Which of the following statements is correct for a two-dimensional haxagonal close-packed layer?

Options

A. Each sphere is surrounded by six spheres
B. Each sphere is surrounded by six voids
C. Each sphere has three voids
D. Each voids is surrounded by three spheres

Explanation

To determine which statement is correct for a two-dimensional hexagonal close-packed (HCP) layer, let's analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Hexagonal Close Packing (HCP):**
- In a two-dimensional hexagonal close-packed structure, spheres (or atoms) are arranged in a hexagonal pattern. Each layer is typically denoted as A, B, and so on, forming an ABAB pattern.

2. **Analyzing the Statements:**
- **Statement 1:** Each sphere is surrounded by six spheres.
- In a 2D HCP layer, each sphere is indeed surrounded by six other spheres. This is a characteristic of the hexagonal arrangement.
- **Conclusion:** This statement is **correct**.

- **Statement 2:** Each sphere is surrounded by six voids.
- In the hexagonal close packing, the voids are the spaces between the spheres. Each sphere is not surrounded by voids; rather, it is surrounded by other spheres.
- **Conclusion:** This statement is **incorrect**.

- **Statement 3:** Each sphere has three voids.
- In a hexagonal arrangement, while there are voids present, each sphere does not have three voids directly associated with it. The voids are formed between the spheres, and the number can vary based on the arrangement.
- **Conclusion:** This statement is **incorrect**.

- **Statement 4:** Each void is surrounded by three spheres.
- In a 2D hexagonal close-packed structure, each void is indeed surrounded by three spheres. This is a defining feature of the arrangement.
- **Conclusion:** This statement is **correct**.

3. **Final Evaluation:**
- From the analysis, we find that **Statement 1** and **Statement 4** are correct.

### Final Answer:
The correct statements for a two-dimensional hexagonal close-packed layer are:
- Each sphere is surrounded by six spheres (Statement 1).
- Each void is surrounded by three spheres (Statement 4).