Question

In a face-centered cubic (fcc) lattice, the number of atoms per unit cell is

• A. 4
• B. 2
• C. 1
• D. 6

Hint:

Remember that in crystal structures, atoms at the corners and faces are shared among multiple unit cells, which affects their contribution to a single unit cell.

Answer 1

The Correct Option is A

Step 1: Picture the fcc cell.
In a face centred cubic cell, atoms sit at all 8 corners and at the centre of all 6 faces. We must count how many atoms belong to one cell.
Step 2: Share of corner atoms.
Each corner atom is shared by 8 cells. So one cell gets only $\frac{1}{8}$ of each corner atom.
Step 3: Total from corners.
There are 8 corners, so the corners give\[ 8 \times \frac{1}{8} = 1 \text{ atom} \]
Step 4: Share of face atoms.
Each face atom is shared by 2 cells. So one cell gets $\frac{1}{2}$ of each face atom.
Step 5: Total from faces.
There are 6 faces, so the faces give\[ 6 \times \frac{1}{2} = 3 \text{ atoms} \]
Step 6: Add them up.
The total is corners plus faces, that is $1 + 3 = 4$ atoms per cell.\[ \boxed{4} \]