A solid has a structure in which A atoms are located at the cube corners of the unit cell, B atoms are located at the cube edges of unit cell and the C atoms at the body centre. Formula of the compound

Options

A. `CAB_(3)`
B. `C_(2)AB_(3)`
C. `CA_(3)B`
D. `C_(2)A_(3)B`

Answer

To determine the formula of the compound based on the given structure of the solid, we need to calculate the number of atoms of A, B, and C present in the unit cell.

### Step-by-Step Solution:

1. **Identify the positions of the atoms:**
- A atoms are located at the corners of the cube.
- B atoms are located at the edges of the cube.
- C atoms are located at the body center of the cube.

2. **Calculate the contribution of A atoms:**
- There are 8 corners in a cube.
- Each corner atom is shared by 8 unit cells, contributing \( \frac{1}{8} \) of an atom to one unit cell.
- Total contribution from A atoms:
\[ \text{Contribution from A} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

3. **Calculate the contribution of B atoms:**
- There are 12 edges in a cube.
- Each edge atom is shared by 4 unit cells, contributing \( \frac{1}{4} \) of an atom to one unit cell.
- Total contribution from B atoms:
\[ \text{Contribution from B} = 12 \times \frac{1}{4} = 3 \text{ atoms} \]

4. **Calculate the contribution of C atoms:**
- There is 1 body center atom in the cube.
- The body center atom is not shared with any other unit cell, contributing 1 full atom to the unit cell.
- Total contribution from C atoms:
\[ \text{Contribution from C} = 1 \text{ atom} \]

5. **Combine the contributions to form the empirical formula:**
- From the contributions calculated:
- A: 1 atom
- B: 3 atoms
- C: 1 atom
- Therefore, the formula of the compound can be written as:
\[ \text{Formula} = A_1B_3C_1 \text{ or simply } AB_3C \]

6. **Final Answer:**
- The formula of the compound is \( C A B_3 \) or \( C A B_3 \).