In a hcp arrangement, each atom at the corner contributes to the unit cell equal to

Options

A. `1//2`
B. `1//8`
C. `1//6`
D. `1//4`

Answer

To determine the contribution of each corner atom in a hexagonal close-packed (hcp) arrangement to the unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the HCP Structure**:
- The hexagonal close-packed (hcp) structure consists of layers of atoms arranged in a specific pattern. Each unit cell in this structure is defined by its hexagonal shape.

2. **Identifying Corner Atoms**:
- In the hcp arrangement, there are atoms located at the corners of the hexagonal base of the unit cell.

3. **Counting Shared Unit Cells**:
- Each corner atom is shared among multiple unit cells. Specifically, in the hcp structure, each corner atom is shared by 6 different unit cells (3 from the bottom layer and 3 from the top layer).

4. **Calculating Contribution**:
- Since each corner atom is shared by 6 unit cells, the contribution of one corner atom to a single unit cell is calculated as:
\[ \text{Contribution of one corner atom} = \frac{1}{6} \]

5. **Conclusion**:
- Therefore, the contribution of each atom at the corner of the hcp unit cell is \( \frac{1}{6} \).

### Final Answer:
The contribution of each atom at the corner of the hcp unit cell is \( \frac{1}{6} \).

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