Final answer:
Element Y, which is an electrical insulator, brittle, and dull, indicating it is a nonmetal, likely has the greater ionization energy compared to element X, which has properties of a metal.
Step-by-step explanation:
The greater ionization energy is a characteristic of nonmetals, which are typically poor conductors of heat and electricity, brittle, and have a dull appearance. An element with these properties, like Y, suggests that it is a nonmetal and would have a high ionization energy. On the other hand, element X has characteristics of a metal, being shiny, malleable, good electrical conductor, and reacting rapidly with water, indicating that it has a lower ionization energy. Therefore, element Y has the greater ionization energy.