Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is:

Options

A. `A_(4)B_(2)O`
B. `A_(2)BO_(4)`
C. `AB_(2)O_(4)`
D. `A_(2)B_(2)O`

Explanation

To solve the problem, we need to analyze the information given about the elements and their arrangement in the crystal structure.

### Step-by-Step Solution:

1. **Identify the Structure of Element B**:
- Element B forms a close-packed structure, specifically a cubic close-packed (ccp) structure. In this structure, atoms are located at the corners and the face centers of the cube.

2. **Calculate the Effective Number of Atoms for B**:
- In a ccp structure, the effective number of atoms (Z) can be calculated using the formula:
\[ Z = \text{Number of corner atoms} + \text{Number of face-centered atoms} \]
- There are 8 corners, each contributing \( \frac{1}{8} \) of an atom, and 6 faces, each contributing \( \frac{1}{2} \) of an atom:
\[ Z = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]
- Thus, the effective number of atoms for B is 4.

3. **Determine the Number of Octahedral Voids**:
- The number of octahedral voids in a ccp structure is equal to the effective number of atoms:
\[ \text{Number of octahedral voids} = Z = 4 \]

4. **Calculate the Number of Atoms of Element A**:
- Element A occupies half of the octahedral voids:
\[ \text{Number of A atoms} = \frac{1}{2} \times \text{Number of octahedral voids} = \frac{1}{2} \times 4 = 2 \]

5. **Determine the Number of Tetrahedral Voids**:
- The number of tetrahedral voids in a ccp structure is twice the effective number of atoms:
\[ \text{Number of tetrahedral voids} = 2 \times Z = 2 \times 4 = 8 \]

6. **Calculate the Number of Oxygen Atoms**:
- Oxygen atoms occupy all the tetrahedral voids:
\[ \text{Number of O atoms} = \text{Number of tetrahedral voids} = 8 \]

7. **Establish the Ratio of A, B, and O**:
- We have:
- A = 2
- B = 4
- O = 8
- The ratio of A:B:O can be simplified:
\[ \text{Ratio} = 2:4:8 = 1:2:4 \]

8. **Write the Formula for the Bimetallic Oxide**:
- Based on the ratio, the formula for the bimetallic oxide can be written as:
\[ \text{Formula} = A_1B_2O_4 \implies AB_2O_4 \]

### Final Answer:
The structure of the bimetallic oxide is \( A_2B_4O_8 \).