Whenever two-demiensional square packing same layers are kept in the way so that the centres are aligned in all three dimensation, coordination numberof each sphere is

Options

A. 6
B. 8
C. 12
D. 10

Explanation

To solve the problem of determining the coordination number of each sphere in a three-dimensional arrangement of two-dimensional square packing, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the 2D Square Packing**:
- In a two-dimensional square packing, each sphere (or atom) is surrounded by four other spheres in the same layer. This arrangement forms a square grid.

2. **Visualize the 3D Arrangement**:
- When layers of this 2D square packing are stacked on top of each other, the centers of the spheres in adjacent layers align vertically.

3. **Identify the Spheres Around a Given Sphere**:
- For a sphere located in the middle of a layer:
- It is in contact with 4 spheres in the same layer (the ones directly adjacent to it).
- There is 1 sphere directly above it in the layer above.
- There is 1 sphere directly below it in the layer below.

4. **Calculate the Coordination Number**:
- The coordination number is defined as the total number of nearest neighbors surrounding a sphere.
- Therefore, for the sphere in question:
- Neighbors in the same layer: 4
- Neighbors in the layer above: 1
- Neighbors in the layer below: 1
- Adding these together gives:
\[ \text{Coordination Number} = 4 (\text{same layer}) + 1 (\text{above}) + 1 (\text{below}) = 6 \]

5. **Conclusion**:
- The coordination number of each sphere in this three-dimensional arrangement of two-dimensional square packing is **6**.

### Final Answer:
The coordination number of each sphere is **6**.

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