Find the molecular formula of a compound made by atoms A and B, where A atoms present at all corners of cubic lattice and B atoms at alternate face centre.

Options

A. AB
B. `AB_(2)`
C. `A_(2)B`
D. `A_(2)B_(3)`

Answer

To find the molecular formula of the compound made by atoms A and B, we will analyze the arrangement of the atoms in the cubic lattice.

### Step-by-Step Solution:

1. **Identify the Position of A Atoms**:
- A atoms are located at all corners of the cubic lattice.
- In a cubic unit cell, there are 8 corners.

2. **Calculate the Contribution of A Atoms**:
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution of A atoms in the unit cell is:
\[ \text{Total A atoms} = 8 \times \frac{1}{8} = 1 \]

3. **Identify the Position of B Atoms**:
- B atoms are located at alternate face centers of the cubic lattice.
- A cubic unit cell has 6 faces, and since B is at alternate face centers, it will occupy 3 of these faces.

4. **Calculate the Contribution of B Atoms**:
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total contribution of B atoms in the unit cell is:
\[ \text{Total B atoms} = 3 \times \frac{1}{2} = \frac{3}{2} \]

5. **Determine the Molecular Formula**:
- We have 1 A atom and \( \frac{3}{2} \) B atoms in the unit cell.
- To express the formula in whole numbers, we can multiply both the number of A and B atoms by 2:
\[ \text{Molecular formula} = A_2B_3 \]

### Final Answer:
The molecular formula of the compound is \( A_2B_3 \).

---