If an atom is present in the centre of the cube, the participation of that atom per unit cell is:

Options

A. `(1)/(4)`
B. 1
C. `(1)/(2)`
D. `(1)/(8)`

Answer

To determine the participation of an atom located at the center of a cube per unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure**:
- A cube has 8 corners, 6 faces, and 1 center. The atom in question is located at the center of the cube.

2. **Identify Atom Contribution**:
- The contribution of an atom to the unit cell depends on its position:
- **Corner Atom**: Each corner atom contributes \( \frac{1}{8} \) to the unit cell because it is shared among 8 adjacent unit cells.
- **Face-Centered Atom**: Each face-centered atom contributes \( \frac{1}{2} \) to the unit cell because it is shared between 2 unit cells.
- **Edge-Centered Atom**: Each edge-centered atom contributes \( \frac{1}{4} \) to the unit cell because it is shared among 4 unit cells.
- **Center Atom**: An atom at the center of the cube is entirely contained within that unit cell.

3. **Calculate Participation**:
- Since the atom is located at the center of the cube, it is not shared with any other unit cell. Therefore, its contribution to the unit cell is 1.

4. **Conclusion**:
- The participation of the atom at the center of the cube per unit cell is **1**.

### Final Answer:
The participation of the atom at the center of the cube per unit cell is **1**.

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