In hexagonal primitive unit cell, the Corner is shared by:

Options

A. 4 unit cells
B. 6 unit cells
C. 3 unit cells
D. 8 unit cells

Answer

To solve the question regarding the sharing of atoms in a hexagonal primitive unit cell, we can break down the process step-by-step.

### Step-by-Step Solution:

1. **Understanding the Structure**:
- A hexagonal primitive unit cell consists of atoms located at specific positions: corners, faces, and the center.

2. **Counting Corner Atoms**:
- In a hexagonal unit cell, there are 12 corner atoms.
- Each corner atom is shared among 6 adjacent unit cells.
- Therefore, the contribution of corner atoms to the unit cell is calculated as:
\[ \text{Contribution from corner atoms} = \frac{12 \text{ corner atoms}}{6} = 2 \text{ atoms} \]

3. **Counting Face Atoms**:
- There are 2 face atoms in a hexagonal unit cell.
- Each face atom is shared between 2 unit cells.
- Thus, the contribution from face atoms is:
\[ \text{Contribution from face atoms} = \frac{2 \text{ face atoms}}{2} = 1 \text{ atom} \]

4. **Counting Center Atoms**:
- In a hexagonal primitive unit cell, there are 3 center atoms.
- These center atoms are not shared with any other unit cell, so their contribution is:
\[ \text{Contribution from center atoms} = 3 \text{ atoms} \]

5. **Total Number of Atoms**:
- Now, we can sum up the contributions from corner, face, and center atoms to find the total number of atoms in the hexagonal primitive unit cell:
\[ \text{Total atoms} = \text{Contribution from corner atoms} + \text{Contribution from face atoms} + \text{Contribution from center atoms} \]
\[ \text{Total atoms} = 2 + 1 + 3 = 6 \text{ atoms} \]

6. **Conclusion**:
- Therefore, in a hexagonal primitive unit cell, the corners are shared by a total of 6 atoms.

### Final Answer:
The corners in a hexagonal primitive unit cell are shared by a total of 6 atoms.

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