Step 1: Evaluate each statement
Statement (A):
The atomic radii order for group 13 elements is asserted as \(\text{Tl} > \text{In} > \text{Al} > \text{Ga} > \text{B}\), contradicting the actual order \(\text{Tl} > \text{In} > \text{Ga} > \text{Al} > \text{B}\).
- This statement is false.
2.Statement (B):
Electronegativity generally decreases down a group. However, the presence of \(d\)-electrons in \(\text{Ga}\), \(\text{In}\), and \(\text{Tl}\) disrupts this simple trend in their electronegativity values.
- This statement is false.
3.Statement (C):
\(\text{Al}\) reacts with dilute \(\text{HCl}\) to produce \(\text{H}_2\):
\[2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2.\]
Additionally, concentrated \(\text{HNO}_3\) passivates \(\text{Al}\) by forming an oxide layer, preventing further reaction.
- This statement is true.
4.Statement (D):
Within group 13, the \(+3\) oxidation state is more stable than \(+1\). The \(+1\) state is observed in \(\text{Tl}\) due to the inert pair effect, but it lacks significant stability across all elements in this group.
- This statement is false.
5.Statement (E):
In \([\text{Al}(\text{H}_2\text{O})_6]^{3+}\), the hybridization of \(\text{Al}\) is \(\text{sp}^3\text{d}^2\), resulting in an octahedral geometry. - This statement is true.
Step 2: Conclusion
Statements (C) and (E) are accurate.
Final Answer: (1).