In which of the following crystal system F.C.C unit cells exists?

Options

A. Cubic, hexagonal
B. Tetragonal, orthorhombic
C. Orthorhobic , cubic
D. Triclinic, monoclinic

Answer

To determine in which crystal systems the Face-Centered Cubic (F.C.C) unit cell exists, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the F.C.C Structure**:
- The F.C.C unit cell has atoms located at each of the corners of the cube and at the centers of each of the cube's faces. This arrangement leads to a high packing efficiency.

2. **Identifying Crystal Systems**:
- There are seven crystal systems: Cubic, Tetragonal, Orthorhombic, Hexagonal, Rhombohedral, Monoclinic, and Triclinic.

3. **Analyzing the Crystal Systems**:
- **Cubic System**: This system includes the F.C.C structure as it is one of the two types of cubic unit cells (the other being Body-Centered Cubic, B.C.C).
- **Orthorhombic System**: This system does not contain the F.C.C structure as it has a different arrangement of atoms.
- **Tetragonal System**: Similar to orthorhombic, this system does not support the F.C.C arrangement.
- **Hexagonal System**: This system also does not include the F.C.C structure.
- **Rhombohedral System**: This system does not contain the F.C.C structure.
- **Monoclinic System**: This system does not contain the F.C.C structure.
- **Triclinic System**: This system does not contain the F.C.C structure.

4. **Conclusion**:
- The F.C.C unit cell is specifically found in the **Cubic** crystal system. Therefore, the answer to the question is that the F.C.C unit cell exists in the **Cubic** system.

### Final Answer:
The F.C.C unit cell exists in the **Cubic** crystal system.

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