Discuss the pattern of variation in the oxidation states of

$(i)$ $B$ to $Tl$ and $(ii)$ $C$ to $Pb$.

$(i)$ $B$ to $TI$ : The electric configuration of group $13$ elements is $n s^{2} n p^{1}$. Therefore, the most common oxidation state exhibited by them should be $+3$. However, it is only boron and aluminium which practically show the $+3$ oxidation state.

The remaining elements, i.e., $Ga$,$In$, $Tl$, show both the $+1$ and $+3$ oxidation states. On moving down the group, the $+1$ state becomes more stable. For example, $\mathrm{Tl}(+1)$ is more stable than $\mathrm{Tl}$ $(+3)$. This is because of the inert pair effect.

The two electrons present in the s-shell are strongly attracted by the nucleus and do not participate in bonding. This inert pair effect becomes more and more prominent on moving down the group. Hence, Ga $(+1)$ is unstable, In $(+1)$ is fairly stable and $\mathrm{Tl}(+1)$ is very stable.

Elements	$\mathrm{B}$	$\mathrm{Al}$	$\mathrm{Ga}, \mathrm{In}, \mathrm{Tl}$
Oxidation number	$+3$	$+3$	$+1,+3$

The stability of the $+3$ oxidation state decreases on moving down the group.

$(ii)$ $\mathrm{C}$ to $\mathrm{Pb}$ : The electronic configuration of group $14$ elements is $n s^{2} n p^{2}$. Therefore, the most common oxidation state exhibited by them should be $+4$. However, the $+2$ oxidation state becomes more and more common on moving down the group. $C$ and $Si$ mostly show the $+4$ state.

On moving down the group, the higher oxidation state becomes less stable. This is because of the inert pair effect. Thus, although $Ge$, $\mathrm{Sn}$ and $\mathrm{Pb}$ show both the $+2$ and $+4$ states, the stability of the lower oxidation state increases and that of the higher oxidation state decreases on moving down the group.

Elements	$\mathrm{C}$	$\mathrm{Si}$	$\mathrm{Ge}, \mathrm{Sn}, \mathrm{Pb}$
Oxidation number	$+4$	$+4$	$+2,+4$