Bragg Diffraction Angle

What is this formula?

Bragg's law calculates the diffraction angle produced when waves such as X-rays are reflected by parallel atomic planes inside a crystal. It relates wavelength, interplanar spacing, and diffraction angle.

When to use it

This formula is used in crystallography, X-ray diffraction, materials science, and solid state physics to analyze crystal structures and determine atomic spacing.

Example

An X-ray beam with wavelength:

λ = 1.54×10^-10 m

is diffracted by crystal planes separated by:

d = 2.00×10^-10 m

for first-order diffraction:

n = 1

Using:

nλ = 2d sin(θ)

Substitution:

1×1.54×10^-10 = 2×2.00×10^-10×sin(θ)

Result:

θ ≈ 0.395 rad

Applications

- X-ray crystallography

- Crystal structure analysis

- Materials science

- Semiconductor characterization

- Solid state physics

- Diffraction experiments