An element crystallises in a b.c.c. lattice. Nearest and next nearest neighbours are respectively

Options

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

Answer

To determine the nearest and next nearest neighbors in a body-centered cubic (BCC) lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the BCC Structure**:
- In a body-centered cubic (BCC) lattice, there is one atom at each of the 8 corners of the cube and one atom at the center of the cube.
- This gives a total of 2 atoms per unit cell (1 from the center and 1 from the corners).

2. **Identifying Nearest Neighbors**:
- The nearest neighbors in a BCC lattice are the atoms that are closest to the central atom.
- In the BCC structure, the central atom has 8 corner atoms as its nearest neighbors.
- Therefore, the number of nearest neighbors is **8**.

3. **Identifying Next Nearest Neighbors**:
- Next nearest neighbors are the atoms that are not directly adjacent but are still relatively close to the central atom.
- In the BCC structure, the next nearest neighbors are the atoms located at the centers of the adjacent BCC cells.
- There are 6 such atoms: one above, one below, one to the left, one to the right, one in front, and one behind the central atom.
- Therefore, the number of next nearest neighbors is **6**.

4. **Final Answer**:
- Thus, for a BCC lattice, the nearest and next nearest neighbors are **8 and 6**, respectively.

### Summary:
- Nearest neighbors: **8**
- Next nearest neighbors: **6**