Maximum possible numbers of two dimensional and three dimensional lattices are respectively

Options

A. 5 and 14
B. 7 and 14
C. 14 and 4
D. 5 and 13

Answer

To solve the question regarding the maximum possible numbers of two-dimensional and three-dimensional lattices, we can break it down into a step-by-step approach.

### Step-by-Step Solution:

1. **Understanding Lattices**:
- A lattice is a regular arrangement of points in space. In two dimensions, these points can be arranged in various patterns, while in three dimensions, they can be arranged in even more complex ways.

2. **Identifying Two-Dimensional Lattices**:
- We can list the common types of two-dimensional lattices:
1. Square Lattice
2. Rectangular Lattice
3. Centered Rectangular Lattice
4. Hexagonal Lattice
5. Parallelogram Lattice
- **Total for 2D**: There are 5 distinct types of two-dimensional lattices.

3. **Identifying Three-Dimensional Lattices**:
- Next, we can list the common types of three-dimensional lattices:
1. Simple Cubic Lattice
2. Body-Centered Cubic Lattice
3. Face-Centered Cubic Lattice
4. Simple Tetragonal Lattice
5. Body-Centered Tetragonal Lattice
6. Simple Orthorhombic Lattice
7. Body-Centered Orthorhombic Lattice
8. Face-Centered Orthorhombic Lattice
9. Simple Monoclinic Lattice
10. Base-Centered Monoclinic Lattice
11. Rhombohedral Lattice
12. Hexagonal Lattice
13. Triclinic Lattice
- **Total for 3D**: There are 14 distinct types of three-dimensional lattices.

4. **Final Answer**:
- Therefore, the maximum possible numbers of two-dimensional and three-dimensional lattices are respectively **5 and 14**.