In a face centred cubic lattice, atom `A` occupies the corner positions and atom `B` occupies the face centred positions. If two atom of `B` is missin from two of the face centred points,, the formula of the compound is `:`

Options

A. `A_(2)B`
B. `AB_(2)`
C. `A_(2)B_(3)`
D. `A_(2)B_(5)`

Explanation

To determine the formula of the compound in a face-centered cubic (FCC) lattice where atom A occupies the corner positions and atom B occupies the face-centered positions, we can follow these steps:

### Step 1: Understand the FCC Lattice Structure
In a face-centered cubic lattice:
- There are 8 corner atoms.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- There are 6 face-centered positions, and each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.

### Step 2: Calculate the Contribution of Atom A
Since atom A occupies the corner positions:
- Total contribution from corner atoms = Number of corners × Contribution per corner
- Total contribution from corner atoms = \( 8 \times \frac{1}{8} = 1 \)

Thus, there is **1 atom of A** in the unit cell.

### Step 3: Calculate the Contribution of Atom B
Atom B occupies the face-centered positions, but we are told that 2 atoms of B are missing from the face-centered points.
- Normally, without any missing atoms, the contribution from face-centered atoms would be:
- Total contribution from face-centered atoms = Number of face centers × Contribution per face center
- Total contribution from face-centered atoms = \( 6 \times \frac{1}{2} = 3 \)

However, since 2 atoms of B are missing, we need to subtract these from the total:
- Remaining atoms of B = \( 3 - 2 = 1 \)

Thus, there is **1 atom of B** in the unit cell.

### Step 4: Determine the Formula of the Compound
Now we have:
- 1 atom of A
- 1 atom of B

The ratio of A to B in the unit cell is:
- A : B = 1 : 1

Thus, the formula of the compound can be written as:
- \( AB \)

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

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