Question

derive Bragg's equation​

Answer 1

Answer:

A simple way to derive the Bragg equation is as follows.

• The path difference between electrons scattered from adjacent crystal planes is 2d sin θ

• For constructive interference between the two scattered beams the difference must be an integer multiple of electron wavelengths, nλ which gives the Bragg equation.

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Answer 2

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$\small\underline\mathcal\pink{{Bragg's\:equation:-}}$ W.H.bragg has proposed an equation to explain the relation between inter planar distance (d),wavelength of x-rays (λ)and angle of diffraction of x-rays (θ ) is called Bragg's equation.

$\small\underline\mathbb\green{{From\:The\: Above \:Diagram}}$

$\blue\longmapsto\:$First X-ray is diffracted from a point A in the first plane and second X-ray is diffracted from point 'B' in the second plane.

$\pink\longmapsto\:$Second X-ray wave travels more distance than first X-ray wave.

$\red\longmapsto\:$The extra distance travelled by second x-ray =CB+BD.

$\orange\longmapsto\:$path difference in first & second layer of second x-ray =CB+BD .

$\purple\longmapsto\:$If waves of two rays exists in same phase then,path difference is equal to an integral multiple of wavelength of x-rays

Therefore,CB + BD = nλ ..........eq no.1

where, n = 1, 2, 3,...........

In traingle ABC,

sinθ = CB/AB =CB/d

CB=d sinθ............eq no.2

In triangle ABD

sinθ=BD/AB=BD/d

BD= d sinθ...........eq no.3

when equation 2,3 are substituted in equation 1 we get

d sinθ + d sinθ

This relation is known as bragg's equation

where,

n= order of diffraction

θ= angle of diffraction

d= inter planar distance

λ= Wavelength of x-rays.

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