To determine the order of enthalpies of hydration of the given metal ions $Ca^{2+}$, $Mn^{2+}$, and $Zn^{2+}$, we need to understand the factors that affect hydration enthalpy. The enthalpy of hydration of an ion is influenced by:

• The charge on the ion: Higher charge generally increases enthalpy of hydration.
• The size of the ion: Smaller ions typically have higher enthalpy of hydration due to a higher charge density.

Both $Ca^{2+}$, $Mn^{2+}$, and $Zn^{2+}$ are divalent cations with a +2 charge. Therefore, we must consider the size and electronic configuration to determine their hydration enthalpies.

1. Calcium ($Ca^{2+}$): It belongs to group 2 and the size is relatively larger compared to the transition metals. As a result, its hydration enthalpy is expected to be lower.
2. Manganese ($Mn^{2+}$): Manganese is a transition metal, and its position in the periodic table suggests that it has a smaller ionic radius than calcium. It has a partially filled d-sub shell that could influence its ability to be hydrated.
3. Zinc ($Zn^{2+}$): Zinc is also a transition metal, and it has a completely filled d-sub shell (d¹⁰). Zinc's ionic radius is smaller than that of calcium and generally comparable to manganese; however, often the complete d-shell gives additional stabilization energy, affecting enthalpy positively.

Among these ions, $Zn^{2+}$ usually exhibits higher hydration enthalpy due to its smaller size and unique electronic configuration. $Mn^{2+}$ is expected to follow and $Ca^{2+}$, being the most sizeable, has the lowest hydration enthalpy.

Therefore, the order of enthalpies of hydration is:

• $Zn^{2+} > Mn^{2+} > Ca^{2+$

The correct answer is: $Zn^{2+} > Mn^{2+} > Ca^{2+}$