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 solve this question, we need to analyze each pair of group 13 elements, considering the trends in atomic and ionic radii as one moves down the group in the periodic table.

1. The given pairs of group 13 elements are:
   • \((\mathrm{B} < \mathrm{Al})\)
   • \((\mathrm{Al} < \mathrm{Ga})\)
   • \((\mathrm{Ga} < \mathrm{In})\)
   • \((\mathrm{In} < \mathrm{Tl})\)
2. Typically, as we move down a group, the atomic radius increases due to the addition of new electron shells. However, due to the poor shielding effect of d and f orbitals, anomalies may occur.
3. By comparing atomic radii:
   • \(\mathrm{B}\) vs \(\mathrm{Al}\): Aluminum (\(\mathrm{Al}\)) has a larger atomic radius than Boron (\(\mathrm{B}\)), which is consistent.
   • \(\mathrm{Al}\) vs \(\mathrm{Ga}\): Generally expected that Ga would have a higher atomic radius than Al, but due to the d-block contraction, Ga actually has a slightly smaller radius than expected, making this pair incorrect.
   • \(\mathrm{Ga}\) vs \(\mathrm{In}\): Indium (\(\mathrm{In}\)) has 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. Therefore, the only incorrect pair is \((\mathrm{Al} < \mathrm{Ga})\).
5. Now, considering the ionic radii of \(\mathrm{Al}^{3+}\) and \(\mathrm{Ga}^{3+}\), typically for cations with the same charge, the ionic radius decreases with a decrease in atomic size and across a period. However, due to d-block contraction, \( \mathrm{Ga}^{3+} \) has a larger ionic radius than \( \mathrm{Al}^{3+} \). This makes Gallium (Ga) the element with a higher ionic radius in the incorrect pair.
6. The atomic number of Gallium (Ga) is 31.

Thus, the element with a higher ionic radius in the incorrect pair is Gallium, and its atomic number is \(31\).

Answer 2

1. Incorrect pair: - $\mathrm{Al}<\mathrm{Ga}$
2. Ionic radius comparison: - $\mathrm{Al}^{3+}<\mathrm{Ga}^{3+}$ 
- The atomic number of $\mathrm{Ga}$ is 31. 
Therefore, the correct answer is (1) 31.