In a hexagonal closest packing in two layers one above the other, the coordination number of each sphere will be 

Options

A. 4
B. 6
C. 8
D. 9

Answer

To determine the coordination number of each sphere in a hexagonal closest packing (HCP) arrangement with two layers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Hexagonal Closest Packing (HCP)**:
- In HCP, the spheres are arranged in a way that maximizes the packing efficiency. The arrangement consists of alternating layers of spheres.

2. **Identifying the Layers**:
- In HCP, there are two types of layers: Layer A and Layer B. The spheres in Layer A are positioned in the gaps of Layer B and vice versa.

3. **Coordination Number Definition**:
- The coordination number of an atom (or sphere) is defined as the number of nearest neighbor atoms (or spheres) that are in contact with it.

4. **Counting Neighbors**:
- Each sphere in Layer A is in contact with:
- **6 spheres in the same layer (Layer A)**: These are the neighboring spheres that form a hexagonal arrangement around it.
- **6 spheres in the layer directly above (Layer B)**: Each sphere in Layer A is directly above a sphere in Layer B.
- **6 spheres in the layer directly below (Layer B)**: Each sphere in Layer A is also directly below a sphere in Layer B.

5. **Calculating the Total Coordination Number**:
- Therefore, the total coordination number for each sphere in HCP is:
\[ \text{Coordination Number} = 6 \text{ (from Layer A)} + 6 \text{ (from Layer B)} = 12 \]

6. **Conclusion**:
- Thus, the coordination number of each sphere in hexagonal closest packing in two layers is **12**.

### Final Answer:
The coordination number of each sphere in hexagonal closest packing in two layers is **12**.

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