Face-centred cubic packing of uniform spherical units is represented by

Options

A. ABAB......
B. ABBAAB...
C. ABCABC.......
D. ABCACBABA.....

Explanation

To solve the question regarding the face-centered cubic (FCC) packing of uniform spherical units, we can break down the solution into several steps:

### Step-by-Step Solution:

1. **Understanding the Structure**:
- In a face-centered cubic (FCC) structure, atoms are located at each of the corners of the cube and at the center of each face of the cube.

**Hint**: Visualize a cube and identify where the atoms are positioned.

2. **Counting the Atoms**:
- Each corner atom is shared by eight adjacent cubes, contributing \( \frac{1}{8} \) of an atom per cube.
- There are 8 corner atoms: \( 8 \times \frac{1}{8} = 1 \) atom from corners.
- Each face-centered atom is shared by two cubes, contributing \( \frac{1}{2} \) of an atom per cube.
- There are 6 face-centered atoms: \( 6 \times \frac{1}{2} = 3 \) atoms from faces.
- Total number of atoms in one FCC unit cell = \( 1 + 3 = 4 \) atoms.

**Hint**: Remember how atoms are shared between unit cells when counting.

3. **Layer Arrangement**:
- The arrangement of atoms in an FCC structure can be represented in layers. The layers can be denoted as A, B, and C.
- The sequence of stacking is such that the first layer is A, the second layer is B (offset), and the third layer is C (offset again), and this pattern repeats.

**Hint**: Think of how layers stack like pancakes, where each layer is slightly offset.

4. **Identifying the Repeating Pattern**:
- The repeating pattern of the layers in FCC is A-B-C. This means that after the third layer (C), the sequence starts again with A.

**Hint**: Look for the sequence that continues indefinitely in the structure.

5. **Conclusion**:
- Therefore, the face-centered cubic packing of uniform spherical units is represented by the repeating sequence A-B-C.

**Final Answer**: The correct representation of the face-centered cubic packing is A-B-C.