\[\theta=\sin^{-1}\left(\frac{n\lambda}{2d}\right)\]
Variables
thetaBragg angle (rad)
ndiffraction order
lambdawavelength of incident radiation (m)
dinterplanar spacing (m)
Description
What is this formula?
This formula calculates the Bragg angle for constructive diffraction of radiation by parallel crystal planes.
When to use it
Use it when the wavelength, diffraction order, and interplanar spacing are known, and the diffraction angle must be calculated.
Example
Data:
n = 1
lambda = 1.54e-10 m
d = 2.00e-10 m
Formula:
theta = asin((n*lambda)/(2*d))
Substitution:
theta = asin((1*1.54e-10)/(2*2.00e-10))
Result:
theta = 0.395 rad
theta = 22.6 degrees
Applications
X-ray diffraction, crystallography, semiconductor materials, mineral identification, lattice spacing analysis, and solid-state physics.