Which of the following orders is incorrect ?

Options

A. a. `N lt O lt F-II^(nd)` ionization energy.
B. b. `Li^(+) gt Na^(+) gt K^(+) -` ionic radius in water.
C. c. `S gt Se gt O -` negative value of electron gain enthalpy
D. d. `Al_(2)O_(3) lt MgO lt K_(2)O -` basic character.

Explanation

To determine which of the following orders is incorrect, we need to analyze the provided options one by one, focusing on the second ionization energy, ionic radius, electron gain enthalpy, and the basic nature of oxides.

### Step-by-Step Solution:

1. **Option A: Second Ionization Energy of N, O, and F**
- We need to consider the electronic configurations of the unipositive ions (N⁺, O⁺, F⁺).
- N⁺: The electronic configuration is 1s² 2s² 2p².
- O⁺: The electronic configuration is 1s² 2s² 2p³.
- F⁺: The electronic configuration is 1s² 2s² 2p⁴.
- The stability of these ions affects their second ionization energies. O⁺ has a half-filled p orbital configuration, which is particularly stable.
- Therefore, the order of second ionization energy should be: O⁺ > F⁺ > N⁺.
- If the order given in the question is different, then option A is incorrect.

2. **Option B: Ionic Radius of Li⁺, Na⁺, and K⁺ in Water**
- The charge density of an ion affects its ionic radius in solution.
- Li⁺ has a higher charge density than Na⁺ and K⁺, leading to more solvation and a smaller effective radius.
- Therefore, the order of ionic radius in water should be: Li⁺ < Na⁺ < K⁺.
- If the order given in the question states otherwise, then option B is incorrect.

3. **Option C: Electron Gain Enthalpy of S, Cl, and O**
- The electron gain enthalpy values are influenced by the atomic size and the ability to accommodate an additional electron.
- Sulfur (S) has a more negative electron gain enthalpy than chlorine (Cl) and oxygen (O) because it has vacant d-orbitals that can accommodate the extra electron, minimizing repulsion.
- The expected order is: S > Cl > O.
- If the order given in the question is different, then option C is incorrect.

4. **Option D: Basic Nature of Oxides (K, Mg, Al)**
- The basic nature of oxides generally decreases across a period and increases down a group.
- Therefore, the order of basic nature for the oxides should be: K₂O > MgO > Al₂O₃.
- If the order given in the question states otherwise, then option D is incorrect.

### Conclusion:
Upon analyzing all options, we can conclude that **Option A** is incorrect regarding the order of second ionization energies of nitrogen, oxygen, and fluorine.