Step 1: Understanding the Concept:
The stoichiometry of a crystalline compound is determined by the number of atoms of each element per unit cell.
In a cubic unit cell, atoms placed at different locations (corners, faces, edges, body center) are shared differently by adjacent unit cells.
The empirical formula represents the ratio of the total contribution of each type of atom to a single unit cell.
Step 2: Key Formula or Approach:
Contribution factors in a cubic unit cell:
- An atom at a **corner** is shared by 8 unit cells, so its contribution to one cell is \(1/8\).
- An atom at the **body center** is not shared by any other unit cell, so its contribution is \(1\).
- An atom at a **face center** is shared by 2 cells, so its contribution is \(1/2\).
- An atom at an **edge center** is shared by 4 cells, so its contribution is \(1/4\).
Step 3: Detailed Explanation:
Let's calculate the effective number of atoms for A and B:
1. Number of atoms of A:
- Atoms of A are located at the corners of a cube.
- A cube has 8 corners.
- Each corner atom contributes \(1/8\) to the unit cell.
- Total number of A atoms = \(8 \times \frac{1}{8} = 1\).
2. Number of atoms of B:
- Atoms of B are located at the body center.
- A cube has 1 body center.
- The body-centered atom is fully contained within the unit cell, contributing \(1\).
- Total number of B atoms = \(1 \times 1 = 1\).
3. Formula Determination:
- The ratio of A atoms to B atoms in the unit cell is \(1 : 1\).
- This gives the simplest empirical formula as \(AB\).
This specific arrangement is found in the cesium chloride (\(CsCl\)) crystal structure.
Step 4: Final Answer:
The simplest formula of the compound is \(AB\), which is option (B).