Choose the correct statements

Options

A. equivalent points in unit cells of a periodic lattice lie on a Bravais lattice
B. equivalent points in unit cells of a periodic lattice do not lie on a Bravais lattice
C. There are four Bravais lattices in two dimension
D. There are five Bravais lattices in three dimensions

Answer

To solve the question of choosing the correct statements regarding Bravais lattices, we will analyze each option provided and determine its validity step by step.

### Step-by-Step Solution:

1. **Understanding Bravais Lattices**:
- Bravais lattices are a set of distinct lattice points that can be used to describe the periodic arrangement of atoms in a crystal. There are 14 distinct Bravais lattices in three dimensions.

2. **Analyzing Option 1**:
- **Statement**: "Equivalent points in unit cells of a periodic lattice lie on a Bravais lattice."
- **Evaluation**: This statement is true. Equivalent points in a unit cell represent the same type of lattice points, and they do indeed lie on a Bravais lattice, which is defined by its periodicity and symmetry.

3. **Analyzing Option 2**:
- **Statement**: "Equivalent points in unit cells of a periodic lattice do not lie on a Bravais lattice."
- **Evaluation**: This statement is false. As established in the evaluation of Option 1, equivalent points do lie on a Bravais lattice.

4. **Analyzing Option 3**:
- **Statement**: "There are four Bravais lattices in two dimensions."
- **Evaluation**: This statement is also false. In two dimensions, there are five Bravais lattices, not four.

5. **Analyzing Option 4**:
- **Statement**: "There are five Bravais lattices in three dimensions."
- **Evaluation**: This statement is incorrect. There are seven types of Bravais lattices in three dimensions.

### Conclusion:
Based on the evaluations:
- The only correct statement is **Option 1**: "Equivalent points in unit cells of a periodic lattice lie on a Bravais lattice."