A compound made up of elements `A` and `B` crystallizes in the cubic structures. Atoms `A` are present on the corners as well as face centres whereas atoms `B` are present on the edge centres centres as well as body centre. What is the formula of the compound? Draw the structure of its unit cell.

Explanation

To determine the formula of the compound made up of elements A and B that crystallizes in a cubic structure, we need to analyze the arrangement of the atoms in the unit cell.

### Step-by-Step Solution:

1. **Identify the Positions of Atoms**:
- Atoms A are located at the corners and face centers of the cubic unit cell.
- Atoms B are located at the edge centers and the body center of the cubic unit cell.

2. **Calculate Contribution of Atoms A**:
- **Corners**: There are 8 corners in a cube. Each corner atom contributes \( \frac{1}{8} \) of its volume to the unit cell.
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom of A} \]
- **Face Centers**: There are 6 face centers in a cube. Each face-centered atom contributes \( \frac{1}{2} \) of its volume to the unit cell.
\[ \text{Contribution from face centers} = 6 \times \frac{1}{2} = 3 \text{ atoms of A} \]
- **Total Contribution of A**:
\[ \text{Total A} = 1 + 3 = 4 \text{ atoms of A} \]

3. **Calculate Contribution of Atoms B**:
- **Edge Centers**: There are 12 edges in a cube. Each edge-centered atom contributes \( \frac{1}{4} \) of its volume to the unit cell.
\[ \text{Contribution from edge centers} = 12 \times \frac{1}{4} = 3 \text{ atoms of B} \]
- **Body Center**: There is 1 body center in a cube. The body-centered atom contributes fully to the unit cell.
\[ \text{Contribution from body center} = 1 \text{ atom of B} \]
- **Total Contribution of B**:
\[ \text{Total B} = 3 + 1 = 4 \text{ atoms of B} \]

4. **Determine the Empirical Formula**:
- From the contributions calculated, we have:
- 4 atoms of A
- 4 atoms of B
- Therefore, the empirical formula of the compound is:
\[ \text{Formula} = A_4B_4 \]
- Simplifying this gives:
\[ \text{Simplest Formula} = AB \]

5. **Draw the Structure of the Unit Cell**:
- The unit cell can be visualized as a cube where:
- Atoms A are at the 8 corners and at the center of each face.
- Atoms B are at the center of each edge and at the center of the cube.

### Summary of the Solution:
The formula of the compound is \( AB \).