The number of atoms per unit cell in a face-centred cube is:

Options

A. 2
B. 3
C. 4
D. 14

Answer

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

### Step-by-Step Solution:

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

2. **Count the Atoms at the Corners**:
- Each corner atom is shared among eight adjacent unit cells. Therefore, the contribution of one corner atom to the unit cell is:
\[ \text{Contribution from corners} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]

3. **Count the Atoms at the Face Centers**:
- Each face-centered atom is shared between two adjacent unit cells. Thus, the contribution of one face-centered atom to the unit cell is:
\[ \text{Contribution from face centers} = 6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Calculate the Total Number of Atoms**:
- Now, we can add the contributions from the corners and the face centers:
\[ \text{Total number of atoms per unit cell} = 1 \text{ (from corners)} + 3 \text{ (from face centers)} = 4 \text{ atoms} \]

5. **Final Answer**:
- Therefore, the total number of atoms per unit cell in a face-centered cubic structure is **4**.