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Question 47 Monochromatic X-rays of wavelength 1 Aare incident on
first order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?
a. 1
b. √3
d. rt 11?
first order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?
a. 1
b. √3
d. rt 11?
Most Upvoted Answer
Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst...
Understanding Bragg's Law
Bragg's Law describes the condition for constructive interference of X-rays scattered from crystal planes. It is given by the formula:
nλ = 2d sin(θ)
Where:
- n = order of reflection (in this case, n=1 for first order)
- λ = wavelength of X-rays
- d = interplanar spacing
- θ = angle of incidence
Given Values
- Wavelength (λ) = 1 Å (Angstrom)
- Angle (θ) = 30°
Calculating Interplanar Spacing (d)
Using Bragg's Law for first-order reflection, we can rearrange the equation to find d:
d = nλ / (2 sin(θ))
Substituting the values:
- n = 1
- λ = 1 Å
- θ = 30° (sin(30°) = 0.5)
Now, substituting these:
d = 1 Å / (2 * 0.5) = 1 Å / 1 = 1 Å
Identifying the Lattice Parameter (a)
For a cubic crystal system, the interplanar spacing d for the (hkl) planes can be expressed as:
d = a / √(h² + k² + l²)
For the (321) plane:
- h = 3, k = 2, l = 1
- h² + k² + l² = 3² + 2² + 1² = 9 + 4 + 1 = 14
Now substituting d:
1 Å = a / √14
Thus, we have:
a = 1 Å * √14
Conclusion
The lattice parameter (a) is √14 Å. Therefore, the correct answer is d. √14.
Bragg's Law describes the condition for constructive interference of X-rays scattered from crystal planes. It is given by the formula:
nλ = 2d sin(θ)
Where:
- n = order of reflection (in this case, n=1 for first order)
- λ = wavelength of X-rays
- d = interplanar spacing
- θ = angle of incidence
Given Values
- Wavelength (λ) = 1 Å (Angstrom)
- Angle (θ) = 30°
Calculating Interplanar Spacing (d)
Using Bragg's Law for first-order reflection, we can rearrange the equation to find d:
d = nλ / (2 sin(θ))
Substituting the values:
- n = 1
- λ = 1 Å
- θ = 30° (sin(30°) = 0.5)
Now, substituting these:
d = 1 Å / (2 * 0.5) = 1 Å / 1 = 1 Å
Identifying the Lattice Parameter (a)
For a cubic crystal system, the interplanar spacing d for the (hkl) planes can be expressed as:
d = a / √(h² + k² + l²)
For the (321) plane:
- h = 3, k = 2, l = 1
- h² + k² + l² = 3² + 2² + 1² = 9 + 4 + 1 = 14
Now substituting d:
1 Å = a / √14
Thus, we have:
a = 1 Å * √14
Conclusion
The lattice parameter (a) is √14 Å. Therefore, the correct answer is d. √14.
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Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11?
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Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11?.
Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question 47 Monochromatic X-rays of wavelength 1 Aare incident onfirst order Bragg reflection from (321) plane occurs at an angle of 30° from the plane then. a=?a. 1b. √3d. rt 11?.
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