To determine the order of lattice enthalpy, we need to understand the factors that influence lattice energy. Lattice energy is the energy released when one mole of an ionic solid is formed from its gaseous ions. It can be influenced by the following factors:
1. **Charge of the Ions**: Lattice energy is directly proportional to the product of the charges of the cation and anion. Higher charges result in higher lattice energy.
2. **Size of the Ions**: Lattice energy is inversely proportional to the distance between the ions, which is influenced by their sizes. Larger ions result in lower lattice energy.
### Step-by-Step Solution:
**Step 1: Analyze the Options**
- We have to analyze the given options based on the size of cations and anions and their charges.
**Step 2: Option 1 Analysis**
- In option 1, the anion remains the same while the cation size increases. According to the principle, as the size of the cation increases, the lattice energy decreases because the distance between the ions increases. Thus, this option is correct.
**Step 3: Option 2 Analysis**
- In option 2, the cation size remains the same while the anion size increases. As the size of the anion increases, the lattice energy should decrease. However, if the problem states that the lattice energy increases, this option is incorrect.
**Step 4: Option 3 Analysis**
- In option 3, the cation is the same and the anion size increases from fluorine to iodine. Again, as the anion size increases, the lattice energy should decrease. If it states that it increases, this option is also incorrect.
**Step 5: Option 4 Analysis**
- In option 4, the cation remains the same while the anion size decreases from iodine to bromine. As the size of the anion decreases, the lattice energy should increase. However, if it states that it increases when it should decrease, this option is incorrect.
**Conclusion:**
Based on the analysis, the correct order of lattice enthalpy is represented by option 1, where the lattice energy decreases as the cation size increases.
