The maximum number of Bravais lattices is shown by tetragonal-type crystals.State whether the given statement is true or false.

Explanation

To determine whether the statement "The maximum number of Bravais lattices is shown by tetragonal-type crystals" is true or false, we can follow these steps:

### Step 1: Understand Bravais Lattices
Bravais lattices are distinct arrangements of points in space that can be used to describe the periodic structure of a crystal. There are 14 unique Bravais lattices in three-dimensional space.

### Step 2: Identify Tetragonal Lattices
Tetragonal crystals can be classified into two types of Bravais lattices:
1. **Primitive Tetragonal (P)**: This lattice has lattice points only at the corners of the unit cell.
2. **Body-Centered Tetragonal (I)**: This lattice has lattice points at the corners and one additional point at the center of the body of the unit cell.

Thus, tetragonal crystals can exhibit a total of **two Bravais lattices**.

### Step 3: Compare with Other Crystal Systems
Next, we compare the tetragonal system with other crystal systems:
- **Cubic**: 3 Bravais lattices (Primitive, Body-Centered, Face-Centered)
- **Orthorhombic**: 4 Bravais lattices (Primitive, Body-Centered, Face-Centered, and Base-Centered)
- **Hexagonal**: 2 Bravais lattices (Primitive and Base-Centered)
- **Rhombohedral**: 1 Bravais lattice (Primitive)
- **Monoclinic**: 2 Bravais lattices (Primitive and Base-Centered)
- **Triclinic**: 1 Bravais lattice (Primitive)

From this comparison, we see that the orthorhombic system has the maximum number of Bravais lattices, which is **four**.

### Step 4: Conclusion
Since the statement claims that tetragonal-type crystals show the maximum number of Bravais lattices, and we have established that orthorhombic crystals show more, we conclude that the statement is **false**.

### Final Answer
The statement is **false**. The maximum number of Bravais lattices is shown by orthorhombic-type crystals, not tetragonal-type crystals.

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