Total number of octahedral voids present per unit cell of ccp unit cell is

Options

A. 8
B. 9
C. 12
D. 4

Answer

To find the total number of octahedral voids present per unit cell of a CCP (Cubic Close Packing) unit cell, which is equivalent to the FCC (Face-Centered Cubic) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the CCP/FCC Unit Cell**:
- The CCP unit cell is the same as the FCC unit cell. In an FCC unit cell, atoms are located at the corners and the centers of each face of the cube.

2. **Identifying the Positions of Octahedral Voids**:
- There are two main positions where octahedral voids are found in the FCC unit cell:
- At the body center of the cube.
- At the edge centers of the cube.

3. **Calculating the Contribution from the Body Center**:
- There is **1 body center** in the cube, and since it belongs entirely to that unit cell, its contribution to the number of octahedral voids is **1**.

4. **Calculating the Contribution from Edge Centers**:
- There are **12 edges** in a cube.
- Each edge center is shared by **4 unit cells**. Therefore, the contribution from each edge center is **1/4**.
- Total contribution from edge centers = Number of edges × Contribution per edge center = \(12 \times \frac{1}{4} = 3\).

5. **Total Number of Octahedral Voids**:
- Now, we can sum the contributions from the body center and the edge centers:
\[ \text{Total octahedral voids} = \text{Contribution from body center} + \text{Contribution from edge centers} = 1 + 3 = 4. \]

6. **Conclusion**:
- Therefore, the total number of octahedral voids present per unit cell of a CCP unit cell is **4**.

### Final Answer:
The total number of octahedral voids present per unit cell of a CCP unit cell is **4**.

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