A solid with formula `ABC_(3)` would probably have

Options

A. A at body centre, B at face centres and C at corners of the cube
B. A at corners of cube, B at body centre C at face centre
C. A at corners of hexagon, B at centres of the hexagon and C inside the hexagonal unit cell
D. A at corner, B at face centre, C at body centre

Answer

To determine the probable structure of a solid with the formula \( ABC_3 \), we will analyze the contributions of each atom type (A, B, and C) based on their positions in the unit cell.

### Step-by-Step Solution:

1. **Identify the Positions of Atoms:**
- **Atom A:** Let's assume atom A is located at the corners of the unit cell.
- **Atom B:** Assume atom B is positioned at the body center of the unit cell.
- **Atom C:** Assume atom C is located at the face centers of the unit cell.

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

3. **Calculate the Contribution of Atom B:**
- There is 1 body center in the unit cell.
- The body center contributes fully (1) to the unit cell.
- Therefore, the total contribution of atom B is:
\[ \text{Contribution of B} = 1 \]

4. **Calculate the Contribution of Atom C:**
- There are 6 faces in a cubic unit cell.
- Each face center atom contributes \( \frac{1}{2} \) to the unit cell.
- Therefore, the total contribution of atom C is:
\[ \text{Contribution of C} = 6 \times \frac{1}{2} = 3 \]

5. **Write the Formula of the Compound:**
- Combining the contributions, we have:
- A: 1
- B: 1
- C: 3
- Thus, the formula of the compound is:
\[ ABC_3 \]

6. **Conclusion:**
- The solid with the formula \( ABC_3 \) is correctly represented by the contributions calculated above. Therefore, the probable structure of the solid is consistent with the formula \( ABC_3 \).

### Final Answer:
The solid with formula \( ABC_3 \) would probably have the structure where A is at the corners, B is at the body center, and C is at the face centers of the unit cell.