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

Options

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

Answer

To determine in which crystal systems the Face-Centered Cubic (FCC) unit cells exist, we will analyze each of the mentioned crystal systems step by step.

### Step 1: Understand the Crystal Systems
The main crystal systems include:
1. Cubic
2. Tetragonal
3. Orthorhombic
4. Rhombohedral (Trigonal)
5. Hexagonal
6. Monoclinic
7. Triclinic

### Step 2: Identify the Unit Cells in Each Crystal System
- **Cubic**: In the cubic crystal system, there are three types of unit cells:
- Simple Cubic
- Body-Centered Cubic (BCC)
- Face-Centered Cubic (FCC)

- **Tetragonal**: In the tetragonal system, the unit cells are:
- Primitive (Simple)
- Body-Centered

- **Orthorhombic**: In the orthorhombic system, the unit cells include:
- Simple Cubic
- Body-Centered
- Face-Centered
- End-Centered

- **Rhombohedral (Trigonal)**: In this system, the only unit cell is:
- Simple Cubic

- **Hexagonal**: The hexagonal system has:
- Primitive (Simple)

- **Monoclinic**: In the monoclinic system, the unit cells are:
- Simple Cubic
- End-Centered

- **Triclinic**: The triclinic system has:
- Primitive (Simple)

### Step 3: Determine the Presence of FCC Unit Cells
Now, we need to check in which of these systems the FCC unit cell exists:
- **Cubic**: Yes, FCC exists.
- **Tetragonal**: No, FCC does not exist.
- **Orthorhombic**: Yes, FCC exists.
- **Rhombohedral (Trigonal)**: No, FCC does not exist.
- **Hexagonal**: No, FCC does not exist.
- **Monoclinic**: No, FCC does not exist.
- **Triclinic**: No, FCC does not exist.

### Conclusion
The FCC unit cell exists in the **Cubic** and **Orthorhombic** crystal systems.

### Final Answer
The correct options where FCC unit cells exist are **Cubic and Orthorhombic**.

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