A fcc unit cell of aluminium contains effectively how many atoms?

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the FCC Structure**:
- An FCC unit cell is a cube where atoms are located at each of the eight corners and at the center of each of the six faces.

2. **Count the Corner Atoms**:
- Each corner atom is shared by 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:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

3. **Count the Face-Centered Atoms**:
- Each face-centered atom is shared by two adjacent unit cells. Therefore, 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:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]

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

### Final Answer:
The FCC unit cell of aluminum contains effectively **4 atoms**.

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