How many nearest neighbours surround each ion in a face-centered cubic lattice of an ionic crystal ?

Options

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

Answer

To determine how many nearest neighbors surround each ion in a face-centered cubic (FCC) lattice of an ionic crystal, we can follow these steps:

### Step 1: Understand the Structure of FCC
A face-centered cubic lattice has atoms located at each of the corners of the cube and at the center of each face of the cube.

### Step 2: Identify the Nearest Neighbors
In an FCC lattice, each ion (or atom) at the corner of the cube is surrounded by ions located at the centers of the adjacent faces. Specifically, each corner ion has:

- 3 nearest neighbors from the face centers on the same face.
- 1 nearest neighbor from the face center on the opposite face.

### Step 3: Count the Nearest Neighbors
For each corner ion in an FCC lattice:
- There are 4 face-centered ions that are in close proximity to the corner ion.

Thus, each ion in an FCC lattice has **12 nearest neighbors**.

### Step 4: Conclusion
Therefore, the number of nearest neighbors surrounding each ion in a face-centered cubic lattice of an ionic crystal is **12**.

### Final Answer
**12 nearest neighbors.**

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