Give the ground-state electron configuration expected for each of the following ions: (a) \(\mathrm{Br}^{-}\); (b) \(\mathrm{Rh}^{3+}\); (c) \(\mathrm{Nb}^{3+}\); (d) \(\mathrm{Te}^{2-}\).

The periodic table is an essential tool in chemistry that organizes all the known elements in an informative array. Elements are arranged in order of increasing atomic number, which is the number of protons in an atom's nucleus. The table is structured by rows known as periods and columns known as groups or families, with each position reflecting an element's atomic structure, including the number of electrons and their arrangement. The periodic table not only enables us to find the atomic number but also provides a visual representation of periodic trends, such as electron configurations, reactivity, and the formation of ions.

When dealing with ion configurations, the periodic table can guide us to understand which electrons will be lost or gained, as elements tend to adopt the electron configuration of their nearest noble gas, leading to a stable, low-energy state. Understanding the layout of the periodic table, including s, p, d, and f blocks, is critical for predicting how atoms will interact to form ions.

The atomic number is a fundamental characteristic of an element that defines its identity. It is equal to the number of protons in the nucleus of an atom, and by extension, it determines the number of electrons in a neutral atom.

In the context of electron configuration, an atom's atomic number allows us to deduce the order in which its electron shells and subshells are filled. A higher atomic number means more electrons, and understanding which orbitals these additional electrons occupy is pivotal. For instance, the atomic number directly influences ion formation, where the total number of electrons will either increase or decrease to form anions or cations.

Understanding the electron configuration of ions requires grasping the process atoms undergo to achieve a more stable, energetically favorable state. Typically, atoms gain or lose electrons to emulate the electron configuration of the closest noble gas, which is often referred to as having a 'full octet' in their outer shell.

For anions, an atom has gained extra electrons, and this surplus must be accounted for when writing the electron configuration. Conversely, cations have lost electrons, requiring us to remove electrons starting from the outermost shell when deducing their electron configuration. This logic is critical in explaining why certain ions have specific charges and helps predict ion behavior during chemical reactions. When an atom forms an ion, it does not alter its atomic number but changes its electron count, profoundly influencing its chemical properties.

Anions and cations are types of ions that form when atoms gain or lose electrons, respectively. Anions carry a negative charge due to the addition of electrons, which increases the electron count beyond the number of protons. These negatively charged ions are usually nonmetals as they have a greater affinity for additional electrons to complete their valence shell.

Cations, on the other hand, have a positive charge as a result of losing electrons, which leaves the atom with fewer electrons than protons. Cations are often metals as they are more inclined to give up their valence electrons to achieve stability. The formation of anions and cations is a core principle in chemistry that facilitates the understanding of ionic bonds, where oppositely charged ions attract each other to form compounds.