In 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 solve the question regarding the contribution of corner atoms in a hexagonal close-packed (hcp) arrangement, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding the HCP Structure**:
- The hexagonal close-packed (hcp) structure is a type of crystal lattice arrangement where atoms are closely packed together. It has a specific arrangement that includes layers of atoms.

2. **Identifying the Unit Cell**:
- In an hcp structure, the unit cell consists of a hexagonal base and two layers of atoms. Each unit cell contains a specific number of atoms.

3. **Counting the Corner Atoms**:
- In the hcp arrangement, there are 12 corner atoms in total: 6 in the top layer and 6 in the bottom layer.

4. **Contribution of Each Corner Atom**:
- Each corner atom is shared among adjacent unit cells. Specifically, each corner atom contributes only a fraction of its total volume to a single unit cell.
- Since each corner atom is shared by 6 different unit cells, the contribution of each corner atom to the unit cell is calculated as:
\[ \text{Contribution of each corner atom} = \frac{1}{6} \]

5. **Conclusion**:
- Therefore, in the hcp arrangement, each atom at the corner contributes \( \frac{1}{6} \) to the unit cell.

### Final Answer:
In hcp arrangement, each atom at the corner contributes to the unit cell equal to \( \frac{1}{6} \).

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