Stability by using charge/radius rule
Please allow me to answer the question in two parts.

Stability of carbonates

We observe this order when we compare the thermal stability of group I-A carbonates: $$\ce{Li2CO3 \lt Na2CO3 \lt K2CO3 \lt Rb2CO3 \lt Cs2CO3}$$

On similar grounds, the thermal stability of group II-A carbonates can be predicted.

This order is in accordance with Fajans' Rules. Here's the table we need to glance at from the Wikipedia page.


  $$\begin{array}{|c|c|} \hline
\mathrm{Ionic} &amp; \text{Covalent}\  \\ \hline
\text{Low positive charge} &amp; \text{High positive charge} \\
\text{Large cation} &amp; \text{Small cation} \\
\text{Small anion} &amp; \text{Large anion} \\ \hline \end{array}$$
  Polarization will be increased by high charge and small size of the cation.


Thus, larger the ratio of charge and radius, higher is the polarization power of the cation, more is the covalent character in the compound and lesser is the ionic character; Ionic compounds are more stable when exposed to heat. A higher ratio will therefore mean lesser stability.

Stability of complex compounds

Thermodynamic stability of complexes, on the other hand, is determined by the Irving–Williams series, according to which general stability sequence of high spin octahedral metal complexes for the replacement of water by other ligands is: 
$$\ce{Mn^2+ &lt; Fe^2+ &lt; Co^2+ &lt; Ni^2+ &lt; Cu^2+ &gt; Zn^2+}$$
Owing to this observation, a lot of theories were formulated to explain this phenomenon. One such theory was that since Crystal Field Theory (CFT) was based on the idea that a purely electrostatic interaction existed between the central metal ion and the ligands, the stability of complexes should be somehow related to the size by charge ratio (otherwise known as the ionic potential) of the central metal atom. [Source]

An interesting thing to note here is that Wikipedia has stated in its article that:


  None of the explanations can satisfactorily explain the success of the Irving–Williams series in predicting the relative stabilities of transition metal complexes.


Thus from manganese till copper, it can be said that higher the ionic potential, more is the stability.