Final answer:
Element III, with the highest first (1142 kJ/mol) and second (2080 kJ/mol) ionization energies, is the likely non-metal among the given elements, as non-metals tend to have higher ionization energies due to stronger electron-nucleus attractions. In contrast, the lower ionization energies of Elements I and II suggest they may be metals or metalloids.
Step-by-step explanation:
To identify the non-metallic element based on first and second ionization energies, one should look for higher IE values, as non-metals generally have higher ionization energies due to their stronger attraction to electrons. In the given data, Element III has the highest first ionization energy (IE1) at 1142 kJ/mol and a second ionization energy (IE2) of 2080 kJ/mol. This suggests that Element III is likely the non-metal as it not only needs more energy to remove the first electron but also a significantly high amount of energy to remove the second electron, which follows the general trend that ionization energy increases across a period from left to right. Consequently, it would be reasonable to give mcq answer that Element III is the non-metal.
Elements I and II have lower IE1 values of 403 kJ/mol and 549 kJ/mol, respectively, indicating they are more likely to be metals or metalloids as their electrons are more easily removable. Given the fact that the ionization energy for metals and some metalloids is lower, their IE2 values of 2640 kJ/mol for Element I and 1060 kJ/mol for Element II also suggest they are less likely to be non-metals. Remember, large jumps in ionization energy usually indicate a new electron shell is being accessed which is a characteristic behavior of metals and metalloids as they lose their valence electrons.