Which of the following crystal systems has maximum number of Bravais lattices?

Options

A. (a) Cubic
B. (b) Hexagonal
C. (c) Triclinic
D. (d) Orthorhombic

Answer

To determine which crystal system has the maximum number of Bravais lattices, we need to analyze the different crystal systems and the types of Bravais lattices associated with each.

### Step-by-Step Solution:

1. **Identify the Crystal Systems**:
There are seven crystal systems in total:
- Cubic
- Tetragonal
- Orthorhombic
- Hexagonal
- Rhombohedral (or Trigonal)
- Monoclinic
- Triclinic

2. **List the Bravais Lattices**:
Bravais lattices are the distinct lattice types that can be formed in three-dimensional space. There are 14 Bravais lattices in total, which can be categorized under the seven crystal systems.

3. **Count Bravais Lattices in Each System**:
- **Cubic**: 3 types (Simple Cubic, Body-Centered Cubic (BCC), Face-Centered Cubic (FCC))
- **Tetragonal**: 2 types (Simple Tetragonal, Body-Centered Tetragonal)
- **Orthorhombic**: 4 types (Simple Orthorhombic, Body-Centered Orthorhombic, Face-Centered Orthorhombic, End-Centered Orthorhombic)
- **Hexagonal**: 1 type (Simple Hexagonal)
- **Rhombohedral**: 1 type (Simple Rhombohedral)
- **Monoclinic**: 2 types (Simple Monoclinic, Base-Centered Monoclinic)
- **Triclinic**: 1 type (Simple Triclinic)

4. **Determine the Maximum**:
From the counts above, we see that:
- Cubic has 3
- Tetragonal has 2
- Orthorhombic has 4
- Hexagonal has 1
- Rhombohedral has 1
- Monoclinic has 2
- Triclinic has 1

The Orthorhombic system has the maximum number of Bravais lattices, which is 4.

5. **Conclusion**:
Therefore, the crystal system with the maximum number of Bravais lattices is **Orthorhombic**.