Bragg's Law & Uses of X-rays
Crystals as gratings; X-rays at work.
Lesson at a glanceShow the key points
- Strong reflection when 2d sin θ = nλ (44.3), θ from the planes.
- Used to measure X-ray wavelengths or crystal structure.
- X-rays: uncharged EM waves, penetrating, ionizing; radiographs, CT, therapy, flaw detection, security.
X-ray wavelengths are about the size of the gaps between atoms, so a crystal acts as a natural diffraction grating for them. That lets us measure X-ray wavelengths and map where atoms sit. And their penetrating power has made them indispensable in hospitals, airports and factories.
Crystals as gratings
A diffraction grating works when its slits are spaced a few times the wavelength. For X-rays (around 0.1 nm) no ruled grating is fine enough, but in 1912 Max von Laue realised that the regular rows of atoms in a crystal, about 0.1–0.5 nm apart, would do the job. W. H. Bragg and his son W. L. Bragg then found a very simple way to think about it.
Bragg’s law
Picture the atoms arranged in parallel planes a distance d apart. An X-ray beam meets the planes at a glancing angle θ (measured from the plane, not from the normal). Each plane reflects a little of the beam, like a mirror. The ray reflected from the next plane down travels an extra distance of 2d sin θ. When that extra path is a whole number of wavelengths, all the reflected waves are in step and add to a strong beam:
Used one way round, a crystal of known spacing measures X-ray wavelengths (an X-ray spectrometer, which is how Moseley measured his lines). Used the other way, X-rays of known wavelength reveal the spacings and arrangement of atoms in a crystal: X-ray crystallography, which later revealed the structure of DNA and of countless proteins.
Copper Kα X-rays (λ = 0.154 nm) fall on a rock-salt crystal whose planes are 0.282 nm apart. At what glancing angles are strong reflections seen?
Properties of X-rays
- They are electromagnetic waves, so they travel at the speed of light and are not deflected by electric or magnetic fields (they carry no charge).
- They pass through many materials opaque to light; how easily depends on thickness, density and the atomic number of the material.
- They blacken photographic film and make some substances fluoresce.
- They ionize the gas they pass through and can eject photoelectrons from metals.
- They damage living cells.
Uses
| Field | How X-rays are used |
|---|---|
| Medicine: diagnosis | Bones absorb far more than flesh, so a radiograph shows fractures, swallowed objects, and diseases of the lungs and teeth. CT scanners combine many X-ray images into 3D maps. |
| Medicine: therapy | Carefully aimed hard X-rays destroy cancer cells and some skin growths. |
| Industry | Radiography finds hidden cracks and bubbles in welds, castings and engine parts without cutting them open. |
| Security | Airport and customs scanners see guns, explosives and smuggled goods inside luggage. |
| Science | Crystallography maps atoms; X-ray spectra identify elements; X-ray telescopes study hot gas around black holes. |
| Art and history | X-rays reveal earlier paintings under a canvas and check whether gems or artworks are genuine. |
- 1Crystal planes spaced d apart reflect X-rays strongly only when 2d sin θ = nλ (θ measured from the planes).
- 2Bragg's law measures X-ray wavelengths (with a known crystal) or crystal structure (with known X-rays).
- 3X-rays: electromagnetic, uncharged, penetrating, ionizing, fogging film, causing fluorescence.
- 4Uses: radiographs, CT, cancer therapy, flaw detection, security scanning, crystallography; all with care, since they harm living tissue.
Check yourself
Keep exploring
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