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 atoms in the cubic structure described in the question.

### Step-by-Step Solution:

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

2. **Count the number of A atoms:**
- A cube has 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 adjacent cubes.
- Therefore, the total contribution of A atoms is:
\[ \text{Total A atoms} = 8 \times \frac{1}{8} = 1 \]

3. **Count the number of B atoms:**
- There is 1 body-centered atom (B) in the cube.
- The contribution of the body-centered atom is 1 because it belongs entirely to that cube.
- Therefore, the total contribution of B atoms is:
\[ \text{Total B atoms} = 1 \]

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

### Final Answer:
The formula of the compound is \( AB \).

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