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

### Core Logic Let's evaluate the anomalies within Group 13 trends: * **Atomic Radius Order:** Due to the poor shielding effect of the filled 3d$3d$ electron subshell in Gallium (transition contraction), its outer valence shell experiences a stronger nuclear pull. Consequently, the atomic radius sequence exhibits an inversion: textCorrect Atomic Size: B < Ga < Al < In < Tl$$\text{Correct Atomic Size: } B < Ga < Al < In < Tl$$ Therefore, the pair (Al < Ga)$(Al < Ga)$ provided in the problem statement is incorrect. * **Ionic Radius Order (M^3+$M^{3+}$):** In the fully ionized +3$+3$ configuration state, the transition contraction anomaly is overridden by standard shell count physics. The ionic radius follows the uniform down-the-group trend: Al^3+ < Ga^3+$$Al^{3+} < Ga^{3+}$$ Hence, Gallium (Ga$Ga$) has the larger ionic radius between the two elements. Its atomic number is 31. ### Pattern Recognition Transition contraction heavily distorts the *atomic* radius profile of Gallium, but standard descending size progression rules are fully restored when evaluating the *ionic* M^3+$M^{3+}$ radius profile. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Classification of Elements and Periodicity in Properties Class 12 Chemistry: The p-Block Elements