If the number of atoms per unit in a crystal is 2, the structure of crystal is:

Options

A. octahedral
B. Body centred cubic
C. Face centred cubic (fcc)
D. Simple cubic

Answer

To determine the structure of a crystal with a given number of atoms per unit cell (Z = 2), we can analyze the contributions of atoms in different types of crystal structures. Here's a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Concept of Z**:
- The number of atoms per unit cell (Z) indicates how many atoms are effectively present in one unit cell of the crystal structure.

2. **Identifying Common Crystal Structures**:
- There are several common types of crystal structures: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC).

3. **Calculating Z for Each Structure**:
- **Simple Cubic (SC)**:
- Atoms are located only at the corners of the cube.
- Contribution from corners: \( Z = 8 \times \frac{1}{8} = 1 \)
- **Body-Centered Cubic (BCC)**:
- Atoms are located at the corners and one atom at the center of the cube.
- Contribution from corners: \( 8 \times \frac{1}{8} = 1 \)
- Contribution from the body center: \( 1 \)
- Total: \( Z = 1 + 1 = 2 \)
- **Face-Centered Cubic (FCC)**:
- Atoms are located at the corners and the centers of the faces.
- Contribution from corners: \( 8 \times \frac{1}{8} = 1 \)
- Contribution from faces: \( 6 \times \frac{1}{2} = 3 \)
- Total: \( Z = 1 + 3 = 4 \)

4. **Conclusion**:
- Since the calculated value of Z for BCC is 2, the structure of the crystal with 2 atoms per unit cell is **Body-Centered Cubic (BCC)**.

### Final Answer:
The structure of the crystal with 2 atoms per unit cell is **Body-Centered Cubic (BCC)**.