The number of nearest neighbours of each atom in cubic close packing (ccp) and body-centred cubic arrangement (bcc) is respectively

Options

A. 12, 12
B. 12, 8
C. 8, 6
D. 8, 8

Answer

To solve the question regarding the number of nearest neighbors of each atom in cubic close packing (CCP) and body-centered cubic (BCC) arrangements, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Coordination Number**:
- The coordination number refers to the number of nearest neighbors surrounding a particular atom in a crystal structure.

2. **Analyzing Cubic Close Packing (CCP)**:
- In CCP, also known as face-centered cubic (FCC), each atom is surrounded by other atoms in a specific arrangement.
- An atom in the CCP structure is in contact with 6 other atoms in its own layer (the same plane).
- Additionally, it is surrounded by 3 atoms from the layer above and 3 atoms from the layer below.
- Therefore, the total coordination number for CCP is calculated as follows:
- Neighbors in the same layer: 6
- Neighbors in the layer above: 3
- Neighbors in the layer below: 3
- Total: \(6 + 3 + 3 = 12\)

3. **Analyzing Body-Centered Cubic (BCC)**:
- In BCC, there is one atom at the center of the cube and 8 atoms at the corners.
- The central atom is surrounded by the 8 corner atoms.
- Therefore, the coordination number for BCC is simply the number of corner atoms surrounding the central atom, which is 8.

4. **Conclusion**:
- The coordination number for cubic close packing (CCP) is 12.
- The coordination number for body-centered cubic (BCC) is 8.
- Hence, the answer to the question is that the number of nearest neighbors of each atom in CCP and BCC is respectively **12 and 8**.

### Final Answer:
- The number of nearest neighbors of each atom in cubic close packing (CCP) and body-centered cubic (BCC) arrangement is **12 and 8** respectively.