Question

Calculate the number of atoms per unit cell in a Face-Centered Cubic (FCC) crystal structure.

• A. \(2\)
• B. \(4\)
• C. \(6\)
• D. \(8\)

Hint:

Remember common crystal structures: SC \(=1\), BCC \(=2\), FCC \(=4\) atoms per unit cell.

Answer 1

The Correct Option is B

Concept: In a Face-Centered Cubic (FCC) crystal structure:
• Atoms are present at the 8 corners
• Atoms are also present at the 6 faces Each corner atom is shared by 8 unit cells and each face-centered atom is shared by 2 unit cells.

Step 1: Contribution of corner atoms. \[ 8 \times \frac{1}{8} = 1 \]

Step 2: Contribution of face-centered atoms. \[ 6 \times \frac{1}{2} = 3 \]

Step 3: Total number of atoms in the unit cell. \[ 1 + 3 = 4 \] Thus, \[ \boxed{4} \]