A compound formed by element A and B crystallize in the cubic structure where A atoms are at the corners of a cube and B atoms are at the centre of the body. The formula of the compounds is

Options

A. AB
B. `AB_(2)`
C. `A_(2)B_(3)`
D. `AB_(3)`

Answer

To determine the formula of the compound formed by elements A and B, we need to analyze the arrangement of the atoms in the cubic structure.

### Step-by-Step Solution:

1. **Identify the Arrangement of Atoms**:
- A atoms are located at the corners of the cube.
- B atoms are located at the body center of the cube.

2. **Calculate the Contribution of A Atoms**:
- A cube has 8 corners.
- Each corner atom is shared by 8 adjacent unit cells.
- Therefore, the contribution of each corner atom is \( \frac{1}{8} \).
- Total contribution from A atoms = Number of corners × Contribution per corner
\[ \text{Total contribution from A} = 8 \times \frac{1}{8} = 1 \]
- Thus, there is 1 A atom per unit cell.

3. **Calculate the Contribution of B Atoms**:
- There is 1 body center in the cube.
- The body center atom is not shared with any other unit cell, so its contribution is 1.
- Thus, there is 1 B atom per unit cell.

4. **Determine the Formula of the Compound**:
- From the contributions calculated:
- Number of A atoms = 1
- Number of B atoms = 1
- Therefore, the formula of the compound can be written as \( AB \).

5. **Conclusion**:
- The formula of the compound formed by elements A and B is \( AB \).