To solve this question, let's analyze the properties of Group 13 elements, also known as the boron family, and verify each given statement:
- Electronegativity: As we move down Group 13 from Boron to Thallium, the electronegativity of the elements generally decreases. However, there might be small anomalies due to inert pair effects in heavier elements, but primarily it decreases. Hence, statement (A) is generally correct.
- Size: Atomic size increases down a group due to the addition of new electron shells. Therefore, statement (B) is correct.
- Ionization Energy: Ionization energy generally decreases down the group due to an increase in atomic size, making outer electrons easier to remove. But, due to poor shielding by d and f orbitals in heavier elements, anomalies can occur. Statement (C) is generally correct when considering the trend but not specifically for every consecutive pair elements.
- Boiling Point: Boron has the highest boiling point in this group. It exhibits strong covalent structures which require a large amount of energy to break. Hence, statement (D) is correct.
- Melting Point: Similarly, Boron has the highest melting point among the Group 13 elements, due to its strong covalent structure. Thus, statement (E) is correct.
Based on the analysis, option "D and E are correct" is indeed the correct answer. Statements D and E correctly highlight that Boron has the highest boiling and melting points, consistent with strong bonding and structure in the element.