How many space lattices are obtainable from the different crystal systems.

Options

A. 7
B. 14
C. 32
D. 230

Answer

To determine how many space lattices can be obtained from the different crystal systems, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Crystal Systems**:
There are 7 crystal systems in three-dimensional space:
- Cubic
- Tetragonal
- Orthorhombic
- Hexagonal
- Rhombohedral
- Monoclinic
- Triclinic

2. **Identify the Bravais Lattices**:
Each crystal system can be associated with specific Bravais lattices. A Bravais lattice is a set of points generated by a set of discrete translation operations.

3. **List the Bravais Lattices for Each Crystal System**:
- **Cubic**:
- Simple Cubic (SC)
- Body-Centered Cubic (BCC)
- Face-Centered Cubic (FCC)
- **Tetragonal**:
- Simple Tetragonal (ST)
- Body-Centered Tetragonal (BCT)
- **Orthorhombic**:
- Simple Orthorhombic (SO)
- Body-Centered Orthorhombic (BCO)
- Face-Centered Orthorhombic (FCO)
- End-Centered Orthorhombic (ECO)
- **Hexagonal**:
- Simple Hexagonal (SH)
- **Rhombohedral**:
- Simple Rhombohedral (SR)
- **Monoclinic**:
- Simple Monoclinic (SM)
- Base-Centered Monoclinic (BCM)
- **Triclinic**:
- Simple Triclinic (ST)

4. **Count the Total Bravais Lattices**:
By counting the Bravais lattices listed above, we find:
- Cubic: 3
- Tetragonal: 2
- Orthorhombic: 4
- Hexagonal: 1
- Rhombohedral: 1
- Monoclinic: 2
- Triclinic: 1

Adding these gives:
\( 3 + 2 + 4 + 1 + 1 + 2 + 1 = 14 \)

5. **Conclusion**:
Therefore, the total number of space lattices obtainable from the different crystal systems is **14**.