Given an alloy of Cu, Ag and Au in which Cu atoms constitute the ccp arrangement . If the hypothetical formula of the alloy is `Cu_4 Ag_3 Au` , the probable locations of Ag and Au atoms are

Options

A. Ag- all tetrahedral voids , Au - all octahedral voids
B. Ag- `3/8th` tetrahedral voids , Au - `1/4th` octahedral voids
C. Ag- 1/2 octahedral voids , Au - 1/2 tetrahedral voids
D. Ag- all octahedral voicks , Au - all tetrahedral voids

Answer

To solve the problem, we need to analyze the arrangement of atoms in the given alloy of copper (Cu), silver (Ag), and gold (Au) based on the provided formula \(Cu_4Ag_3Au\). The copper atoms are arranged in a cubic close-packed (CCP) structure, also known as face-centered cubic (FCC).

### Step-by-Step Solution:

1. **Understanding the CCP (FCC) Structure:**
- In a face-centered cubic (FCC) structure, atoms are located at the corners and the centers of each face of the cube.
- Each corner atom contributes \( \frac{1}{8} \) to the unit cell, and each face-centered atom contributes \( \frac{1}{2} \).

2. **Calculating the Number of Atoms in FCC:**
- There are 8 corner atoms and 6 face-centered atoms in an FCC unit cell.
- Total contribution from corner atoms: \( 8 \times \frac{1}{8} = 1 \)
- Total contribution from face-centered atoms: \( 6 \times \frac{1}{2} = 3 \)
- Therefore, total number of atoms per unit cell = \( 1 + 3 = 4 \) atoms.

3. **Identifying the Voids in FCC:**
- In an FCC unit cell, the number of tetrahedral voids is double the number of atoms, which means there are \( 4 \times 2 = 8 \) tetrahedral voids.
- The number of octahedral voids is equal to the number of atoms, which means there are \( 4 \) octahedral voids.

4. **Analyzing the Alloy Composition:**
- The formula \( Cu_4Ag_3Au \) indicates that there are 4 copper atoms, 3 silver atoms, and 1 gold atom in the alloy.
- This means we need to place 3 silver atoms and 1 gold atom in the voids of the FCC structure.

5. **Possible Arrangements of Silver and Gold:**
- **Arrangement 1:** Silver occupies tetrahedral voids and gold occupies octahedral voids.
- Silver: 3 atoms can occupy \( \frac{3}{8} \) of the tetrahedral voids.
- Gold: 1 atom can occupy \( \frac{1}{4} \) of the octahedral voids.
- **Arrangement 2:** Silver occupies octahedral voids and gold occupies tetrahedral voids.
- Silver: 3 atoms can occupy \( \frac{3}{4} \) of the octahedral voids.
- Gold: 1 atom can occupy \( \frac{1}{8} \) of the tetrahedral voids.

6. **Evaluating the Options:**
- Option 1: Silver occupies all tetrahedral voids, gold occupies all octahedral voids (Incorrect).
- Option 2: Silver occupies \( \frac{3}{8} \) of tetrahedral voids, gold occupies \( \frac{1}{4} \) of octahedral voids (Correct).
- Option 3: Silver occupies half octahedral voids, gold occupies half tetrahedral voids (Incorrect).
- Option 4: Silver occupies all octahedral voids, gold occupies all tetrahedral voids (Incorrect).

### Conclusion:
The correct arrangement is given in **Option 2**: Silver occupies \( \frac{3}{8} \) of the tetrahedral voids, and gold occupies \( \frac{1}{4} \) of the octahedral voids.