Write the ground state electron configuration for (a) \(\mathrm{Mg}, \mathrm{Mg}^{2+}\) (b) \(\mathrm{N}, \mathrm{N}^{3-}\) (c) \(\mathrm{Ti}, \mathrm{Ti}^{4+}\) (d) \(\mathrm{Sn}^{2+}, \mathrm{Sn}^{4+}\)

Understanding the ground state electron configuration is fundamental in chemistry and physics, as it describes the arrangement of electrons in an atom's orbitals at its most energetically stable. Electrons fill subshells (s, p, d, f and so on) in a way that minimizes the energy of the atom. This filling order is dictated by the principles of quantum mechanics.

For example, the ground state configuration for a neutral magnesium (Mg) atom, which has an atomic number of 12, is written as 1s² 2s² 2p⁶ 3s². This notation shows that the 1s subshell is filled with two electrons, the 2s subshell is also filled with two electrons, the 2p subshell is filled with six electrons, and the 3s subshell contains the remaining two electrons to make up a total of 12 electrons. As atoms increase in atomic number, the electron configurations become more complex, but the 'building-up' (or Aufbau) principle helps to determine the sequence in which orbitals are filled.

We must include the Pauli Exclusion Principle, which states that no two electrons can have the same set of four quantum numbers, leading to the orderly fill of electrons within subshells and orbitals. Moreover, Hund's Rule indicates that electrons will fill an unoccupied orbital before they pair up in an already occupied one, which affects the electron configuration when dealing with subshells that have more than one orbital, such as p, d, or f subshells.

The Periodic Table is not just a simple chart but a powerful tool for predicting the properties of elements, including their electron configurations. Each column, known as a group, contains elements with similar properties and the same number of electrons in their outermost shell, or valence shell.

When writing electron configurations, the periodic table outlines the order in which subshells are filled: elements in the first two groups fill the s subshell, while elements in groups 13 to 18 fill the p subshell. Transition metals, found in the middle section, are involved in filling the d subshell, and the lanthanides and actinides at the bottom fill the f subshell. The row, or period, indicates the number of electron shells.

Memorizing the order of subshell filling can be challenging, but there's a mnemonic tool: the n + l rule, where n is the principal quantum number and l is the azimuthal quantum number for the subshell (s=0, p=1, d=2, f=3). Electrons enter the available subshell with the lowest sum of n + l, and if two subshells have the same sum, the one with the lower n value fills first. This can be visualized by a diagonal rule on the periodic table, which leads through the s, p, d, and f blocks in the correct order for electron configuration.

Cations are positively charged ions that are formed when an atom loses one or more electrons; anions are negatively charged ions, created when an atom gains electrons. The electron configurations of these ions are essential for understanding chemical bonding and reactions.

For cations, since they lose electrons, their configuration is determined by removing electrons from the outermost shell. For magnesium, after it loses two electrons to become Mg²⁺, the electron configuration ends at 2p⁶ because the 3s electrons are lost. This removal typically happens from the highest energy level, or the outermost shell first. In transition metals like titanium (Ti), electrons are removed from the s orbital before the d orbitals, following the (n+1)s > nd rule.

Anions, on the other hand, gain electrons and their configuration is found by adding electrons to the outer shell. Nitrogen, upon gaining three electrons to become N³⁻, achieves a noble gas configuration by filling its 2p subshell to achieve the stable arrangement of 2p⁶. When elements form anions, the added electrons occupy the lowest-energy orbital available.

It's important to remember that changes in electron configuration affect the chemical properties of the ions. Cations typically become smaller than their neutral atoms due to a decrease in electron-electron repulsion, while anions become larger due to increased electron-electron repulsion. These size differences, along with changes in electron configuration, can greatly influence the behavior of ions in chemical reactions and in the formation of compounds.