In a face centred cubic lattice unit cell is shared equally by how many unit cells?

Options

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

Explanation

To solve the question of how many unit cells share a face-centered cubic (FCC) lattice unit cell equally, we can follow these steps:

### Step 1: Understand the Structure of FCC
A face-centered cubic (FCC) lattice has atoms located at each of the corners of the cube and at the centers of each of the cube's faces.

### Step 2: Identify the Faces of the Cube
In a cubic lattice, there are a total of 6 faces. Each face of the cube has one atom located at its center.

### Step 3: Determine Sharing of Atoms
Each face-centered atom is shared between two adjacent unit cells. Therefore, each face-centered atom contributes half of its volume to each of the two unit cells it is shared with.

### Step 4: Calculate the Total Sharing
Since there are 6 faces in a face-centered cubic lattice and each face-centered atom is shared equally between 2 unit cells, we can conclude that each face-centered atom is effectively shared by 2 unit cells.

### Step 5: Conclusion
Thus, the face-centered cubic lattice unit cell is shared equally by **6 unit cells**.

### Final Answer
The answer is **6 unit cells**.

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