2.10 Predict the ground-state clectron configuration of the following metal ions: (a) \(\mathrm{Mn}^{+} ;\)(b) \(\mathrm{Os}^{2+}\); (c) \(\mathrm{Rh}^{4}\); (d) \(\mathrm{Hg}^{2+}\).

Understanding the Aufbau principle is foundational for predicting electron configurations. This german term, meaning 'building up', refers to the rule that electrons occupy the lowest available energy level before filling higher levels. Electrons are like guests at a hotel; they prefer to fill up the lower floors before moving to higher ones.

According to the Aufbau principle, electrons are added one by one to the orbitals in a way that minimizes the energy of the atom. This process is akin to moving up a staircase, starting at the bottom and going to the next step only once the current one is fully occupied. The sequence in which orbitals are filled follows a specific order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on, accounting for the complexities of electron interaction and energy levels. This order can be navigated using an 'Aufbau diagram' that visually supports this stepped approach.

When predicting the electron configuration of metal ions in the exercise, removing electrons due to ionization starts from the highest energy level orbitals, following the rule 'last in, first out'.

Ground-state refers to the lowest energy state of an atom, where all its electrons are in the lowest possible energy levels and orbitals according to the Aufbau principle and other rules of electron configuration. It's the electron version of chilling at home in the most comfortable chair, whereas excited state is like being at a party—higher energy and less stable.

For elements on the periodic table, the ground-state is their default electron configuration when they're not reacting with other elements or absorbing energy. It’s important for predicting how atoms will interact during chemical reactions. In the context of the solved exercise, we look for the ground-state electron configurations of metal ions, aiming to understand how the removal of electrons affects their stability and reactivity.

The periodic table is not just a chart of elements; it's a map to understanding the fundamental properties of atoms, including their electron configurations. Much like a geographical map shows you landscapes, the periodic table shows landscapes of atomic characteristics, such as electronegativity and ionization energies.

This table groups elements by shared traits and increasing atomic number, offering insights into their electronic structure. The horizontal rows are called periods and the vertical columns are known as groups or families. Elements within the same group have similar electron configurations in their outer shells, indicating similar chemical behaviors. When determining the electron configurations for ground states or metal ions, we first locate the element on the periodic table and then use its position to discern the number of electrons and the expected arrangement.

Metal ions are atoms of metal that have lost or (less commonly) gained electrons, hence carrying a charge. Losing electrons often endows the metal ions with a positive charge, denoted by a plus sign and a numeral to indicate the charge magnitude. The process of becoming an ion is called ionization and it's like giving away tickets to an inviting electron concert—fewer tickets, fewer attendees, and a less 'neutral' crowd.

When metals form ions, they generally lose electrons from the s-orbital, and if necessary, from d-orbitals as in the case of transition metals. This loss alters the electron configuration and the chemical properties of the metal, which is essential in technologies like batteries and metal plating. In the exercise, we are examining how the electron configurations of various metal ions differ from their neutral counterparts. This knowledge helps in predicting how these ions will bond and react with other elements in chemical compounds.