---
title: "X-Ray Diffraction and the Bragg Condition"
description: "Planes of atoms reflect X-rays that reinforce only at angles satisfying the Bragg condition, so a diffraction pattern is a map of atomic spacing. Crystal structures, and the shape of DNA, were read th"
canonical: https://lightmysky.com/learn/science/x-ray-diffraction-and-the-bragg-condition-mt_qEDplGeIkB
source: https://lightmysky.com/learn/science/x-ray-diffraction-and-the-bragg-condition-mt_qEDplGeIkB.md
retrieved: 2026-09-12
---

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# X-Ray Diffraction and the Bragg Condition

Planes of atoms reflect X-rays that reinforce only at angles satisfying the Bragg condition, so a diffraction pattern is a map of atomic spacing. Crystal structures, and the shape of DNA, were read this way.

Subject: Science · Area: Waves, Light & Sound · Ages 20 to 22
Page: https://lightmysky.com/learn/science/x-ray-diffraction-and-the-bragg-condition-mt_qEDplGeIkB

## Ready when they can

- Applies the Bragg condition to get a plane spacing from a measured angle
- Explains why X-rays rather than visible light are needed for atomic spacings
- Describes what a diffraction pattern reveals about the arrangement of atoms

## Lesson: Reading atomic spacing from X-ray spots

Picture X-rays glancing off stacked planes of atoms. The lower ray travels extra: twice the plane spacing times sine of the glancing angle. When that extra equals a whole number of wavelengths, crest meets crest and you get a bright spot. That match, whole wavelengths equal twice spacing times sine, is the Bragg condition. Note the angle is measured from the surface itself, not from the normal.

The trick only works when the wavelength matches the structure size. Neighboring atomic planes sit about 0.1 nm apart, far below visible light, so visible light washes over crystals with no pattern. X-rays near 0.1 nm fit the atomic scale, which is why the 1912 crystal experiment proved X-rays are waves.

**Example.** Table salt planes sit 0.252 nm apart, and the first-order spot appears at a glancing angle of 18.1 degrees. Twice 0.252 times sine of 18.1 degrees gives 0.157 nm, squarely in the X-ray range. Wider spacings bend to smaller angles, so each measured angle converts directly into a spacing.

**Tip.** Spot positions encode the lattice geometry and spacings, while spot brightness encodes what sits at each lattice point. Only special angles satisfy the match, so crystals give sharp spots instead of a smooth glow. Higher orders need larger sines, capped at one, so only a few orders ever appear.

**Recap.** Match the wavelength to the atomic scale, and each spot angle converts into a plane spacing.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Intensity in Single-Slit and Double-Slit Diffraction](https://lightmysky.com/learn/science/intensity-in-single-slit-and-double-slit-diffraction-mt_HURhzZdIkM)

## Opens up

- [Fourier Analysis and the Wave Packet](https://lightmysky.com/learn/science/fourier-analysis-and-the-wave-packet-mt_1ZaojWUZEw)
- [Single-Crystal Diffraction: From Reflections to a Refined Structure](https://lightmysky.com/learn/science/single-crystal-diffraction-from-reflections-to-a-refined-structure-mt_7PjfoEu-WE)
- [Crystal Lattices, the Reciprocal Lattice and Bloch's Theorem](https://lightmysky.com/learn/science/crystal-lattices-the-reciprocal-lattice-and-blochs-theorem-mt_nbNnHpGnZI)