In hexagonal close packing , the difference in the number of tetrahedral and octahedral voids per unit cell is

Explanation

To solve the problem regarding the difference in the number of tetrahedral and octahedral voids per unit cell in hexagonal close packing (HCP), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure**: In hexagonal close packing (HCP), the arrangement of atoms leads to the formation of both tetrahedral and octahedral voids.

2. **Determine the Number of Atoms per Unit Cell**: In HCP, the number of atoms per unit cell (denoted as Z) is 6. This means there are 6 atoms present in one unit cell of HCP.

3. **Calculate the Number of Octahedral Voids**: The number of octahedral voids in a close-packed structure is equal to the number of atoms present in the unit cell. Therefore, in HCP, the number of octahedral voids is also 6.

4. **Calculate the Number of Tetrahedral Voids**: The number of tetrahedral voids is twice the number of octahedral voids in close-packed structures. Thus, the number of tetrahedral voids is 2 × 6 = 12.

5. **Find the Difference**: To find the difference between the number of tetrahedral and octahedral voids, we subtract the number of octahedral voids from the number of tetrahedral voids:
\[ \text{Difference} = \text{Number of Tetrahedral Voids} - \text{Number of Octahedral Voids} = 12 - 6 = 6. \]

### Final Answer:
The difference in the number of tetrahedral and octahedral voids per unit cell in hexagonal close packing is **6**.

---