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

Options

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

Answer

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

### Step 1: Understand the FCC Structure
In a face-centered cubic (FCC) unit cell, atoms are located at each of the corners and at the center of each face of the cube.

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

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

### Step 4: Calculate the Total Number of Atoms
Now, we can add the contributions from the corner and face-centered atoms:
\[ \text{Total effective number of atoms} = \text{Contribution from corners} + \text{Contribution from faces} = 1 + 3 = 4 \text{ atoms} \]

### Conclusion
Thus, the effective number of atoms in a face-centered cubic unit cell of aluminum is **4**.

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