In fcc lattice ,A, B, C,D atoms are arranged at corner , face centre , ocatahedral void and tetrahedral void respectively , then the body diagonal contains :

Options

A. `2A,C,2D`
B. `2A, 2B , 2C`
C. `2A, 2B,D`
D. `2A,2D`

Answer

To solve the problem regarding the arrangement of atoms in a face-centered cubic (FCC) lattice, we need to analyze the positions of the atoms and voids specified in the question.

### Step-by-Step Solution:

1. **Understanding the FCC Lattice Structure**:
- In an FCC lattice, atoms are located at the corners and the centers of each face of the cube.
- Specifically, there are 8 corner atoms and 6 face-centered atoms.

2. **Identifying Atom Positions**:
- According to the problem:
- A atoms are located at the corners of the cube.
- B atoms are located at the face centers.
- C atoms are located in the octahedral voids (which are at the body center and edge centers).
- D atoms are located in the tetrahedral voids (which are located along the body diagonals).

3. **Analyzing the Body Diagonal**:
- The body diagonal of the cube connects two opposite corners and passes through the body center.
- In an FCC lattice, the body diagonal contains:
- 2 corner atoms (A) at the ends of the diagonal.
- 1 octahedral void (C) at the body center.
- 2 tetrahedral voids (D) along the body diagonal.

4. **Counting Atoms on the Body Diagonal**:
- Therefore, along the body diagonal, we have:
- 2 A atoms (from the corners),
- 1 C atom (from the octahedral void at the body center),
- 2 D atoms (from the tetrahedral voids).

5. **Final Composition of the Body Diagonal**:
- The total composition of the body diagonal is:
- 2 A + 1 C + 2 D.

### Conclusion:
Thus, the body diagonal contains **2 A atoms, 1 C atom, and 2 D atoms**.

### Answer:
The body diagonal contains: **2A, C, and 2D**.

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