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At what angles of incidence x rays of wave lengrh 5A will produce diffracted beam from the (110) planes in a simple cubic latice with a=10 A?
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At what angles of incidence x rays of wave lengrh 5A will produce diff...
Angles of Incidence for X-rays on (110) planes in a Simple Cubic Lattice

Given:
- Wavelength of X-rays (λ) = 5 Å
- Lattice constant (a) = 10 Å

Calculation:
The Miller indices for the (110) planes in a simple cubic lattice are (1 1 0).
The Bragg's Law for diffraction is given by:
nλ = 2d sinθ
Where:
- n = order of diffraction (1 for first order)
- λ = wavelength of X-rays
- d = interplanar spacing
- θ = angle of incidence
For the (110) planes in a simple cubic lattice:
d = a / sqrt(h^2 + k^2 + l^2)
d = 10 Å / sqrt(1^2 + 1^2 + 0^2)
d = 10 Å / sqrt(2)
d = 10 Å / 1.414
d = 7.07 Å
Plugging the values into Bragg's Law:
5 Å = 2 * 7.07 Å * sinθ
sinθ = 5 Å / (2 * 7.07 Å)
sinθ = 0.3536
θ = sin^(-1)(0.3536)
θ ≈ 20.61°
Therefore, the angle of incidence for X-rays with a wavelength of 5 Å on the (110) planes in a simple cubic lattice is approximately 20.61°.
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At what angles of incidence x rays of wave lengrh 5A will produce diffracted beam from the (110) planes in a simple cubic latice with a=10 A?
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