Q. Explain Bragg's law. A monochromatic X-ray is incident on a crystal. By rotation the crystal, two successive reflections are obtained at angles of 10.0° and 23.0°. the inter planer spacing of the crystal is 2.8 À. Calculate the wavelength of X-ray.

Bragg's Law : In  1912, Bragg developed a theory to explain the diffraction by a crystal grating. He supposed that the incident wave undergoes reflection at various parallel plane of atoms in the crystal, with each plane reflect a small part of incident radiation according to ordinary laws of reflection. The diffracted beams are found only when the various plane of atom interfere constructively.

Let us consider a set of parallel atomic plane in a crystal separated by a distance'd' known as interplaner spacing. Let a X ray beam is incident at a glancing angle q. It is scattered by the atom like P and Q in any direction.

Constructive interference will take place between the parallel scattered wavelets if the path difference between the wavelets scattered from two successive atomic plane is integral multiple of wavelength.

Consider two parallel rays R1 and R2, reflected by two atoms P and Q in two adjacent layers. The ray reflected from P goes to R1' and from Q goes to R2'. Draw PA and PB normal to R2 and R2' respectively. Each of these lines, makes an angle q with PQ which is equal to d (inter planar spacing).