In the face centered per unit cell, the lattice points are present at the:

Options

A. corners of unit cell only
B. corners and centre of the unit cell
C. corners and centre of each face of the unit cell
D. face centres of the unit cell

Answer

To solve the question regarding the location of lattice points in a face-centered unit cell, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Unit Cell Structure**:
- A face-centered cubic (FCC) unit cell is a type of crystal structure. It consists of atoms located at specific positions within the cube.

2. **Identifying the Lattice Points**:
- In a face-centered unit cell, there are lattice points located at:
- The **corners** of the cube.
- The **centers of each face** of the cube.

3. **Counting the Lattice Points**:
- **Corners**: A cube has 8 corners. Each corner atom is shared among 8 adjacent unit cells, contributing 1/8 of an atom to each unit cell.
- **Face Centers**: A cube has 6 faces. Each face-centered atom is shared between 2 adjacent unit cells, contributing 1/2 of an atom to each unit cell.

4. **Calculating Total Contribution**:
- From the corners: \(8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom}\)
- From the face centers: \(6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms}\)
- Total atoms in a face-centered unit cell = \(1 + 3 = 4 \text{ atoms}\)

5. **Conclusion**:
- Therefore, in a face-centered unit cell, the lattice points are present at the corners and the center of each face of the unit cell.

### Final Answer:
The correct option is: **Corners and center of each face of the unit cell**.

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