A compound is formed by elements `A` and `B`. This crystallises in the cubic structure when atoms `A` are at the corners of the cube and atoms `B` are at the centre of the body.The simplest formula of the compound is

Options

A. AB
B. `AB_(2)`
C. `A_(2)B`
D. `AB_(4)`

Answer

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

### Step-by-Step Solution:

1. **Understand the Structure**:
The problem states that atoms A are located at the corners of a cube, and atoms B are at the center of the body of the cube.

2. **Count the Atoms of A**:
- A cube has 8 corners.
- Each corner atom is shared among 8 adjacent unit cells.
- Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Total contribution from all 8 corners:
\[ \text{Contribution from A} = 8 \times \frac{1}{8} = 1 \text{ atom of A} \]

3. **Count the Atoms of B**:
- There is 1 atom of B located at the center of the body of the cube.
- This atom is not shared with any other unit cell.
- Therefore, the contribution from B is simply:
\[ \text{Contribution from B} = 1 \text{ atom of B} \]

4. **Determine the Simplest Formula**:
- From the contributions, we have 1 atom of A and 1 atom of B.
- The simplest formula of the compound can be written as:
\[ \text{Formula} = AB \]

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

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