The number of atoms present in FCC unit cells.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the number of atoms present in a Face-Centered Cubic (FCC) unit cell, we can break down the calculation step by step.

### Step-by-Step Solution:

1. **Understanding the FCC Structure**:
- In an FCC unit cell, atoms are located at each of the corners of the cube and at the center of each face of the cube.

2. **Counting Corner Atoms**:
- There are 8 corners in a cube.
- Each corner atom is shared among 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Total contribution from corner atoms:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]

3. **Counting Face-Centered Atoms**:
- There are 6 faces on a cube.
- Each face-centered atom is shared between 2 adjacent unit cells. Therefore, the contribution of each face-centered atom to the unit cell is \( \frac{1}{2} \).
- Total contribution from face-centered atoms:
\[ 6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Total Number of Atoms in FCC Unit Cell**:
- Now, we add the contributions from the corner atoms and the face-centered atoms:
\[ 1 \text{ (from corners)} + 3 \text{ (from faces)} = 4 \text{ atoms} \]

### Final Answer:
The total number of atoms present in an FCC unit cell is **4**.

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