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Th e distance b etween two successive (110) planes in a simple cubic lattice with lattice parameter
‘a’ is
- a)√2a
- b)√3a
- c)2√2a
- d)a/√2
Correct answer is option 'D'. Can you explain this answer?
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Th e distance b etween two successive (110) planes in a simple cubic l...
Understanding (110) Planes in a Simple Cubic Lattice
In a simple cubic lattice, the distance between successive planes can be derived using the Miller indices. The (110) planes indicate specific orientations in the crystal structure.
Distance Calculation Formula
To find the distance 'd' between successive (hkl) planes:
- The formula is given by:
d = a / sqrt(h^2 + k^2 + l^2)
Where 'h', 'k', and 'l' are the Miller indices.
Applying the Formula
For the (110) planes:
- h = 1, k = 1, l = 0
Plugging these values into the formula:
- d = a / sqrt(1^2 + 1^2 + 0^2)
- d = a / sqrt(2)
This indicates that the distance between the (110) planes is a / sqrt(2).
Conclusion
The correct answer is option 'D', which states that the distance between two successive (110) planes in a simple cubic lattice is a / sqrt(2). Understanding the relation of Miller indices to lattice parameters helps in visualizing the crystal structure efficiently, making it a crucial concept in solid-state physics and materials science.
In a simple cubic lattice, the distance between successive planes can be derived using the Miller indices. The (110) planes indicate specific orientations in the crystal structure.
Distance Calculation Formula
To find the distance 'd' between successive (hkl) planes:
- The formula is given by:
d = a / sqrt(h^2 + k^2 + l^2)
Where 'h', 'k', and 'l' are the Miller indices.
Applying the Formula
For the (110) planes:
- h = 1, k = 1, l = 0
Plugging these values into the formula:
- d = a / sqrt(1^2 + 1^2 + 0^2)
- d = a / sqrt(2)
This indicates that the distance between the (110) planes is a / sqrt(2).
Conclusion
The correct answer is option 'D', which states that the distance between two successive (110) planes in a simple cubic lattice is a / sqrt(2). Understanding the relation of Miller indices to lattice parameters helps in visualizing the crystal structure efficiently, making it a crucial concept in solid-state physics and materials science.
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Th e distance b etween two successive (110) planes in a simple cubic l...
1/√2×a
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Th e distance b etween two successive (110) planes in a simple cubic lattice with lattice parameter‘a’isa)√2ab)√3ac)2√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?
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Th e distance b etween two successive (110) planes in a simple cubic lattice with lattice parameter‘a’isa)√2ab)√3ac)2√2ad)a/√2Correct answer is option 'D'. 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 Th e distance b etween two successive (110) planes in a simple cubic lattice with lattice parameter‘a’isa)√2ab)√3ac)2√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Th e distance b etween two successive (110) planes in a simple cubic lattice with lattice parameter‘a’isa)√2ab)√3ac)2√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?.
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