How many kinds of space lattices are possible in a crystal?

Options

A. `23`
B. `7`
C. `230`
D. `14`

Answer

To determine how many kinds of space lattices are possible in a crystal, we can categorize them based on their crystal systems. Here’s a step-by-step solution:

### Step 1: Identify the Crystal Systems
There are seven types of crystal systems in crystallography:
1. Triclinic
2. Monoclinic
3. Orthorhombic
4. Tetragonal
5. Rhombohedral
6. Hexagonal
7. Cubic

### Step 2: Count the Space Lattices for Each Crystal System
Now, we will count the number of distinct space lattices for each of these crystal systems:
- **Triclinic:** 1 space lattice
- **Monoclinic:** 2 space lattices
- **Orthorhombic:** 4 space lattices
- **Tetragonal:** 2 space lattices
- **Rhombohedral:** 1 space lattice
- **Hexagonal:** 1 space lattice
- **Cubic:** 3 space lattices

### Step 3: Sum the Total Number of Space Lattices
Now, we will add the number of space lattices from each crystal system:
- Triclinic: 1
- Monoclinic: 2
- Orthorhombic: 4
- Tetragonal: 2
- Rhombohedral: 1
- Hexagonal: 1
- Cubic: 3

Total = 1 + 2 + 4 + 2 + 1 + 1 + 3 = 14

### Conclusion
Thus, the total number of kinds of space lattices possible in a crystal is **14**.