Q11 / 150 · MHT CET 2026 (11 April Shift 2) · Chemistry
What is the number of neighbouring spheres for any particle in the fcc crystal lattice ?
- A$6$
- B$8$
- C$10$
- Correct answerD$12$
Solution
In a face-centered cubic (fcc) crystal lattice, the coordination number is defined as the number of nearest neighbouring spheres for any given particle.
Considering a face-centered atom, it is in contact with $4$ corner atoms in its own plane. Additionally, it is in contact with $4$ face-centered atoms in the plane immediately above it and $4$ face-centered atoms in the plane immediately below it.
Total number of nearest neighbours $= 4 + 4 + 4 = 12$.
Thus, the coordination number for any particle in an fcc lattice is $12$.
Answer: $12$
Considering a face-centered atom, it is in contact with $4$ corner atoms in its own plane. Additionally, it is in contact with $4$ face-centered atoms in the plane immediately above it and $4$ face-centered atoms in the plane immediately below it.
Total number of nearest neighbours $= 4 + 4 + 4 = 12$.
Thus, the coordination number for any particle in an fcc lattice is $12$.
Answer: $12$
Hence, the correct answer is option: 'D'.