in the cubic packing , the unit cell has ………. .

Options

A. 4 tetrahedral voids each of which is shared by four adjacent unit cells
B. 4 tetrahedral voids within the unit cell
C. 8 tetrahedral voids each of the which is shared by four adjacent unit cells
D. 8 tetrahedral voids within the unit cells.

Answer

To solve the question regarding the cubic packing and the number of tetrahedral voids in the unit cell, let's break it down step by step:

### Step-by-Step Solution:

1. **Understanding Cubic Packing**:
- Cubic packing refers to the arrangement of atoms in a three-dimensional cubic structure. The most common types of cubic packing are simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC), also known as cubic close packing (CCP).

2. **Identifying Tetrahedral Voids**:
- Tetrahedral voids are spaces in the crystal lattice where smaller atoms can fit between larger atoms. In cubic packing, these voids are formed due to the arrangement of the atoms.

3. **Analyzing the FCC Structure**:
- In the face-centered cubic (FCC) structure, there are atoms located at each corner of the cube and at the centers of each face. This arrangement creates specific voids within the unit cell.

4. **Counting Tetrahedral Voids**:
- In an FCC unit cell, there are a total of **8 tetrahedral voids**. Each body diagonal of the cube contains 2 tetrahedral voids, and since there are 4 body diagonals in the cube, the total number of tetrahedral voids is:
\[ 4 \text{ (body diagonals)} \times 2 \text{ (voids per diagonal)} = 8 \text{ tetrahedral voids} \]

5. **Determining the Sharing of Voids**:
- Each of these tetrahedral voids is located entirely within the unit cell and is not shared with adjacent unit cells. Therefore, all 8 tetrahedral voids are counted as being within the unit cell.

6. **Final Answer**:
- Based on the analysis, the correct answer to the question is that the unit cell has **8 tetrahedral voids within the unit cell**.

### Conclusion:
The answer to the question is **Option D**: "eight tetrahedral voids within the unit cell."

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