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Derive Braggs law & X-rays of unknown wavelength give first order Bragg's reflection at glancing angle of 20" with (2 1 2) planes of copper having FCC structure.

Find one wavelength of X-rays, if the lattice constant for copper is 3.615A0 . -

Mumbai university > FE > SEM 1 > Applied Physics 1

Marks: 7M

Year: May 2015

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Bragg’s law-

Bragg emphasized on parallel planes & the set of planes are considered as Bragg’s planes. When X-rays are allowed to be incident on this planes, diffraction takes place & diffracted pattern gives information about the structure.

Let us consider parallel planes-

Let AB be my incident ray, which gets reflected along BC, another parallel beam gets incident along E, gets reflected along EF. Drop perpendicular from B such that it meets DE & EF along P & Q.

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Now,

∆ = PE + EQ

∴ ∆ = BE.sin θ + BE.sin θ

∴ ∆ = 2 BE.sin θ

∴ ∆ = 2d.sin θ

But, ∆ = nλ ………here we consider constructive interference

∴ nλ = 2d.sinθ

This, is the required expression for Bragg's Law

Given:

n=1

θ=20

Miller indices is (2 1 2)

a = 3.615A or 3.615×1010

To find: λ=?

Solution:

d=a22+12+22

=3.615×10109

=3.615×10103

d= 1.205×10-10 m

By Bragg’s law-

nλ=2d.sinθ

λ=2×1.205×1010sin20/1

λ=8.243×1011m

λ=0.824A

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