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A beam of x-ray of wavelength 0.071 nm is diffracted by (110) plane of rock salt with lattice constant (a) 0.28nm. find the glancing angle for the second order diffraction

User Gre
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I got you.

The glancing angle for the second order diffraction of X-rays with a wavelength of 0.071 nm diffracted by the (110) plane of rock salt with a lattice constant of 0.28 nm can be calculated using Bragg's law:

2d sinθ = nλ

where d is the interplanar spacing of the (110) plane, n is the order of the diffraction, λ is the wavelength of the X-rays, and θ is the glancing angle.

For the second order diffraction (n = 2), we have:

2d sinθ = 2λ

The interplanar spacing of the (110) plane can be calculated using the formula:

d = a/√(h^2 + k^2 + l^2)

where a is the lattice constant, and h, k, and l are the Miller indices of the (110) plane. For rock salt, h = 1, k = 1, and l = 0 for the (110) plane.

Substituting the values given in the problem, we get:

d = 0.28 nm / √(1^2 + 1^2 + 0^2) = 0.14 nm

Substituting the values for d, n, and λ, we get:

2(0.14 nm) sinθ = 2(0.071 nm)

Simplifying, we get:

sinθ = 0.51

Taking the inverse sine, we get:

θ = 30.2 degrees

Therefore, the glancing angle for the second order diffraction is approximately 30.2 degrees.
User SimonG
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