Explain Bragg's law of diffraction? How X-rays are used to find the interplanar spacing in crystal lattice

Bragg's Law of Diffraction is a special case of Laue diffraction and provides the conditions for diffraction of monochromatic X-rays from a crystal lattice. The law was first proposed by William Lawrence Bragg and William Henry Bragg in 1913.

The law states that nλ = 2d sin θ, where:

• n is the order of diffraction, which is an integer.
• λ is the wavelength of incident wave.
• d is the distance between atomic layers in a crystal.
• θ is the angle of incidence for an X-ray hitting the crystal surface.

The Bragg's Law is used to find the interplanar spacing in a crystal lattice by using X-rays in the following way:

1. X-rays are fired at a crystal. When these X-rays hit the crystal, they are diffracted by the crystal lattice.

2. The X-rays are diffracted in such a way that they constructively interfere only when the conditions set by Bragg's Law are met.

3. By measuring the angle (θ) at which the X-rays are diffracted and knowing the wavelength (λ) of the X-rays, the interplanar spacing (d) can be calculated using the Bragg's Law equation.

4. The interplanar spacing gives information about the arrangement of atoms in the crystal lattice, which is crucial in determining the crystal's structure.

5. By varying the angle of incidence, we can get information about different planes in the crystal lattice.