An alloy of copper and gold crystallizes in cubic lattic, in which the `Au-` atoms occupy the lattice points at the corners of cube and `Cu-` atoms occupy the centre of each face. The formula of this alloy is `:`

Explanation

To find the formula of the alloy of copper (Cu) and gold (Au) that crystallizes in a cubic lattice, we need to 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:**
- Gold (Au) atoms occupy the corners of the cubic unit cell.
- Copper (Cu) atoms occupy the centers of each face of the cubic unit cell.

2. **Calculate Contribution of Gold Atoms:**
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 adjacent unit cells.
- There are 8 corners in a cube.
- Therefore, the total contribution of Au atoms = \( 8 \times \frac{1}{8} = 1 \) Au atom.

3. **Calculate Contribution of Copper Atoms:**
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared between 2 adjacent unit cells.
- There are 6 faces in a cube.
- Therefore, the total contribution of Cu atoms = \( 6 \times \frac{1}{2} = 3 \) Cu atoms.

4. **Write the Formula of the Alloy:**
- From the contributions calculated:
- Au = 1
- Cu = 3
- The formula of the alloy can be written as \( \text{Au}_1\text{Cu}_3 \) or simply \( \text{AuCu}_3 \).

### Final Answer:
The formula of the alloy is \( \text{AuCu}_3 \).

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