Which of the following crystal systems exist in bcc, end-centred, fcc, as well as primitive unit cell?

Options

A. Hexagonal
B. Cubic
C. Triclinic
D. Orthorhombic

Explanation

To determine which crystal system exists in body-centered cubic (BCC), end-centered cubic (FCC), face-centered cubic (FCC), and primitive unit cell, we can analyze the characteristics of each crystal system.

### Step-by-Step Solution:

1. **Understanding Crystal Systems**:
- There are seven crystal systems: cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic. Each system has specific properties regarding the lengths of the unit cell edges and the angles between them.

2. **Identifying the Unit Cells**:
- **BCC (Body-Centered Cubic)**: This structure has one atom at each corner of the cube and one atom in the center of the cube.
- **FCC (Face-Centered Cubic)**: This structure has one atom at each corner of the cube and one atom at the center of each face of the cube.
- **End-Centered**: This refers to a unit cell that has atoms at the corners and an additional atom at the center of one of the faces.
- **Primitive Unit Cell**: This is the simplest unit cell that can be repeated to form the entire crystal lattice.

3. **Checking for Orthorhombic System**:
- The orthorhombic system is defined by having three unequal axes (a, b, c) that are all at right angles (90 degrees) to each other.
- It can accommodate various types of unit cells, including primitive, body-centered, and face-centered.

4. **Examples of Orthorhombic Structures**:
- **Primitive**: Rhombic sulfur (S8).
- **Body-Centered**: Magnesium sulfate heptahydrate (MgSO4·7H2O).
- **Face-Centered**: Barium sulfate (BaSO4).
- **End-Centered**: Potassium nitrate (KNO3).

5. **Conclusion**:
- The orthorhombic crystal system can exist in all four types of unit cells: BCC, end-centered, FCC, and primitive. Therefore, the answer to the question is **orthorhombic**.

### Final Answer:
The crystal system that exists in BCC, end-centered, FCC, and primitive unit cell is **orthorhombic**.