The number of octahedral voids in a unit cell of a cubical closest packed structure is:

Options

A. 1
B. 2
C. 4
D. 8

Answer

To find the number of octahedral voids in a unit cell of a cubical closest packed structure, we can follow these steps:

### Step 1: Understand the Structure
In a cubical closest packed (CCP) structure, also known as face-centered cubic (FCC), the arrangement of atoms creates specific types of voids. The two main types of voids are tetrahedral and octahedral voids.

### Step 2: Identify the Location of Octahedral Voids
In a CCP structure, octahedral voids are located:
- At the center of the cube (1 void).
- At the edge centers (12 edges in total).

### Step 3: Calculate the Contribution from Edge Centers
Each edge of the cube has an octahedral void located at its center. However, each edge center is shared by 4 adjacent unit cells. Therefore, the contribution from the edge centers is calculated as follows:
- Number of edge centers = 12
- Contribution from each edge center = 1/4 (since it is shared by 4 unit cells)

So, the total contribution from the edge centers is:
\[ \text{Total from edge centers} = 12 \times \frac{1}{4} = 3 \]

### Step 4: Add the Contribution from the Body Center
There is 1 octahedral void at the body center of the cube.

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

### Conclusion
Therefore, the total number of octahedral voids in a unit cell of a cubical closest packed structure is **4**.

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