The correct order of hydration enthalpies of alkali metal ions is:

First, let us recall the basic idea of hydration enthalpy. Hydration enthalpy (symbol $$\Delta H_{hyd}$$) is the enthalpy change when one mole of gaseous ions is surrounded by water molecules to form the hydrated ion. The magnitude of $$\Delta H_{hyd}$$ depends on the electrostatic attraction between the ion and the polar water molecules.

The general proportionality that chemists use is

$$\Delta H_{hyd} \;\propto\; \dfrac{Z^{2}}{r}$$

where $$Z$$ is the charge on the ion and $$r$$ is its ionic radius. We state this relationship because, from Coulomb’s law, a small, highly charged ion has a large charge density, produces a strong electric field, and therefore attracts the water dipoles more strongly; this releases more energy, giving a larger (more negative) hydration enthalpy.

In the alkali-metal family every ion carries the same charge magnitude, namely $$Z = +1$$. Because $$Z$$ is identical for $$Li^{+}$$, $$Na^{+}$$, $$K^{+}$$, $$Rb^{+}$$ and $$Cs^{+}$$, we can simplify the proportionality to

$$\Delta H_{hyd} \;\propto\; \dfrac{1}{r}$$

So, now the rule becomes extremely clear: the smaller the ionic radius, the larger (more exothermic) the hydration enthalpy.

Let us write the experimentally established order of ionic radii for the alkali-metal ions. Going down the group, extra shells of electrons are added, so the radius increases:

$$r(Li^{+}) \lt r(Na^{+}) \lt r(K^{+}) \lt r(Rb^{+}) \lt r(Cs^{+})$$

Because hydration enthalpy varies inversely with radius, we simply reverse this radius order to obtain the hydration-enthalpy order:

$$\Delta H_{hyd}(Li^{+}) \gt \Delta H_{hyd}(Na^{+}) \gt \Delta H_{hyd}(K^{+}) \gt \Delta H_{hyd}(Rb^{+}) \gt \Delta H_{hyd}(Cs^{+})$$

Removing the symbols and writing the ions one after another, we have

$$Li^{+} \;>\; Na^{+} \;>\; K^{+} \;>\; Rb^{+} \;>\; Cs^{+}$$

We now compare this logically derived sequence with the four answer choices. Option 3 (often labelled option C) shows exactly this order:

$$Li^{+} \gt Na^{+} \gt K^{+} \gt Rb^{+} \gt Cs^{+}$$

None of the other options match the correct theoretical trend. Therefore our deduction is consistent with experimental data and textbook reasoning.

Hence, the correct answer is Option 3.