A compound formed by elements A and B has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres. The formula of the compound will be

Options

A. `A_(8)B_(6)=A_(4)B_(3)`
B. `A_(8)B_(4)=A_(2)B`
C. `AB_(3)`
D. `A_(2)B_(3)`

Explanation

To determine the formula of the compound formed by elements A and B with the given cubic structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Positions of Atoms:**
- A atoms are located at the corners of the cube.
- B atoms are located at the face centers of the cube.

2. **Count the Number of A Atoms:**
- A cube has 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 atoms in the unit cell is:
\[ \text{Total A atoms} = 8 \times \frac{1}{8} = 1 \]

3. **Count the Number of B Atoms:**
- A cube has 6 faces.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared between 2 adjacent unit cells.
- Therefore, the total contribution of B atoms in the unit cell is:
\[ \text{Total B atoms} = 6 \times \frac{1}{2} = 3 \]

4. **Write the Empirical Formula:**
- From the contributions calculated, we find that there is 1 A atom and 3 B atoms in the unit cell.
- Thus, the empirical formula of the compound is:
\[ \text{Formula} = AB_3 \]

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

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