A family of planes of spacing 0.2518 nm of NaCI crystal reflects a beam of X-ray in first order at an angle of 30°. The wavelength of X-rays is:

Bragg’s Law:

Bragg's Law relates the angle θ (at which there is a maximum in diffracted intensity ) to the wavelength of X-rays and the interlayer distance d between the planes of atoms/ions/molecules in the lattice. Condition for constructive interference (maxima in the reflected).

nλ = 2d sinθ

λ = Wavelength of the X-ray

d = distance of crystal layers

θ = incident angle (the angle between the incident plane and the scattering plane)

n = integer (order)

This condition is known as Bragg’s law

Calculation:

For 1^st order, n = 1.

λ = 2d sinθ = 2 × 0.2518 × sin 30°

λ = 0.2518 nm

• X-ray diffraction is one of the earliest methods for studying the structure of solids.
• In the process of diffraction, electromagnetic waves of a given frequency but different phases interact to produce constructive interference (bright spots on the film exposed to the light) and destructive interference (dark spots).
• By a careful analysis of the diffraction patterns, very accurate values of the lattice parameters (unit cell dimensions) can be inferred.