Question

The number of lattice points in a face-centered cubic (FCC) unit cell is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Remember: FCC unit cell = 4 atoms, BCC = 2 atoms, Simple cubic = 1 atom.

Answer 1

The Correct Option is D

Step 1: Atoms in corners.
Each FCC unit cell has atoms at 8 corners. Contribution from each corner = $\tfrac{1}{8}$. \[ 8 \times \tfrac{1}{8} = 1 \ \text{atom from corners} \]

Step 2: Atoms on faces.
Each of the 6 faces has one atom at its center. Contribution from each face = $\tfrac{1}{2}$. \[ 6 \times \tfrac{1}{2} = 3 \ \text{atoms from faces} \]

Step 3: Total lattice points.
\[ 1 + 3 = 4 \]

Final Answer:
\[ \boxed{4} \]