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The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.
Correct answer is '3.031'. Can you explain this answer?
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The Bragg angle corresponding to the first order reflection from (1,1,...
where a = interatomic distance
d = interplanar distance
h,k,l = Miller indices.
According to the problem h = k = I = 1 (being d111 plane)
q = 30°, I = 1.75 x 10-10m, n = 1
from bragg’s equation 2d sin q = nl, we have
Solving we have a = 3.031Å
Most Upvoted Answer
The Bragg angle corresponding to the first order reflection from (1,1,...
Degrees.
The Bragg angle is given by the equation:
2dsinθ = nλ
where d is the spacing between the crystal planes, θ is the Bragg angle, n is the order of the reflection, and λ is the wavelength of the incident radiation.
For the first order reflection from (1,1,1) planes, n = 1 and d is the spacing between adjacent (1,1,1) planes, which is given by:
d = a/√(h^2+k^2+l^2)
where a is the lattice parameter and h, k, and l are the Miller indices of the crystal planes.
For (1,1,1) planes, h = k = l = 1, so:
d = a/√(1^2+1^2+1^2) = a/√3
Substituting n = 1, d = a/√3, and θ = 30 degrees into the Bragg equation, we get:
2(a/√3)sin30 = λ
Simplifying and solving for λ, we get:
λ = 2a/(√3)
Therefore, the wavelength of the incident radiation is determined by the lattice parameter of the crystal.
The Bragg angle is given by the equation:
2dsinθ = nλ
where d is the spacing between the crystal planes, θ is the Bragg angle, n is the order of the reflection, and λ is the wavelength of the incident radiation.
For the first order reflection from (1,1,1) planes, n = 1 and d is the spacing between adjacent (1,1,1) planes, which is given by:
d = a/√(h^2+k^2+l^2)
where a is the lattice parameter and h, k, and l are the Miller indices of the crystal planes.
For (1,1,1) planes, h = k = l = 1, so:
d = a/√(1^2+1^2+1^2) = a/√3
Substituting n = 1, d = a/√3, and θ = 30 degrees into the Bragg equation, we get:
2(a/√3)sin30 = λ
Simplifying and solving for λ, we get:
λ = 2a/(√3)
Therefore, the wavelength of the incident radiation is determined by the lattice parameter of the crystal.
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The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.Correct answer is '3.031'. Can you explain this answer?
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The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.Correct answer is '3.031'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.Correct answer is '3.031'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Bragg angle corresponding to the first order reflection from (1,1,1) planes in a crystal is 30° when X - rays of wavelength 1.75Å are used. Calculate the interatomic spacing.Correct answer is '3.031'. Can you explain this answer?.
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