Bragg Equation
Definition and meaning of Bragg Equation in chemistry.
The Bragg equation, nλ = 2d sin θ, relates the wavelength of X-rays diffracted by a crystal to the spacing between its atomic planes and the angle of incidence at which constructive interference occurs.
In more detail
When X-rays strike a crystal, each set of parallel atomic planes reflects part of the beam. Constructive interference (a detectable diffraction peak) occurs only when the extra path length traveled by rays reflecting from successive planes, 2d sin θ, equals a whole number of wavelengths, nλ. By measuring the angles θ at which peaks appear for X-rays of known wavelength λ, the interplanar spacing d can be calculated, making the equation the foundation of X-ray crystallography for determining crystal structures.
Key facts
| Formula | nλ = 2d sin θ |
|---|---|
| Variables | n = integer order, λ = X-ray wavelength, d = interplanar spacing, θ = angle of incidence/reflection |
| Proposed by | William Lawrence Bragg and William Henry Bragg, 1913 |
| Field | Physical Chemistry |
Using Cu Kα X-rays (λ = 0.154 nm) on a sodium chloride crystal, a strong first-order (n = 1) reflection is observed at θ = 15.9°. Solving d = λ/(2 sin θ) gives an interplanar spacing of about 0.282 nm, matching the known spacing between adjacent Na⁺ and Cl⁻ planes in the NaCl rock-salt structure.
Frequently asked questions
Why must the angle in the Bragg equation be measured from the crystal plane, not the normal?
Bragg's law defines θ as the glancing angle between the incident beam and the atomic plane itself (as in reflection), unlike Snell's law, which uses the angle from the normal; this convention comes from treating diffraction as reflection off successive lattice planes.
What does the order n represent?
n is a positive integer (1, 2, 3...) indicating how many whole wavelengths fit into the path difference between reflections from adjacent planes; higher-order reflections appear at larger angles for the same plane spacing.