The first four ionization energies of an element are approximately \(579 \mathrm{~kJ} / \mathrm{mol}, 1980 \mathrm{~kJ} / \mathrm{mol}, 2963 \mathrm{~kJ} /\) mol, and \(6180 \mathrm{~kJ} / \mathrm{mol}\). To which periodic group does this element belong?

First, identify the point at which there is a major leap in the ionization energies. Looking at the given data, the first two ionization energies: \(579 \mathrm{~kJ/mol}\) and \(1980 \mathrm{~kJ/mol}\) indicate the removal of an electron from the same energy level since the change in energy is relatively small. The jump from \(1980 \mathrm{~kJ/mol}\) to \(2963 \mathrm{~kJ/mol}\) is also relatively small, suggesting that the third electron is still in the same energy level. However, the energy leap to remove the fourth electron, from \(2963 \mathrm{~kJ/mol}\) to \(6180 \mathrm{~kJ/mol}\) is significantly large. This significant rise represents the removal of an electron from a new, closer energy level to the nucleus.

The considerable increase in energy after removing the third electron means that the initial atom had three electrons in its outermost shell or energy level. As it is known that the Periodic table is arranged in such way that elements in the same group have similar valence electron configuration, this information can be used to deduce which group the element belongs to: Since there is a big jump in ionization energy after the third electron is removed, this suggests that the element initially had three valence (outer shell) electrons, so it must belong to Group 3.