A compound is formed by elements A and B. This crystallizes in the cubic structure when atoms are the corners of the cube and atoms B are at the centre of the body. The simplest formula of the compounds 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 need to analyze the arrangement of the atoms in the cubic structure as described in the question.

### Step-by-Step Solution:

1. **Identify the Structure**:
The problem states that element A occupies the corners of the cube, while element B is located at the center of the body of the cube. This indicates that we are dealing with a body-centered cubic (BCC) structure.

2. **Count the Atoms of A**:
In a cubic lattice, there are 8 corners. Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 adjacent unit cells. Therefore, the total contribution of A from the corners is:
\[ \text{Total contribution of A} = 8 \times \frac{1}{8} = 1 \text{ atom of A} \]

3. **Count the Atoms of B**:
The atom B is located at the center of the body of the cube. Since this atom is not shared with any other unit cell, its contribution to the unit cell is:
\[ \text{Total contribution of B} = 1 \text{ atom of B} \]

4. **Determine the Simplest Formula**:
Now that we have the total contributions from both elements, we can express the simplest formula of the compound. We have 1 atom of A and 1 atom of B, which gives us the formula:
\[ \text{Simplest formula} = AB \]

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