In which of the following options the order of arrangement does not agree with the variation of property in indicated against it ?

Options

A. `I lt Na lt C1 lt F` (increasing electron gain enthalpy)
B. `Li lt Na lt K lt Rb` (increasing metallic radius )
C. `A1^(3+) lt Mg^(2+) lt Na^(+) lt F^(-)` (inreasing ionic size )
D. `B lt C lt N lt O` (inreasing first ionisation enthalpy )

Explanation

To solve the question regarding the order of arrangement that does not agree with the variation of properties indicated, we will analyze the options provided in the question step by step.

### Step 1: Understanding Electron Gain Enthalpy
- **Concept**: Electron gain enthalpy refers to the energy change when an electron is added to a neutral atom in the gas phase. Generally, smaller atoms have a more negative electron gain enthalpy because they can stabilize the added electron better due to their higher effective nuclear charge.
- **Trend**: For halogens (F, Cl, Br, I), as we move down the group, the atomic size increases, leading to a decrease in electron gain enthalpy (less negative). However, fluorine has a unique case due to its small size and high electron-electron repulsion when an extra electron is added.

### Step 2: Analyzing the Order of Halogens
- **Order Given**: F > Cl > Br > I (in terms of increasing electron gain enthalpy).
- **Correct Order**: The correct order should be Cl > F > Br > I because the electron gain enthalpy of fluorine is less negative than chlorine due to the increased electron-electron repulsion in the small fluorine atom.
- **Conclusion**: This order does not agree with the expected trend.

### Step 3: Understanding Metallic Radii
- **Concept**: Metallic radius increases down a group due to the addition of electron shells.
- **Order Given**: Li < Na < K < Rb (in terms of increasing metallic radius).
- **Conclusion**: This order is correct as the size increases down the group.

### Step 4: Analyzing Ionic Sizes
- **Concept**: Cations are smaller than their parent atoms, and anions are larger. The order of ionic size is influenced by the charge and the number of electrons.
- **Order Given**: Al³⁺ < Mg²⁺ < Na⁺ < F⁻ (in terms of increasing ionic size).
- **Conclusion**: This order is correct as the ionic size increases from cations to anions.

### Step 5: Understanding Ionization Energy
- **Concept**: Ionization energy generally increases across a period due to increasing nuclear charge and decreasing atomic radius.
- **Order Given**: B < C < N < O (in terms of increasing first ionization enthalpy).
- **Correct Order**: The correct order should be B < C < N > O. Oxygen has a lower ionization energy than nitrogen due to electron-electron repulsion in the p-orbitals.
- **Conclusion**: This order does not agree with the expected trend.

### Final Conclusion
The orders that do not agree with the variation of properties are:
1. Increasing electron gain enthalpy for halogens (F, Cl, Br, I).
2. Increasing first ionization enthalpy for B, C, N, O.

### Summary of Incorrect Orders:
- **Option 1**: Electron gain enthalpy of halogens (F, Cl, Br, I).
- **Option 4**: First ionization enthalpy of B, C, N, O.