A compound contains two types of atoms X and Y. it crystallises in a cubic lattice with atoms X at the corners of the unit cell and atoms Y at the body centre. The simplest possible formula of this compound is

Options

A. `X_(8)Y`
B. `X_(2)Y`
C. XY
D. `XY_(8)`

Answer

To determine the simplest possible formula of the compound containing atoms X and Y in a cubic lattice, we will analyze the contributions of each type of atom in the unit cell.

### Step-by-Step Solution:

1. **Identify the Position of Atoms in the Unit Cell:**
- Atoms X are located at the corners of the cubic unit cell.
- Atom Y is located at the body center of the cubic unit cell.

2. **Calculate the Contribution of Atom X:**
- In a cubic lattice, there are 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution of atom X from the corners is:
\[ \text{Contribution of X} = 8 \times \frac{1}{8} = 1 \]

3. **Calculate the Contribution of Atom Y:**
- There is 1 atom Y located at the body center.
- The contribution of atom Y is:
\[ \text{Contribution of Y} = 1 \times 1 = 1 \]

4. **Determine the Ratio of Atoms:**
- From the contributions calculated:
- Number of X atoms = 1
- Number of Y atoms = 1
- The simplest ratio of X to Y is:
\[ \text{Ratio} = \frac{1}{1} = 1 \]

5. **Write the Simplest Formula:**
- The simplest formula of the compound based on the ratio of atoms is:
\[ \text{Formula} = XY \]

### Conclusion:
The simplest possible formula of the compound is \( XY \).