Number of atoms in fcc unit cell is

Options

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

Explanation

To determine the number of atoms in a face-centered cubic (FCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of FCC:**
- In a face-centered cubic unit cell, atoms are located at each of the eight corners of the cube and at the centers of each of the six faces.

2. **Calculate Contribution from Corner Atoms:**
- Each corner atom is shared among eight adjacent unit cells. Therefore, the contribution of one corner atom to the unit cell is \( \frac{1}{8} \).
- Since there are 8 corners in a cube, the total contribution from the corner atoms is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \]

3. **Calculate Contribution from Face-Centered Atoms:**
- Each face-centered atom is shared between two unit cells. Thus, the contribution of one face-centered atom to the unit cell is \( \frac{1}{2} \).
- Since there are 6 faces in a cube, the total contribution from the face-centered atoms is:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \]

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

Thus, the total number of atoms in a face-centered cubic unit cell is **4**.

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

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