Question

State and obtain Bragg's Law.

Accepted Answer

Bragg Law

This law simply states that when the $X - ray$ is incident onto a crystal surface, its angle of incidence is $θ$ and it is reflected back with the same angle of scattering $θ$ . And if the path difference $d$ is equal to a whole number $n$ of wavelength, constructive interference will occur.

Bragg’s equation is: $nλ = 2 dsinθ$

When the incident angle equals the reflecting angle, the phases of the $2$ beams of $X - ray$ coincide. The $2$ beams of incident ray are parallel till point $z$ . Point $z$ is the point where the top beam strikes the top layer. The next beam passes up to the next layer and is scattered by $B$ . This beam has travelled an extra distance of $AB + BC$ than the previous one. This distance is an integral multiple of the wavelength of the ray.

So, $nλ = AB + BC (but, AB = BC)$

Hence, we can say: $nλ = 2 AB . . . . . (1)$

In triangle $ABz$ : $d$ is the hypotenuse and $AB$ is opposite to angle $θ$ .

$\sin θ = \frac{P}{H}$

Where $P =$ Perpendicular and $H =$ Hypotenuse

Here, $\sin θ = \frac{AB}{d}$

Hence, $AB = d \sin θ . . . . . (2)$

Now put the value of $AB$ obtained in equation $(2)$ in equation $(1)$ . We get,

$nλ = 2 dsinθ$

Hence, it is the required answer.

Bragg’s Law explains the molecular structure and crystals being identified using X-ray diffraction techniques. It gives us the relationship between the incident X-ray light and its reflection from the crystal surface.

State and obtain Bragg's Law.

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