To determine the correct order of decreasing ionic character for the compounds \( \text{PbCl}_2 \), \( \text{PbF}_2 \), \( \text{PbI}_2 \), and \( \text{PbBr}_2 \), we need to consider the factors that influence ionic character, particularly the size of the cations and anions involved.
### Step-by-Step Solution:
1. **Identify the Cation and Anions**:
- The cation in all cases is lead (Pb).
- The anions vary: \( \text{Cl}^- \) (chloride), \( \text{F}^- \) (fluoride), \( \text{I}^- \) (iodide), and \( \text{Br}^- \) (bromide).
2. **Consider the Size of the Anions**:
- As we move down the group of halogens (from fluorine to iodine), the size of the anions increases.
- The order of anion size is: \( \text{F}^- < \text{Cl}^- < \text{Br}^- < \text{I}^- \).
3. **Analyze Ionic Character**:
- Ionic character is influenced by the size of the ions. A smaller cation and a larger anion typically result in a higher ionic character.
- The larger the anion, the more polarizable it is, which can lead to a decrease in ionic character due to increased covalent character.
4. **Apply Fajans' Rules**:
- According to Fajans' rules, a smaller cation will polarize a larger anion more effectively, leading to increased covalent character and decreased ionic character.
- In this case, \( \text{Pb}^{2+} \) is the same for all, but the anion size increases from \( \text{F}^- \) to \( \text{I}^- \).
5. **Rank the Compounds**:
- \( \text{PbF}_2 \): Smallest anion, highest ionic character.
- \( \text{PbCl}_2 \): Next smallest anion, second highest ionic character.
- \( \text{PbBr}_2 \): Larger than chloride, lower ionic character.
- \( \text{PbI}_2 \): Largest anion, lowest ionic character.
6. **Final Order**:
- Therefore, the correct order of decreasing ionic character is:
\[
\text{PbF}_2 > \text{PbCl}_2 > \text{PbBr}_2 > \text{PbI}_2
\]
### Conclusion:
The final order of decreasing ionic character is:
\[
\text{PbF}_2 > \text{PbCl}_2 > \text{PbBr}_2 > \text{PbI}_2
\]
