerfeld presented the joint work of Friedrich, Knipping and Laue to the Munich Academy. It was published as Interferenzerscheinungen bei Röntgenstrahlen (Interference phenomena with X-rays) in Annalen der Physik. The biography sums up the result: it established that X-rays are electromagnetic in nature and opened the way to the work of the Braggs.
Worked example 1: is a crystal a good grating for X-rays?
Laue estimated the spacing from the density. Try it for rock salt. PubChem lists the density of sodium chloride as 2.17 g/cm³, and its molar mass is 58.44 g/mol.
Volume per NaCl unit. 58.44 / (2.17 × 6.022 × 10²³) = 4.47 × 10⁻²³ cm³.
Volume per ion. Each unit has two ions: 2.24 × 10⁻²³ cm³.
Spacing. Take the cube root: about 2.8 × 10⁻⁸ cm, or 0.28 nm.
That is Laue's order of 10⁻⁸ cm. Compare wavelengths with this spacing a = 0.28 nm:
Visible light, 500 nm: λ/a ≈ 1800. Far too long to diffract.
X-rays, 0.10 nm: λ/a ≈ 0.36. Ideal for diffraction.
Worked example 2: diffraction by a row of atoms
Treat one row of atoms with spacing a as a grating. For a beam hitting the row at right angles, waves from neighbouring atoms reinforce when a sin θ = hλ, where θ is the angle from the beam and h is a whole number.
With a = 0.282 nm and λ = 0.10 nm:
h = 1. sin θ = 0.10/0.282 = 0.355, so θ ≈ 20.8°.
h = 2. sin θ = 0.709, so θ ≈ 45.2°.
h = 3. sin θ = 1.06, which is impossible, so there is no third order.
For visible light at 500 nm, sin θ would be about 1800 for h = 1, so only the straight-through beam exists. That is why crystals had never shown diffraction with ordinary light.
A real crystal has three such rows in different directions, and all three conditions must hold at once. Laue's lecture explains that each spot corresponds to three whole numbers. That is a strict requirement, and it explains why only certain spots appear. The story of Lawrence Bragg shows how Bragg turned the same physics into reflection from planes.
Common mistakes with crystal diffraction
Using visible-light intuition. A grating works only when λ is comparable with, or smaller than, the spacing.
Forgetting the order limit. If hλ/a exceeds 1, that order does not exist.
Mixing units. Keep a and λ both in nanometres.
Treating one row as the whole crystal. Three conditions, one per direction, must be met together.
The JEE (Advanced) 2026 syllabus lists Young's double slit, single-slit diffraction and X-rays, so the path-difference reasoning carries over. Check the current year's brochure. If wavefronts and path differences are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What can a student take from how Laue worked?
Estimate before you experiment. Two orders of magnitude told him the idea could work.
Borrow from another field. He applied what he knew about optical gratings to X-rays.
Work with experimenters. Laue supplied the idea and the theory; Friedrich and Knipping made it real.
Be honest about uncertainty. His lecture says he trusted the ratios of his three numbers more than his first wavelength values.
Practice routine: estimate the ion spacing in potassium chloride from a density and molar mass you look up, find the diffraction angles for λ = 0.15 nm on a row with a = 0.30 nm, and explain why h = 0 always exists.
Next step: write the ratio λ/a for visible light and for X-rays on one line, and explain in a sentence what it tells you.
