Identify the elements involved

The lists compare group 13 elements: $\mathrm{B},\ \mathrm{Al},\ \mathrm{Ga},\ \mathrm{In},\ \mathrm{Tl}$

Match D: Atomic radius

Down the group, atomic radius generally increases, but due to poor shielding by $d$-electrons, $\mathrm{Ga}$ is slightly smaller than expected.

Hence the order is: $\mathrm{B} > \mathrm{Al} > \mathrm{Tl} > \mathrm{In} > \mathrm{Ga}$ when written in decreasing order of the given List II pattern? Let us inspect the options carefully.

Known actual trend in atomic radii is approximately: $\mathrm{B} < \mathrm{Al} > \mathrm{Ga} < \mathrm{In} \approx \mathrm{Tl}$ More precisely among these choices, the decreasing order is: $\mathrm{Tl} > \mathrm{In} > \mathrm{Al} > \mathrm{Ga} > \mathrm{B}$ This matches III: $\mathrm{Tl} > \mathrm{In} > \mathrm{Al} > \mathrm{Ga} > \mathrm{B}$

So, $D \to III$

Match B: Ionic radius of $\mathrm{M^{3+}}$

For group 13 trivalent ions:

• $\mathrm{B^{3+}}$ is extremely small
• due to $d$-block contraction, $\mathrm{Ga^{3+}}$ is close to or slightly smaller than $\mathrm{Al^{3+}}$
• then radius increases to $\mathrm{In^{3+}}$ and $\mathrm{Tl^{3+}}$

Thus decreasing order is: $\mathrm{Tl^{3+}} > \mathrm{In^{3+}} > \mathrm{Ga^{3+}} > \mathrm{Al^{3+}} > \mathrm{B^{3+}}$ Since standard data often gives $\mathrm{Al^{3+}} < \mathrm{Ga^{3+}}$ or nearly close, among the listed patterns the accepted order is: $\mathrm{Tl} > \mathrm{In} > \mathrm{Ga} > \mathrm{Al} > \mathrm{B}$ which matches I: $\mathrm{Tl} > \mathrm{In} > \mathrm{Ga} > \mathrm{Al} > \mathrm{B}$

So, $B \to I$

Match C: First ionization enthalpy $\Delta_i H_1$

General trend in group 13:

• $\mathrm{B}$ has highest
• then decreases to $\mathrm{Al}$
• $\mathrm{Ga}$ is slightly higher than $\mathrm{Al}$ due to poor shielding by $d$ electrons
• decreases to $\mathrm{In}$
• increases again for $\mathrm{Tl}$ due to lanthanide contraction and inert pair effect

Therefore the decreasing order is: $\mathrm{B} > \mathrm{Tl} > \mathrm{Al} \approx \mathrm{Ga} > \mathrm{In}$ This matches II.

So, $C \to II$

Match A: Melting point

For group 13 elements, the melting points follow approximately:

• $\mathrm{B}$ has extremely high melting point (covalent network solid)
• $\mathrm{Al}$ is fairly high
• $\mathrm{Ga}$ is very low
• $\mathrm{In}$ moderate
• $\mathrm{Tl}$ higher than In but less than Al

Decreasing order is: $\mathrm{B} > \mathrm{Al} > \mathrm{Tl} > \mathrm{In} > \mathrm{Ga}$ This matches IV.

So, $A \to IV$

Final matching

$A \to IV,\quad B \to I,\quad C \to II,\quad D \to III$

Choose the correct option

This corresponds to Option A.