Question

Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. $(\mathrm{B}<\mathrm{Al}),(\mathrm{Al}<\mathrm{Ga}),(\mathrm{Ga}<\mathrm{In})$ and $(\mathrm{In}<\mathrm{Tl})$ Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius $\left(\mathrm{M}^{3+}\right)$ than the other one. The atomic number of the element (X) is

• A. 31
• B. 49
• C. 13
• D. 81

Hint:

The atomic radius and ionic radius depend on the atomic number and the periodic trends.

Answer 1

The Correct Option is A

To resolve this query, an analysis of each pair of Group 13 elements is required, examining the trends in atomic and ionic radii down the group.

1. The provided Group 13 element pairs are:
   • \((\mathrm{B} < \mathrm{Al})\)
   • \((\mathrm{Al} < \mathrm{Ga})\)
   • \((\mathrm{Ga} < \mathrm{In})\)
   • \((\mathrm{In} < \mathrm{Tl})\)
2. Generally, atomic radius increases down a group due to additional electron shells. However, deviations can occur owing to inadequate shielding by d and f orbitals.
3. Atomic radii comparisons:
   • \(\mathrm{B}\) vs \(\mathrm{Al}\): Aluminum (\(\mathrm{Al}\)) exhibits a larger atomic radius than Boron (\(\mathrm{B}\)), as expected.
   • \(\mathrm{Al}\) vs \(\mathrm{Ga}\): Typically, Ga is expected to have a greater atomic radius than Al. However, due to d-block contraction, Ga's radius is slightly smaller than anticipated, rendering this pair incorrect.
   • \(\mathrm{Ga}\) vs \(\mathrm{In}\): Indium (\(\mathrm{In}\)) possesses a larger atomic radius than Gallium (\(\mathrm{Ga}\)), which is correct.
   • \(\mathrm{In}\) vs \(\mathrm{Tl}\): Thallium (\(\mathrm{Tl}\)) has a larger atomic radius than Indium (\(\mathrm{In}\)), which is correct.
4. Consequently, the only incorrect pair is \((\mathrm{Al} < \mathrm{Ga})\).
5. Now, considering the ionic radii of \(\mathrm{Al}^{3+}\) and \(\mathrm{Ga}^{3+}\), for cations of the same charge, ionic radius usually decreases with atomic size and across a period. However, d-block contraction results in \( \mathrm{Ga}^{3+} \) having a larger ionic radius than \( \mathrm{Al}^{3+} \). Therefore, Gallium (Ga) has the greater ionic radius within the incorrect pair.
6. Gallium (Ga) has an atomic number of 31.

Thus, the element with the larger ionic radius in the incorrect pair is Gallium, with an atomic number of \(31\).