\(2.8\) Give the ground-state clectron configuration expected for each of the following ions: (a) \(\mathrm{Ga}^{+}\); (b) \(\mathrm{Tc}^{4+}\); (c) \(\mathrm{Se}^{4+}\); (d) \(\mathrm{Br}^{3+}\).

Understanding electron configuration is essential for studying chemistry, particularly when examining how atoms interact to form compounds. Electron configuration describes the arrangement of electrons around the nucleus of an atom or ion in atomic orbitals. The configuration follows a specific order, often represented using the Aufbau principle, which dictates that electrons fill lower-energy orbitals before occupying higher-energy ones.

For example, the electron configuration for a neutral carbon atom, with six electrons, is written as \(1s^22s^22p^2\). When an atom gains or loses electrons to form an ion, its electron configuration changes accordingly. In the case of the ion \(\mathrm{Ga}^+\), the loss of one electron from the neutral gallium atom alters its electron configuration to \( [Ar]3d^{10}4s^24p^0\), matching that of the zinc atom with 30 electrons.

The fundamental chemical principles that govern electron configuration include the laws of quantum mechanics and the periodic nature of the elements. Quantum mechanics explain how electrons exist in quantized energy states within an atom, leading to the discrete electron shells and subshells revealed on the periodic table.

Chemical principles also dictate that elements with similar electron configurations will exhibit similar chemical behaviors, which is why the periodic table is organized into groups and periods. For instance, all noble gases have full electron shells, making them largely unreactive. Additionally, ions will typically attain a noble gas electron configuration when possible. This is evident with ions such as \(\mathrm{Se}^{4+}\), which attains a noble gas configuration similar to neon after losing electrons.

Ions are atoms or molecules that have lost or gained electrons, resulting in a net electrical charge. The ionic charge is typically denoted by a superscript after the chemical symbol, such as \(\mathrm{Tc}^{4+}\) indicating a technetium ion with a 4+ charge. This ionic charge is critical when determining the resulting electron configuration, as it directly influences the total number of electrons present in the ion. In determining configurations as shown in our exercises, one must add or remove the number of electrons corresponding to the charge, relative to the neutral atom state. For instance, to get the electron configuration of \(\mathrm{Br}^{3+}\), we remove three electrons from the neutral bromine atom because its charge is 3+.

Understanding ionic charge facilitates predictions about the chemical properties of ions, including their reaction tendencies and formation of chemical bonds.

The periodic table is not only a tool for understanding atomic structure but also a guide for predicting the properties of ions. Ions often form by elements seeking to attain stability through a closed-shell electron configuration of the nearest noble gas, as this is a particularly stable arrangement.

When studying ions, the periodic table can help us predict which electrons will be lost or gained to form a particular charge. Elements in group 1, for instance, tend to lose one electron to form 1+ ions, while group 17 elements commonly gain one electron to form 1- ions. These processes are driven by the element's desire to achieve the electron configuration of their nearest noble gas. Hence, learning the trends of the periodic table allows you to better understand the formation and configuration of ions, and why \(\mathrm{Ga}^{+}\) will have the electron configuration as a \(\mathrm{Zn}\) atom.