Which of the following is the correct order with respect to the property indicated?

The correct option is K₂O > Na₂O > Al₂O₃ (Basic nature).

Let us analyze each of the given options to understand the correct order of the properties:

1. Basic nature of oxides: K₂O > Na₂O > Al₂O₃
- The basic character of oxides depends on the metallic character of the element forming the oxide. The more metallic the element, the more basic its oxide will be.
- Metallic character increases down a group and decreases across a period from left to right.
- Potassium ($K$) and Sodium ($\mathrm{Na}$) belong to Group 1 (alkali metals), which are highly electropositive and form strongly basic oxides. Since potassium lies below sodium in Group 1, it is more metallic, making $K_{2}O$ more basic than ${\mathrm{Na}}_{2}O$.
- Aluminium ($\mathrm{Al}$) is a Group 13 metal. Its oxide, ${\mathrm{Al}}_2{O}_3$, is amphoteric (shows both acidic and basic properties) and is significantly less basic than the alkali metal oxides.
- Therefore, the correct decreasing order of basic nature is:
$K_{2}O>{\mathrm{Na}}_{2}O>{\mathrm{Al}}_2{O}_3$

2. Ionisation energy: Cl > F
- Ionisation energy is the energy required to remove an electron from an isolated gaseous atom.
- As we move down a group, the atomic size increases and shielding effect increases, making it easier to remove an electron. Consequently, ionisation energy decreases down the group.
- Fluorine ($F$) and Chlorine ($\mathrm{Cl}$) belong to Group 17 (halogens), with $F$ sitting above $\mathrm{Cl}$.
- Thus, fluorine has a higher ionisation energy than chlorine ($F>\mathrm{Cl}$). The order Cl > F is incorrect.

3. Metallic character: K > Na > Al > Mg
- Metallic character (electropositive character) increases down a group and decreases from left to right across a period.
- Looking at the positions of the elements in the periodic table:
- Group 1: $K>\mathrm{Na}$
- Period 3: $\mathrm{Na}>\mathrm{Mg}>\mathrm{Al}$
- Comparing them all, the correct decreasing order of metallic character is K > Na > Mg > Al. The order given in the option (K > Na > Al > Mg) is incorrect.