A beam of X-rays of wavelength 0.071nm is diffracted by (110) plane of rock salt with lattice constant of 0.28nm. Find the glancing angle for the second order diffraction.
Answers
Answer:
Explanation:
Sol: Given data are:
Wavelength (λ) of X-rays = 0.071 nm
Lattice constant (a) = 0.28 nm
Plane (hkl) = (110)
Order of diffraction = 2
Glancing angle θ = ?
Bragg’s law is 2d sin θ = nλ
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Substitute in Bragg’s equation
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The glancing angle for the second order diffraction is 21.01֯
Given:
Wavelength of X rays λ= 0.071 nm
Lattice constant a = 0.28 nm
(h k l) Plane = (110)
Order of diffraction = 2
To find:
The glancing angle ɵ
Solution:
According to Bragg’s law,
2dsinɵ = n λ
The equation provides an explanation for why crystal faces reflect X-ray photons at specific angles of incidence (θ,λ).
The variable λ determines the wavelength of the incident X-ray beam, the variable d denotes the spacing between the atomic layers, and the variable n is an integer.
Repeating the face-centred cubic unit cell creates the structure of Rocksalt. That is Rock salt has FCC structure. Therefore,
d=a/√(h^2+k^2+l^2 )
(0.28*10^(-9))/√(1^2+1^2+0^2 ) m=(0.28*10^(-9))/√2 m
Substituting this in Bragg’s equation we get,
2*(0.28*10^(-9))/√2*sinθ=2*0.071*10^(-9)
sinθ= √2*0.071/0.28=0.3586
θ=sin^(-1)(0.3586) = 21.01° ≈21°
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