The number of nearest neighbours of each sphere in hexagonal closed packing pattern in its own layer will be

Options

A. 4
B. `6`
C. `12`
D. `8`

Answer

To determine the number of nearest neighbors of each sphere in the hexagonal closed packing (HCP) pattern in its own layer, we can follow these steps:

### Step 1: Understand the Structure of HCP
Hexagonal close packing (HCP) consists of layers of spheres arranged in a specific pattern. The arrangement is AB-AB type, meaning that the first layer (A) is followed by a second layer (B), and then the third layer (C) is identical to the first layer (A).

**Hint:** Remember that in HCP, the arrangement alternates between two types of layers (A and B).

### Step 2: Analyze One Layer
In one layer (let’s consider the A layer), each sphere is surrounded by other spheres. The arrangement is such that each sphere in the layer touches other spheres.

**Hint:** Visualize the arrangement of spheres in a 2D plane to see how they are positioned relative to each other.

### Step 3: Count the Nearest Neighbors
In the A layer, if you select one sphere, it will be surrounded by 6 other spheres that are in the same layer. These spheres are positioned around the selected sphere in a hexagonal formation.

**Hint:** Count the spheres that are directly adjacent to the chosen sphere in the layer.

### Step 4: Conclusion
Thus, the number of nearest neighbors of each sphere in the hexagonal closed packing pattern in its own layer is 6.

**Final Answer:** The number of nearest neighbors of each sphere in hexagonal closed packing in its own layer is **6**.