The unit cell of a binary compound of A and B has ccp structure with A atoms occupying the corners and B atoms occupying the centres of each face of the unit cell. If during crystallisation of the alloy, in the unit cell 4 atoms of A are missing, the overall composition per unit cell is :

Options

A. `AB_(6)`
B. `AB_(4)`
C. `AB_(8)`
D. `A_(6)B_(24)`

Explanation

To solve the problem, we need to determine the overall composition of the unit cell of the binary compound AB, given that A atoms occupy the corners and B atoms occupy the centers of the faces of the unit cell, and that 4 A atoms are missing.

### Step-by-Step Solution:

1. **Identify the Structure**:
The unit cell has a cubic close-packed (ccp) structure. In this structure:
- A atoms are located at the corners of the cube.
- B atoms are located at the centers of each face of the cube.

2. **Count the Atoms in the Unit Cell**:
- **A Atoms**: In a cube, there are 8 corners. Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell. Therefore, the total contribution from the corner A atoms is:
\[ \text{Total A atoms} = 8 \times \frac{1}{8} = 1 \text{ atom} \]
- However, we are told that 4 A atoms are missing. Thus, the effective number of A atoms in the unit cell is:
\[ \text{Effective A atoms} = 1 - 4 = -3 \text{ atoms} \]
This indicates that we need to reconsider the contribution of A atoms. Since we have 4 missing, we must assume that there were originally 5 A atoms (1 from the corners and 4 missing).

3. **Calculate the Contribution of B Atoms**:
- **B Atoms**: There are 6 faces in the cube, and each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell. Therefore, the total contribution from the B atoms is:
\[ \text{Total B atoms} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Determine the Overall Composition**:
- Now we have:
- Effective A atoms = 1 (after accounting for the missing atoms)
- B atoms = 3
- The ratio of A to B is:
\[ \text{Ratio of A to B} = 1 : 3 \]

5. **Convert to Whole Numbers**:
- To express this in the simplest whole number ratio, we can multiply both sides by 2:
\[ 1 \times 2 : 3 \times 2 = 2 : 6 \]
- Thus, the formula for the compound can be expressed as \( A_2B_6 \).

### Final Answer:
The overall composition per unit cell is \( A_2B_6 \).