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The angle at which the first order Bragg reflection is observed from (110) plane in a simple cubic unit cell of side 3.238 Å when chromium Ka radiation of wavelength 2.29 Å is used, is:
- a)300
- b)450
- c)600
- d)900
Correct answer is option 'A'. Can you explain this answer?
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The angle at which the first order Bragg reflection is observed from (...
Solution:
The formula for calculating the Bragg angle is given by:
nλ = 2d sinθ
where n = order of reflection, λ = wavelength of radiation, d = interplanar spacing, and θ = Bragg angle.
Given,
λ = 2.29 Å
a = 3.238 Å
Plane of reflection is (110) plane in a simple cubic unit cell.
Finding the interplanar spacing:
The interplanar spacing for the (110) plane in a simple cubic unit cell is given by:
d = a/√(h^2+k^2+l^2)
where h, k, and l are the Miller indices for the plane of reflection.
For the (110) plane, h = 1, k = 1, and l = 0.
So,
d = a/√(1^2+1^2+0^2) = a/√2
Substituting the values, we get:
d = 3.238/√2 = 2.292 Å
Calculating the Bragg angle:
We need to find the Bragg angle for the first order reflection (n=1).
Substituting the values, we get:
1 × 2.29 = 2 × 2.292 × sinθ
sinθ = 1/2
θ = sin^-1(1/2) = 30°
Therefore, the angle at which the first order Bragg reflection is observed from (110) plane in a simple cubic unit cell of side 3.238 when chromium Ka radiation of wavelength 2.29 is used, is 30°. Hence, option A is the correct answer.
The formula for calculating the Bragg angle is given by:
nλ = 2d sinθ
where n = order of reflection, λ = wavelength of radiation, d = interplanar spacing, and θ = Bragg angle.
Given,
λ = 2.29 Å
a = 3.238 Å
Plane of reflection is (110) plane in a simple cubic unit cell.
Finding the interplanar spacing:
The interplanar spacing for the (110) plane in a simple cubic unit cell is given by:
d = a/√(h^2+k^2+l^2)
where h, k, and l are the Miller indices for the plane of reflection.
For the (110) plane, h = 1, k = 1, and l = 0.
So,
d = a/√(1^2+1^2+0^2) = a/√2
Substituting the values, we get:
d = 3.238/√2 = 2.292 Å
Calculating the Bragg angle:
We need to find the Bragg angle for the first order reflection (n=1).
Substituting the values, we get:
1 × 2.29 = 2 × 2.292 × sinθ
sinθ = 1/2
θ = sin^-1(1/2) = 30°
Therefore, the angle at which the first order Bragg reflection is observed from (110) plane in a simple cubic unit cell of side 3.238 when chromium Ka radiation of wavelength 2.29 is used, is 30°. Hence, option A is the correct answer.
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The angle at which the first order Bragg reflection is observed from (110) plane in a simple cubic unit cell of side 3.238 Å when chromium Ka radiation of wavelength 2.29 Å is used, is:a)300b)450c)600d)900Correct answer is option 'A'. Can you explain this answer?
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