An element crystallises in a faces centered cubic lattice. Hence, its unit cell contains

Options

A. 14 atoms of the element and 8 of them belong to the unit cell
B. 14 atoms of the element and 4 of them belongs to the unit cell
C. 8 atoms of the unit cell and only 1 of them belongs to the cell
D. 8 atoms of the unit cell and only 2 of them belong to the cell

Answer

To determine how many atoms are present in a unit cell of a face-centered cubic (FCC) lattice, we can follow these steps:

### Step 1: Understand the Structure of FCC
In a face-centered cubic lattice, atoms are located at the corners of the cube and at the centers of each face of the cube.

### Step 2: Count the Atoms at the Corners
There are 8 corners in a cube. Each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is:
\[ \text{Contribution from corner atoms} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

### Step 3: Count the Atoms on the Faces
There are 6 faces in a cube, and each face atom is shared by 2 adjacent unit cells. Therefore, the contribution of each face atom to the unit cell is:
\[ \text{Contribution from face atoms} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]

### Step 4: Calculate Total Atoms in the Unit Cell
Now, we can add the contributions from the corner and face atoms to find the total number of atoms in the unit cell:
\[ \text{Total atoms in the unit cell} = 1 + 3 = 4 \text{ atoms} \]

### Step 5: Conclusion
Thus, in a face-centered cubic lattice, the unit cell contains a total of 4 atoms.

### Final Answer
The unit cell of an element crystallizing in a face-centered cubic lattice contains **4 atoms**.

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