For each of the following ground-state ions, predict the type of orbital \((1 s, 2 p, 3 d, 4 f\), and so on) in which the electrons of highest energy will reside: (a) \(\mathrm{Fe}^{2+}\); (b) \(\mathrm{Bi}^{3+}\); (c) \(\mathrm{As}^{3+}\); (d) \(\mathrm{Os}^{+}\).

Understanding electronic configuration is essential for grasping how electrons are distributed within an atom or ion. The configuration tells us the location of electrons in terms of atomic orbitals, which are specific regions around the nucleus where electrons are likely to be found.

Electrons are arranged in orbitals according to the Aufbau Principle, which states that electrons fill the lowest energy orbitals first before moving to higher ones. This principle creates a predictable pattern that can be represented by a series of numbers and letters, such as 1s, 2s, 3p, and so on. The numbers indicate the energy level, while the letters represent the shape of the orbital (s, p, d, f).

In the case of neutral atoms, their electronic configurations follow this pattern strictly. However, when atoms form ions, they gain or lose electrons usually starting from the outermost orbitals, which are the highest energy levels. For instance, the neutral iron atom (Fe) has the configuration [Ar] 4s2 3d6, but the Fe2+ ion loses two electrons to become [Ar] 3d6, adjusting the overall electronic configuration to reflect a lower energy state.

Atomic orbitals form the very basis of electronic configuration. They describe the wave-like behavior of an electron in an atom and predict the electron's location relative to the nucleus. An orbital can contain a maximum of two electrons with opposite spins.

These orbitals come in various shapes and sizes—spherical (s), dumbbell-shaped (p), clover-shaped (d), and complex (f). Each shape corresponds to a different type of orbital that can be found at various energy levels. For example, the 1s orbital is a spherical shape and is found at the lowest energy level, while a 3d orbital has a clover shape and is present in higher energy levels.

Because each type of orbital has a specific maximum capacity of electrons it can hold (2 for s, 6 for p, 10 for d, and 14 for f), understanding the size and shape of these orbitals is crucial in predicting how electrons populate an atom's electron cloud. It is important to realize the three-dimensional aspect of these orbitals as it affects how atoms interact, bond, and form chemical structures.

When atoms gain or lose electrons, they become ions, which have a net charge due to the imbalance between the number of protons (positively charged) and electrons (negatively charged).

The electron configuration of an ion differs from its neutral atom because it reflects the change in the number of electrons. For example, when bismuth (Bi) becomes Bi3+ by losing three electrons, we remove those electrons from the orbitals containing the highest energy electrons first. Since neutral bismuth has the configuration [Xe] 4f14 5d10 6s2 6p3, the Bi3+ ion will have the configuration [Xe] 4f14 5d10 6s2 after losing three electrons from the 6p orbital.

The electron configurations of ions are critical in chemistry because they determine the chemical and physical properties of the substance, including how they bond and interact with other chemicals. An ion's reactive behavior and role in forming compounds are influenced by its electron configuration, making it a central concept in understanding chemical reactions.