Out of seven crystal systems how many have body centred unit cell ?

Options

A. 4
B. 3
C. 2
D. 7

Answer

To determine how many of the seven crystal systems have a body-centered unit cell (BCC), we can analyze each of the crystal systems one by one.

### Step-by-Step Solution:

1. **List the Seven Crystal Systems**:
The seven crystal systems are:
- Cubic
- Tetragonal
- Hexagonal
- Trigonal (or Rhombohedral)
- Orthorhombic
- Monoclinic
- Triclinic

2. **Identify Body-Centered Unit Cells**:
A body-centered unit cell is characterized by having one atom at each corner of the cube and one atom in the center of the cube. This configuration is found in the following crystal systems:
- **Cubic**: The body-centered cubic (BCC) structure is a type of cubic crystal system.
- **Tetragonal**: The tetragonal system can also have a body-centered unit cell, where the base is square and the height is different.
- **Orthorhombic**: The orthorhombic system can also accommodate a body-centered unit cell.

3. **Examine Other Crystal Systems**:
- **Hexagonal**: This system does not have a body-centered unit cell.
- **Trigonal (Rhombohedral)**: This system does not have a body-centered unit cell.
- **Monoclinic**: This system does not have a body-centered unit cell.
- **Triclinic**: This system does not have a body-centered unit cell.

4. **Count the Systems with BCC**:
From our analysis, the crystal systems that have body-centered unit cells are:
- Cubic
- Tetragonal
- Orthorhombic

Therefore, there are **three crystal systems** that have body-centered unit cells.

5. **Conclusion**:
The answer to the question is that **three out of the seven crystal systems have a body-centered unit cell**.

### Final Answer:
**Three crystal systems have body-centered unit cells.**