Final answer:
Element X is most likely from Group 14 (Carbon family) due to the large increase in ionization energy after the fourth ionization, aligning with the expected ionization energy pattern for a Group 14 element with four valence electrons.
The correct answer is option c) Group 14 (Carbon family)
Step-by-step explanation:
The question relates to the determination of the group in the periodic table to which element X belongs based on its successive ionization energies. Ionization energy (IE) is the energy required to remove an electron from an atom or ion in its gaseous state. Looking at the provided ionization energies for element X (1E1 = 786.3 kJ/mol; 1E2 = 1580 kJ/mol; 1E3 = 3230 kJ/mol; 1E4 = 4360 kJ/mol; 1E5 = 16,000 kJ/mol; 1E6 = 20,000 kJ/mol), there is a significant increase in the energy required between the fourth and fifth ionizations. This suggests that the element has four valence electrons and the relatively low energies for the first four ionizations followed by a large jump before the fifth ionization indicate that element X is likely to be from Group 14 (Carbon family), where it is typical to have a large energy gap after the removal of the valence electrons.
Group 17 (Halogens) elements would not fit this pattern, as they have seven valence electrons, and an alkali metal (Group 1) would have a single valence electron with a subsequent large increase in ionization energy after the first electron is removed. An alkaline earth metal from Group 2 would show a significant increase after the removal of two electrons. Therefore, based on the presented data and the periodic trends, element X is most likely a member of the Group 14 (Carbon family).