The Reflection of X-rays by Crystals
One whole-number rule, 2d sinθ = nλ, turns a crystal's X-ray reflections into the positions of its atoms.
Bounce X-rays off a crystal and, at just a few sharp angles, they flash back bright — and those angles tell you exactly how far apart the atoms are stacked.
The big idea
A crystal is atoms arranged in perfectly regular, repeating layers. Shine X-rays on it — light whose waves are about the size of an atom — and each layer acts like a faint mirror, reflecting a little of the beam. Most of the time the reflections from the many layers fall out of step and cancel, and almost nothing comes back. But at certain special angles every little reflection lines up in step and adds together into one bright beam.
Lawrence Bragg found the rule for those angles, and it is beautifully simple: twice the spacing between layers, times the sine of the angle, equals a whole number of wavelengths. Turn it around and the angle you measure hands you the spacing of the atoms. A measurement you can make from outside the crystal becomes a ruler for the inside.
How it came about
In 1912 Max von Laue showed that crystals scatter X-rays into a pattern of spots — proof in one stroke that X-rays are waves and that crystals are orderly atomic lattices. The pattern was striking but hard to read. A 22-year-old Cambridge student, William Lawrence Bragg, found a far simpler way to see it: picture the crystal as stacks of mirror-like layers.
His father, William Henry Bragg, a physics professor at Leeds, built the instrument to put the idea to work — an X-ray spectrometer that measured each reflection precisely. Father and son began reading crystal after crystal. In 1915 they shared the Nobel Prize in Physics; Lawrence, at 25, is still the youngest person ever to win it — though the shared honour partly hid how much of the key idea had been the son's.
Why it mattered
For the first time, people could find out where atoms actually sit. The Braggs showed that ordinary table salt contains no salt 'molecules' at all — just sodium and chlorine ions alternating in a grid — and mapped diamond, quartz and dozens of minerals. The technique they founded, X-ray crystallography, went on to reveal the structures of DNA, proteins, vitamins and medicines. Almost everything we know about the shapes of molecules began with bouncing X-rays off a crystal.
A way to picture it
Think of soldiers marching across a field ribbed with parallel ditches. If the ditches are spaced so that everyone steps over them in stride, the ranks stay together and march as one. Space them wrong and the ranks fall out of step and the column blurs. X-rays reflecting from atomic layers are like this: only when the extra distance down to the next layer is a whole number of wave-steps do all the reflections come back in unison — and shine.
Where it sits
This is the experimental partner to the era's atomic ideas. Dalton and Avogadro had argued that matter is made of atoms; the Braggs let us look at where those atoms are. Their X-ray pictures later supplied the dimensions of the DNA helix that Watson and Crick assembled, and grew into the whole field of structural biology — a line that runs from a salt crystal in 1913 all the way to today's prediction of protein shapes.