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Explain with example how to determine crystal structure by Braggs X-ray spectrometer.
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W.L Bragg’s explained the phenomenon of X-ray diffraction from a single crystal shown as follows

When a beam of X-rays is incident on a crystal it is scattered by individual atoms of the rich atomic planes. Thus, each atom become a source of scattered radiation. The atomic planes responsible for the X-ray diffraction are called BRAGG’S PLANES. Therefore the sets of Braggs planes constitute the crystal grating. Bragg’s scattering or Bragg’s diffraction is also referred as Braggs reflection. Bragg derived a law called Bragg’s law to explain the X-ray diffraction effect.

Here a beam of X-ray is incident on a set of parallel planes of a crystal. The rays makes a glancing angle θ and are practically reflected from different successive planes. The phase relationship of the scattered rays can be determined from their path differences. Here two parallel X-rays are reflected from two consecutive planes PI and P2. The path differences between then as shown

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$ δ=MB+BN=2MB=2ABsinθ$ Here AB = d, the interplanar spacing of the crystal. Hence,

$ δ= 2dsinθ$

The two diffracted rays reinforce each other when they interfere constructively when their path difference δ is equal to nλ

Hence, 2dsinθ = n λ

This is called Bragg’s law.

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