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A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :
- a)2a
- b)2√2 a
- c)√2a
- d)a/√2
Correct answer is option 'D'. Can you explain this answer?
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A metal crystallises in a face centred cubic structure. If the edge le...
In FCC unit cell atoms are in contant along face diagonal
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A metal crystallises in a face centred cubic structure. If the edge le...
Understanding Face-Centered Cubic Structure
In a face-centered cubic (FCC) structure, atoms are located at each of the corners and the centers of each face of the cube. This arrangement is essential for determining the closest approach between two atoms.
Unit Cell Dimensions
- The edge length of the unit cell is denoted as 'a'.
- In an FCC lattice, the coordination number is 12, meaning each atom is in contact with 12 other atoms.
Closest Approach Calculation
- The closest approach between two atoms occurs along the face diagonal of the cube.
- A face diagonal can be calculated using the Pythagorean theorem:
- The length of the face diagonal = √(a^2 + a^2) = √(2a^2) = a√2.
Atomic Radius in FCC
- In an FCC lattice, the face diagonal is equal to four atomic radii (r):
- Face diagonal = 4r.
Relating Atomic Radius to Edge Length
- Therefore, we can relate the atomic radius to the edge length:
- 4r = a√2
- r = a√2 / 4 = a / (2√2).
Finding Closest Approach
- The closest distance between the centers of two adjacent atoms is:
- Closest approach = 2r = 2(a / (2√2)) = a/√2.
Conclusion
- The closest approach between two atoms in a face-centered cubic structure is indeed a/√2.
- Thus, the correct answer is option 'D'.
In a face-centered cubic (FCC) structure, atoms are located at each of the corners and the centers of each face of the cube. This arrangement is essential for determining the closest approach between two atoms.
Unit Cell Dimensions
- The edge length of the unit cell is denoted as 'a'.
- In an FCC lattice, the coordination number is 12, meaning each atom is in contact with 12 other atoms.
Closest Approach Calculation
- The closest approach between two atoms occurs along the face diagonal of the cube.
- A face diagonal can be calculated using the Pythagorean theorem:
- The length of the face diagonal = √(a^2 + a^2) = √(2a^2) = a√2.
Atomic Radius in FCC
- In an FCC lattice, the face diagonal is equal to four atomic radii (r):
- Face diagonal = 4r.
Relating Atomic Radius to Edge Length
- Therefore, we can relate the atomic radius to the edge length:
- 4r = a√2
- r = a√2 / 4 = a / (2√2).
Finding Closest Approach
- The closest distance between the centers of two adjacent atoms is:
- Closest approach = 2r = 2(a / (2√2)) = a/√2.
Conclusion
- The closest approach between two atoms in a face-centered cubic structure is indeed a/√2.
- Thus, the correct answer is option 'D'.
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A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?
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A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?.
A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?.
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A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :a)2ab)2√2 ac)√2ad)a/√2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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