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 cubic close-packed (ccp) unit cell, we can follow these steps:

### Step 1: Understand the Structure of ccp Unit Cell
The cubic close-packed (ccp) structure, also known as face-centered cubic (fcc), consists of atoms located at each of the corners and the centers of each face of the cube.

### Step 2: Identify the Locations of Octahedral Voids
In a ccp unit cell, octahedral voids are formed in two main locations:
1. At the center of the unit cell (1 void).
2. At the edge centers of the cube (12 edges).

### Step 3: Calculate the Contribution of Edge Center Voids
Each edge of the cube has an octahedral void located at its center. Since there are 12 edges in a cube, we have:
- Total edge voids = 12

However, each edge void is shared among 4 adjacent unit cells. Therefore, the contribution of each edge void to the unit cell is:
- Contribution per edge void = 1/4

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

### Step 4: Calculate the Contribution of the Body Center Void
There is 1 octahedral void located at the center of the unit cell. This void is not shared with any other unit cell, so its contribution is:
- Contribution from body center void = 1

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

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

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