Final answer:
The element with the given successive ionization energies 738; 1,450; 7,734; and 10,550 kJ/mol on the third row of the periodic table is magnesium (Mg), suggested by the considerable increase in ionization energy after the second IE.
Step-by-step explanation:
The student is asking to identify an element with a particular set of successive ionization energies (IEs). Ionization energies refer to the energy required to remove electrons from an atom. In this case, the given ionization energies are 738; 1,450; 7,734; and 10,550 kJ/mol. A significant jump in ionization energy typically indicates that we have moved to a new electron shell, which suggests the number of valence electrons in the element.
An element in the third row of the periodic table, with such a pattern of ionization energies, particularly with a large jump occurring after the second ionization energy, likely refers to a member of the alkaline earth metals (Group 2), because it suggests the element has two valence electrons. When looking at the third row of the periodic table, the alkaline earth metal is magnesium (Mg), with an atomic number of 12. Therefore, the element represented by 8135X, based on the provided ionization energies, is most likely magnesium.