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Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 are
a. (321)
b. (123)
c. (310)
d. None?
a. (321)
b. (123)
c. (310)
d. None?
Most Upvoted Answer
Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respe...
Understanding Miller Indices
Miller indices are a notation system in crystallography for planes in crystal (Bravais) lattices. They are denoted by three integers (h, k, l) corresponding to the intercepts of the plane on the crystal axes.
Given Problem Statement
- A plane makes intercepts of 1 on the a-axis and 2 on the b-axis.
- The intercept on the c-axis is not specified, implying it is infinite (meaning it does not intercept).
- The ratio a:b:c is given as 3:2:1.
Steps to Determine Miller Indices
- Identify Intercepts:
- Intercept on the a-axis = 1 (1/3 from the ratio)
- Intercept on the b-axis = 2 (2/2 from the ratio)
- Intercept on the c-axis = ∞
- Reciprocal of Intercepts:
- a = 1 → 1/1 = 1 (for a=1)
- b = 2 → 1/2 = 0.5 (for b=2)
- c = ∞ → 1/∞ = 0
- Clearing Fractions:
- To eliminate fractions, multiply by the least common multiple, which is 2:
- 2(1) : 2(0.5) : 2(0) = 2 : 1 : 0
- Final Miller Indices:
- This translates to (210).
Conclusion
The Miller indices of the plane described are (210), which indicates it is not listed among the options provided. Therefore, the correct answer is:
Answer: d. None
This solution highlights the step-by-step process to derive Miller indices while ensuring clarity and conciseness in the explanation.
Miller indices are a notation system in crystallography for planes in crystal (Bravais) lattices. They are denoted by three integers (h, k, l) corresponding to the intercepts of the plane on the crystal axes.
Given Problem Statement
- A plane makes intercepts of 1 on the a-axis and 2 on the b-axis.
- The intercept on the c-axis is not specified, implying it is infinite (meaning it does not intercept).
- The ratio a:b:c is given as 3:2:1.
Steps to Determine Miller Indices
- Identify Intercepts:
- Intercept on the a-axis = 1 (1/3 from the ratio)
- Intercept on the b-axis = 2 (2/2 from the ratio)
- Intercept on the c-axis = ∞
- Reciprocal of Intercepts:
- a = 1 → 1/1 = 1 (for a=1)
- b = 2 → 1/2 = 0.5 (for b=2)
- c = ∞ → 1/∞ = 0
- Clearing Fractions:
- To eliminate fractions, multiply by the least common multiple, which is 2:
- 2(1) : 2(0.5) : 2(0) = 2 : 1 : 0
- Final Miller Indices:
- This translates to (210).
Conclusion
The Miller indices of the plane described are (210), which indicates it is not listed among the options provided. Therefore, the correct answer is:
Answer: d. None
This solution highlights the step-by-step process to derive Miller indices while ensuring clarity and conciseness in the explanation.
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Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None?
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Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None?.
Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question 45 A plane makes intercepts of 1 and 2 Aon a and b axis respectively nut parallel to axis then Miller Indices if a:b:c= 3:2:1 area. (321)b. (123)c. (310)d. None?.
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