In the body centered unit cell, the lattice point are present at the:

Options

A. corners of the unit cell only
B. corners and centre of the unit cell
C. corners and centre of each face of the unit cell
D. corners and at one set of faces of unit cell

Answer

To solve the question regarding the lattice points in a body-centered unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Unit Cell**:
A unit cell is the smallest repeating unit in a crystal lattice that shows the full symmetry of the structure. In a body-centered cubic (BCC) unit cell, the arrangement of atoms is specific.

2. **Identifying Lattice Points**:
In a body-centered cubic unit cell, atoms are located at specific positions:
- **Corners of the Unit Cell**: There are 8 corners in a cubic unit cell.
- **Center of the Unit Cell**: There is 1 atom located at the center of the unit cell.

3. **Counting the Atoms**:
- Each corner atom is shared among 8 adjacent unit cells, meaning each corner contributes 1/8 of an atom to the unit cell.
- Therefore, the contribution from the 8 corner atoms is:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- The center atom is not shared and contributes fully:
\[ 1 \text{ center atom} = 1 \text{ atom} \]

4. **Total Atoms in BCC**:
Adding the contributions together gives:
\[ 1 \text{ (from corners)} + 1 \text{ (from center)} = 2 \text{ atoms} \]

5. **Conclusion**:
Thus, in a body-centered unit cell, the lattice points are present at the corners and at the center of the unit cell. Therefore, the correct answer is: **corners and center of the unit cell**.

### Final Answer:
The lattice points in a body-centered unit cell are present at the **corners and the center of the unit cell**.

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