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

Options

A. `P_2Q_3`
B. `P_4Q`
C. `P_4Q_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 positions of P and Q atoms
- P atoms are located at the corners of the unit cell.
- Q atoms are located at the face centers of the unit cell.

### Step 2: Count the total number of P atoms
- In a complete FCC unit cell, there are 8 corners.
- Since 2 P atoms are missing from 2 corners, the effective number of P atoms at the corners is:
\[ 8 - 2 = 6 \text{ (corners)} \]

### Step 3: Calculate the contribution of P atoms
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution of P atoms from the corners is:
\[ 6 \text{ corners} \times \frac{1}{8} = \frac{6}{8} = \frac{3}{4} \text{ P atoms} \]

### Step 4: Count the total number of Q atoms
- In a FCC unit cell, there are 6 face centers.
- Each face center atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total contribution of Q atoms from the face centers is:
\[ 6 \text{ faces} \times \frac{1}{2} = 3 \text{ Q atoms} \]

### Step 5: Combine the contributions of P and Q atoms
- We have \( \frac{3}{4} \) P atoms and \( 3 \) Q atoms.
- To express the formula, we need to eliminate the fraction. We can do this by multiplying both contributions by 4 (the denominator of the fraction):
\[ P: \frac{3}{4} \times 4 = 3 \quad \text{and} \quad Q: 3 \times 4 = 12 \]

### Step 6: Write the formula in the simplest ratio
- The ratio of P to Q is:
\[ P:Q = 3:12 \]
- To simplify this ratio, we divide both numbers by 3:
\[ P:Q = 1:4 \]

### Final Formula
- Therefore, the formula of the compound is:
\[ PQ_4 \]