Electron Configuration

Electrons do not orbit a nucleus randomly. They occupy a precisely organised set of discrete energy levels, and every electron in every atom can be fully located within that organisation using four quantum numbers. ^[1] This hierarchical structure is enforced by the Pauli exclusion principle, which dictates that it is impossible for any two electrons within a single atom to possess an identical set of four quantum numbers. ^[1] Each combination of quantum numbers functions like a unique address - no two electrons can occupy the same address. This constraint forces electrons into a structured hierarchy of shells and subshells, and it is that hierarchy that determines how an element bonds, what ions it forms, and ultimately what minerals it can build.

The Four Quantum Numbers

The principal quantum number n can take any positive integer value (1, 2, 3, …) and is the primary determinant of an electron’s energy. ^[1] Higher n means higher energy and, statistically, greater distance from the nucleus. Each value of n defines a shell: n = 1 is the K shell, n = 2 the L shell, n = 3 the M shell, n = 4 the N shell, and so on.

The angular momentum quantum number l has integer values from 0 up to n - 1 and distinguishes subshells within a shell - regions of space that have different geometrical shapes. ^[1] The highest possible subshell number restrictively tops out at n - 1; consequently, the n = 1 (K) shell contains solely the s subshell, the n = 2 (L) shell supports only s and p subshells, and thus the pattern continues. ^[1] The subshells are labelled with letters: l = 0 is s, l = 1 is p, l = 2 is d, l = 3 is f. A subshell is conventionally identified by combining its principal quantum number with its letter - the p subshell in the L shell is written 2p, the d subshell in the M shell is written 3d, and so forth.

The magnetic quantum number m_l has integer values between -l and +l and distinguishes the individual orbitals within a subshell - orbitals with the same shape but different spatial orientations. ^[1] The number of orbitals in a subshell is 2l + 1: the s subshell (l = 0) contains exactly one orbital, the p subshell (l = 1) contains three, the d subshell (l = 2) contains five, and the f subshell (l = 3) contains seven.

The spin quantum number m_s can take only two values, +½ and -½, and distinguishes the two electrons that may occupy a single orbital. ^[1] Electrons behave as if spinning on an axis, and the two spin values represent opposite spin directions. Because a spinning charged particle generates a magnetic field, each electron acts like a tiny magnet. When two electrons share an orbital with opposite spins, their magnetic moments cancel and no net magnetism results. When an atom has more electrons spinning one way than the other - that is, when its subshells are not fully paired - a net magnetic moment arises, which is why metallic iron and the mineral magnetite are magnetic. ^[1]

Orbital Geometry

The shape of an orbital is determined by its subshell (the l value). The s subshell has l = 0, giving m_l = 0 - only one orbital, and that orbital is spherically symmetric around the nucleus. ^[1] The p subshell has l = 1, giving m_l = -1, 0, and +1 - three orbitals, each shaped like a dumbbell (two lobes on opposite sides of the nucleus) and oriented along one of the three mutually perpendicular spatial axes. ^[1] The d subshell has l = 2, giving five orbitals (m_l = -2, -1, 0, +1, +2); four of them have a four-lobed (quadralobate) geometry, while the fifth has a bilobed shape with a torus (a donut-shaped ring) encircling it in a perpendicular plane. ^[1] The f orbitals have still more complex geometries. The shapes of these orbitals have direct consequences for crystal chemistry: covalent bonding requires specific orbital overlap geometries, so the three-dimensional arrangement of p, d, and hybrid orbitals governs what bond angles are possible and what crystal structures result.

Filling Order

Given the energy hierarchy described by the quantum numbers, electrons fill orbitals from the lowest energy upward as the atomic number increases. ^[1] For most elements this means progressing 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p and so on. The 4s subshell has lower energy than the 3d, which is why potassium and calcium fill 4s before any 3d electrons appear. The filling order explains the structure of the periodic table: elements in the same column have the same valence electron configuration, which is why they share similar chemical properties.

One important subtlety concerns the transition metals (elements 21-30, Sc through Zn), whose valence electrons occupy both the 4s and 3d subshells. The 4s fills first during electron addition, but when electrons are removed to form ions, they come first from the subshell with the highest principal quantum number - which is the 4s - even though the 4s has lower energy than the 3d. ^[1] This asymmetry between filling and emptying order means the transition metals can lose different numbers of electrons depending on the conditions, which is why they commonly occur in more than one oxidation state.

Noble-Gas Cores and Valence Electrons

In all elements except the noble gases themselves, the electron configuration consists of two parts: an inner core, in which every subshell within the inner shells is completely filled, plus one or more outer valence electrons in subshells that are not yet full. ^[1] The valence electrons are the chemically active ones - they are what an atom uses to bond, to form ions, and to interact with other atoms. The core electrons are shielded by the outer electrons from neighbouring atoms and play no direct role in bonding.

When an atom’s inner shell structure exactly matches the electron arrangement of a noble gas, it possesses what is termed a noble-gas core. ^[1] Sodium, for instance, has the full electron configuration of neon (its noble-gas core) plus a single 3s valence electron. If the core consists of a noble-gas configuration plus an entirely filled d or f subshell, it is called a pseudo-noble-gas core. ^[1] Arsenic provides an example: it has filled 1s, 2s, 2p, 3s, 3p, 4s, and 3d subshells as its pseudo-noble-gas core, with three 4p valence electrons on top. Noble gases themselves have noble-gas cores and no valence electrons - that complete-shell configuration is the low-energy state that all other elements are trying to achieve.

Formation of Ions

When an atom gains or loses electrons, the imbalance between proton count and electron count gives it a net electric charge - it becomes an ion. Atoms with more electrons than protons are anions with a net negative charge; atoms with fewer electrons than protons are cations with a net positive charge. The magnitude of that charge is the atom’s valence or oxidation state. ^[1]

Whether an element forms an anion or cation follows directly from its valence electron configuration, because atoms tend to gain or lose electrons in whatever way brings them closest to a full-shell noble-gas arrangement. ^[1] Metals have noble-gas or pseudo-noble-gas cores plus a small number of valence electrons. Stripping away those few outer electrons requires relatively little energy and leaves behind a complete, stable inner shell - so metals form cations. ^[1] Non-metals occupy the right side of the periodic table with valence subshells that are nearly full - they need only a few more electrons to reach a stable configuration, so they readily accept electrons from metals and form anions. ^[1]

The transition metals complicate this picture because both their 4s and remaining 3d electrons are available to be removed. As a result, many transition metals can exist in multiple oxidation states depending on how many 3d electrons are lost in addition to the 4s electrons. Iron is the most geologically important example: it occurs as divalent Fe²⁺, known as ferrous iron, and as trivalent Fe³⁺, known as ferric iron, and the redox conditions in the environment of formation determine which form a growing mineral incorporates. ^[1] Manganese and chromium are most commonly divalent and trivalent respectively, but both are also capable of higher oxidation states under the right conditions. ^[1] The ability to vary oxidation state is what makes transition metals so geochemically versatile and why their minerals form in such a range of environments.

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