Mumbai university > FE > SEM 1 > Applied Physics 1

Marks: 7M

Year: May 2013

Consider a regular arrangement of atoms with inter-planar distance "d". An X-ray beam is incident upon the surface at glancing angle "θ"

Let us assume that the path difference between the scattered rays BC and EF as ∆=nλ thus producing constructive interference.

Now,

∆ = PE + EQ

∴ ∆ = BE.sin θ + BE.sin θ

∴ ∆ = 2BE.sin θ

∴ ∆ = 2d.sin θ

But, ∆ = nλ

∴ nλ = 2d.sinθ

This, is the required expression for Bragg's Law

Why X-Rays are used:-

• Crystal structure is analyzed by using the diffraction pattern found after an electromagnetic wave is incident upon it.

• In order to get a regular diffraction pattern, the incident wave should have a wavelength comparable to the dimension of the object being observed.

• The dimensions of atom are of the order 10-10 m, which is comparable to the wavelength of X-ray.

• Hence, X-rays and not γ-rays are used to analyze crystals.

From the X-ray diffraction pattern, the inter-planar spacing can be obtained using Bragg’s Law