Three element `A,B,C` crystallize into a cubic solid lattice.Atoms `A` occupy the corners `B` atoms the cube centres and atom `C` the edge .The formula of the compound is

Options

A. ABC
B. `ABC_(2)`
C. `ABC_(3)`
D. `ABC_(4)`

Answer

To determine the formula of the compound formed by elements A, B, and C in a cubic solid lattice, we need to analyze the contribution of each type of atom based on their positions in the lattice.

### Step-by-Step Solution:

1. **Identify the Position of Atoms:**
- Atoms A occupy the corners of the cube.
- Atoms B occupy the body center of the cube.
- Atoms C occupy the edges of the cube.

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

4. **Calculate the Contribution of Atom C:**
- There are 12 edges in a cube.
- Each edge atom contributes \( \frac{1}{4} \) of an atom to the unit cell.
- Therefore, the total contribution of C is:
\[ \text{Contribution of C} = 12 \times \frac{1}{4} = 3 \]

5. **Summarize the Contributions:**
- From the calculations:
- Contribution of A = 1
- Contribution of B = 1
- Contribution of C = 3

6. **Write the Formula of the Compound:**
- The formula can be written based on the contributions of each atom:
\[ \text{Formula} = A^1 B^1 C^3 = ABC_3 \]

### Final Answer:
The formula of the compound is \( ABC_3 \).