Q.What is the inert pair effect? Using this idea, explain why thallium is more stable in the $+1$ oxidation state than in the $+3$ state, even though $+3$ is the group oxidation state for Group 13.

[!TLDR] The inert pair effect is the reluctance of the outer $ns^2$ pair to bond in heavier p-block elements, making a lower oxidation state (2 less than the group state) increasingly stable down the group. [!ANSWER] Because thallium's $6s^2$ pair resists bonding (poor shielding by the intervening d/f electrons plus relativistic contraction), $\text{Tl}^{+}$ (using only the $6p$ electron) is more stable than $\text{Tl}^{3+}$, so $\text{Tl}^{3+}$ compounds are strong oxidisers that revert to $\text{Tl}^{+}$.

The inert pair effect describes the increasing reluctance of the outermost $ns^2$ electron pair to take part in bonding as one descends a p-block group, so that an oxidation state two units below the nominal group oxidation state becomes progressively more stable for the heavier members. Two factors drive this: the filled inner $d$ (and, lower still, $f$) subshells of the heavier elements shield the nucleus poorly, so the outer $ns$ electrons are held unusually tightly and close to the nucleus; and for the very heaviest elements, relativistic effects further contract and stabilise the $ns$ orbital. For Group 13, whose nominal group oxidation state is $+3$ (using all three valence electrons, $ns^2np^1$), the inert-pair state is $+1$ (using only the single $np$ electron and leaving the $ns^2$ pair non-bonding). This effect is negligible for boron and aluminium, appears mildly for gallium and indium, and becomes dominant for thallium: thallium's $6s^2$ pair is held so tightly that $\text{Tl}^{+}$ compounds are in fact more thermodynamically stable than $\text{Tl}^{3+}$ compounds, the reverse of the situation for boron and aluminium, whose $+3$ state is essentially the only one seen under ordinary conditions. A direct consequence is that $\text{Tl}^{3+}$ is a comparatively strong oxidising agent in aqueous solution: it readily accepts two electrons and is reduced to the more stable $\text{Tl}^{+}$ state, releasing energy in the process, exactly analogous to how $\text{Pb}^{4+}$/$\text{PbO}_2$ behaves as a strong oxidiser in Group 14. [!ANSWER] Thallium's inert $6s^2$ pair resists bonding, so $+1$ is more stable than the group's nominal $+3$ state, making $\text{Tl}^{3+}$ compounds strong, easily-reduced oxidising agents.

Define the inert pair effect and its causes (poor inner-shell shielding, relativistic contraction), then apply it specifically to compare thallium's $+1$ and $+3$ states and their relative stability/redox behaviour.

Describing the inert pair effect only for lead/tin (Group 14) and forgetting it applies equally, in fact most dramatically, to thallium in Group 13; stating that Tl3+ is stable rather than recognising it is a strong oxidiser precisely because it is not.