A compound formed by elements A and B crystallizes in the cubic arrangement in which atoms A are at the corners of the cube and atoms B at the face centres. What is the formula of the compound?

Explanation

To determine the formula of the compound formed by elements A and B, we need to analyze the arrangement of the atoms in the cubic unit cell.

### Step 1: Identify the number of A atoms in the unit cell
- In a cubic arrangement, the atoms A are located at the corners of the cube.
- There are 8 corners in a cube.
- Each corner atom is shared by 8 adjacent cubes.

**Calculation:**
Number of A atoms contributed by the corners = Number of corners × Contribution per corner
= 8 corners × (1/8) = 1 A atom

### Step 2: Identify the number of B atoms in the unit cell
- The atoms B are located at the face centers of the cube.
- There are 6 faces in a cube.
- Each face-centered atom is shared by 2 adjacent cubes.

**Calculation:**
Number of B atoms contributed by the face centers = Number of faces × Contribution per face
= 6 faces × (1/2) = 3 B atoms

### Step 3: Write the empirical formula
- From the calculations, we have determined that there is 1 A atom and 3 B atoms in the unit cell.
- Therefore, the formula of the compound can be expressed as \( A_1B_3 \) or simply \( AB_3 \).

### Final Answer:
The formula of the compound is \( AB_3 \).

---