Step 1: Understanding the Question:
The coordination number is the number of nearest neighbors an atom has in a crystal lattice. We need to determine this value specifically for the FCC arrangement. Step 2: Key Formula or Approach:
Visualize or calculate the surrounding atoms for a single atom in a close-packed lattice. FCC is also known as Cubic Close Packed (CCP). Step 3: Detailed Explanation:
1. In an FCC unit cell, atoms are at the corners and the centers of each face.
2. Consider an atom at the center of a face. It is in contact with:
- 4 atoms at the corners of its own face.
- 4 atoms at the centers of faces in the unit cell above it.
- 4 atoms at the centers of faces in the unit cell below it.
3. Summing these: \(4 + 4 + 4 = 12\).
4. Thus, each atom has 12 nearest neighbors at a distance of \(a/\sqrt{2}\). Step 4: Final Answer:
The coordination number in FCC is 12 (C).