The first four ionization energies of an element are approximately \(738 \mathrm{~kJ} / \mathrm{mol}, \quad 1450 \mathrm{~kJ} / \mathrm{mol}, 7.7 \times\) \(10^{3} \mathrm{~kJ} / \mathrm{mol}\), and \(1.1 \times 10^{4} \mathrm{~kJ} / \mathrm{mol}\). To which periodic group does this element belong? Why?

Understanding the configuration of electrons in an element is crucial to identifying its place on the Periodic Table. The process involves comparing ionization energies, which represent the energy required to remove an electron from an atom. When analyzing successive ionization energies, a significant increase typically indicates the removal of an electron from a new, closer energy level to the nucleus, after the valence electrons have been removed.

To identify a periodic group from ionization energies, one must look for this telltale jump. In the exercise, the ionization energies surge from the second to the third ionization energy. This large increase signifies that the first two electrons are easier to remove and are most likely the valence electrons. As we know that elements in the same group have the same number of valence electrons, we can deduce that an element with two valence electrons falls into Group 2 of the Periodic Table.

Valence electrons are the outermost electrons of an atom and are involved in chemical bonding. The number of valence electrons can be inferred from the pattern of ionization energies. Ions with low ionization energies lose electrons easily, corresponding to the valence electrons.

In the provided exercise, the element's second ionization energy is noticeably lower than its third, suggesting the presence of two valence electrons. This is because removing the third electron requires breaking into a new shell that is closer to the nucleus and more tightly bound. So, the significant leap in energy required to remove the third electron is indicative of having cleared the valence shell, thus highlighting that the element has two valence electrons.

The Periodic Table is structured in such a way that elements with similar properties and the same number of valence electrons are placed within the same group, which are the columns of the table. These groups are numbered from 1 to 18.

Group 2, often referred to as the alkaline earth metals, includes elements like beryllium, magnesium, and calcium among others. They all have two valence electrons, which dictates their chemical reactivity and typical +2 oxidation state. Understanding the groupings of the Periodic Table is vital as it allows prediction of an element's properties based on its position, and in turn, this framework can be used to deduce the group number, as shown in the exercise, from an element's ionization energies.