Discuss the pattern of variation in the oxidation states of $(i)$ $B$ to $Tl$ and $(ii)$ $C$ to $Pb$.

(N/A) $(i)$ $B$ to $Tl$: The electronic configuration of group $13$ elements is $ns^2 np^1$. Therefore,the most common oxidation state exhibited by them should be $+3$. However,only boron and aluminium practically show the $+3$ oxidation state. The remaining elements,i.e.,$Ga$,$In$,$Tl$,show both $+1$ and $+3$ oxidation states. On moving down the group,the $+1$ state becomes more stable due to 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 effect becomes more prominent down the group. Hence,$Ga(+1)$ is unstable,$In(+1)$ is fairly stable,and $Tl(+1)$ is very stable. The stability of the $+3$ oxidation state decreases down the group.

Group $13$ element	Oxidation state
$B$	$+3$
$Al$	$+3$
$Ga, In, Tl$	$+1, +3$

$(ii)$ $C$ to $Pb$: The electronic configuration of group $14$ elements is $ns^2 np^2$. Therefore,the most common oxidation state should be $+4$. However,the $+2$ oxidation state becomes more common down the group. $C$ and $Si$ mostly show the $+4$ state. On moving down the group,the higher oxidation state becomes less stable due to the inert pair effect. Thus,although $Ge$,$Sn$,and $Pb$ show both $+2$ and $+4$ states,the stability of the lower oxidation state $(+2)$ increases and that of the higher oxidation state $(+4)$ decreases down the group.

Group $14$ element	Oxidation state
$C$	$+4$
$Si$	$+4$
$Ge, Sn, Pb$	$+2, +4$

Stability of $+2$ state increases: $C < Si < Ge < Sn < Pb$
Stability of $+4$ state decreases: $C > Si > Ge > Sn > Pb$