In a face centred cubic (f.c.c.) arrangement, the number of atoms per unit cell is

Options

A. 8
B. 2
C. 1
D. 4

Answer

To determine the number of atoms per unit cell in a face-centered cubic (FCC) arrangement, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the FCC Structure**:
- In a face-centered cubic (FCC) unit cell, atoms are located at each of the eight corners of the cube and at the center of each of the six faces.

2. **Counting the Contribution from Corner Atoms**:
- Each corner atom is shared by eight adjacent unit cells. Therefore, the contribution of one corner atom to the unit cell is \( \frac{1}{8} \).
- Since there are 8 corners in a cube, the total contribution from the corner atoms is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \]

3. **Counting the Contribution from Face Atoms**:
- Each face atom is shared by two adjacent unit cells. Therefore, the contribution of one face atom to the unit cell is \( \frac{1}{2} \).
- Since there are 6 faces in a cube, the total contribution from the face atoms is:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \]

4. **Calculating Total Number of Atoms per Unit Cell**:
- Now, we can add the contributions from the corner and face atoms to find the total number of atoms per unit cell (Z):
\[ Z = \text{Contribution from corners} + \text{Contribution from faces} = 1 + 3 = 4 \]

5. **Conclusion**:
- Therefore, the number of atoms per unit cell in a face-centered cubic arrangement is **4**.

### Final Answer:
The number of atoms per unit cell in a face-centered cubic (FCC) arrangement is **4**.