An element A and B constiture bcc type crystalline structure. Element A occupies body centre position and B is at the corners of cube. What is the formula of the compound ? What are the coordination numbers of A and B?

Explanation

To solve the problem, we need to analyze the body-centered cubic (BCC) structure and determine the formula of the compound formed by elements A and B, as well as their coordination numbers.

### Step-by-Step Solution:

1. **Understanding the BCC Structure**:
- In a BCC structure, there is one atom located at the body center and atoms located at the corners of the cube.

2. **Identifying the Atoms**:
- Element A occupies the body center position.
- Element B occupies the corners of the cube.

3. **Counting the Atoms in the Unit Cell**:
- **Element A**: There is 1 atom of A at the body center.
- **Element B**: There are 8 corners in a cube, and each corner atom is shared by 8 adjacent cubes. Therefore, the contribution of B from the corners is:
\[ \text{Number of B atoms} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom of B} \]

4. **Determining the Formula of the Compound**:
- From the counts above, we have 1 atom of A and 1 atom of B in the unit cell.
- Thus, the formula of the compound is:
\[ \text{Formula} = AB \]

5. **Finding the Coordination Numbers**:
- **Coordination Number of A**: In a BCC structure, the atom at the body center (A) is surrounded by 8 corner atoms (B). Therefore, the coordination number of A is:
\[ \text{Coordination number of A} = 8 \]
- **Coordination Number of B**: Each corner atom (B) is also surrounded by 8 atoms (the body center atom A and the other corner atoms). Thus, the coordination number of B is:
\[ \text{Coordination number of B} = 8 \]

### Final Answers:
- **Formula of the compound**: AB
- **Coordination number of A**: 8
- **Coordination number of B**: 8