In fcc arrangement of P and Q atoms, where P atom are at the corners of the unit cell, Q atom at the face centres and two atom are missing from two corners in each unit cell, then the formula of the compound is :

Options

A. `P_(2)O_(3)`
B. `P_(4)Q`
C. `P_(4)Q_(5)`
D. `PQ_(4)`

Explanation

To determine the formula of the compound formed by P and Q atoms in a face-centered cubic (FCC) arrangement, we will follow these steps:

### Step 1: Identify the arrangement of atoms
In the FCC arrangement:
- P atoms are located at the corners of the unit cell.
- Q atoms are located at the face centers of the unit cell.
- Two P atoms are missing from two corners.

### Step 2: Count the contribution of P atoms
1. **Total corners in a unit cell**: There are 8 corners.
2. **Contribution of P atoms**: Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
3. **Missing atoms**: Since 2 P atoms are missing, we effectively have 6 P atoms at the corners.
4. **Total contribution of P atoms**:
\[ \text{Total contribution of P} = 6 \times \frac{1}{8} = \frac{6}{8} = \frac{3}{4} \]

### Step 3: Count the contribution of Q atoms
1. **Total face centers in a unit cell**: There are 6 faces.
2. **Contribution of Q atoms**: Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
3. **Total contribution of Q atoms**:
\[ \text{Total contribution of Q} = 6 \times \frac{1}{2} = 3 \]

### Step 4: Determine the ratio of P to Q
Now we have:
- Contribution of P = \( \frac{3}{4} \)
- Contribution of Q = \( 3 \)

To find the ratio of P to Q, we write:
\[ \text{Ratio of P to Q} = \frac{\frac{3}{4}}{3} = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4} \]

### Step 5: Write the formula
The ratio of P to Q is \( 1:4 \). Therefore, the formula of the compound can be written as:
\[ \text{Formula} = P_1Q_4 \quad \text{or} \quad PQ_4 \]

### Final Answer
The formula of the compound is \( PQ_4 \).

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