In a cubic crystal structure, divalent metal-ion is located at the body -centered position, the smaller tetravalent metal ions are located at each corner and the `O^(2-)` ions are located half way along each of the edges of the cube. The number of nearest neighbour for oxygen is

Options

A. 4
B. 6
C. 2
D. 8

Answer

To find the number of nearest neighbors for the \( O^{2-} \) ions located at the edge centers of a cubic crystal structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the positions of the ions:**
- The divalent metal ion is located at the body center of the cube.
- The tetravalent metal ions are located at each of the eight corners of the cube.
- The \( O^{2-} \) ions are located at the midpoints of each edge of the cube.

2. **Determine the number of nearest neighbors for \( O^{2-} \):**
- Each edge of the cube has an \( O^{2-} \) ion at its center.
- Each edge center \( O^{2-} \) ion is shared by four unit cells, but for the purpose of finding nearest neighbors, we only need to consider the atoms that are closest to it.

3. **Analyze the nearest neighbors:**
- For an \( O^{2-} \) ion located at the center of an edge, the nearest neighbors will be the two corner ions that are located at the ends of that edge.
- Since there are two corners at either end of the edge where the \( O^{2-} \) ion is located, these two corner ions are the nearest neighbors.

4. **Count the nearest neighbors:**
- Therefore, the total number of nearest neighbors for each \( O^{2-} \) ion at the edge center is **2**.

### Final Answer:
The number of nearest neighbors for the \( O^{2-} \) ions is **2**.

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