6.4 Electronic Structure of Atoms (Electron Configurations)

Electronic Structure of Atoms

Electron configuration describes how electrons are distributed among an atom's orbitals. Understanding this arrangement is central to predicting chemical behavior, because the way electrons fill energy levels determines how an element reacts, bonds, and interacts with other elements.

The periodic table itself is organized around these electron arrangements. Elements in the same group share similar outer-electron setups, which is why they tend to have similar chemical properties.

Electron Configuration Principles

Three rules govern how electrons fill orbitals:

Aufbau principle: Electrons fill orbitals in order of increasing energy, starting with the lowest available. An orbital is a specific region in space where an electron is most likely to be found. The filling order is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f

Notice that 4s fills before 3d. The energy levels don't always go in neat numerical order, so memorizing (or using a diagonal filling diagram for) this sequence matters.

Hund's rule: When filling orbitals of equal energy (like the three 2p orbitals), electrons spread out and occupy them singly before pairing up. This minimizes electron-electron repulsion, since electrons with the same spin in separate orbitals repel each other less.

Pauli exclusion principle: Each orbital holds a maximum of two electrons, and those two must have opposite spins. More precisely, no two electrons in an atom can share the same set of four quantum numbers.

Writing an Electron Configuration

1. Find the element's atomic number (Z), which equals its number of electrons (for a neutral atom).
2. Fill orbitals in the Aufbau order listed above.
3. Apply Hund's rule within each sublevel.
4. Write each sublevel with a superscript showing how many electrons it contains.

Example: Carbon (Z = 6) has 6 electrons. Fill in order: $1s^2\, 2s^2\, 2p^2$. The two 2p electrons occupy separate orbitals (Hund's rule) with parallel spins.

A sublevel (or subshell) is a group of orbitals with the same energy within a given shell. For instance, the 2p sublevel contains three orbitals, each able to hold 2 electrons, for a total capacity of 6.

Quantum Numbers and Electron Properties

Every electron in an atom is described by a unique set of four quantum numbers:

• Principal quantum number ($n$): Indicates the main energy level (shell). $n = 1, 2, 3, \ldots$ Higher $n$ means higher energy and greater average distance from the nucleus.
• Angular momentum quantum number ($l$): Describes the shape of the orbital. Values range from 0 to $n - 1$. Each value corresponds to a sublevel: $l = 0$ is s, $l = 1$ is p, $l = 2$ is d, $l = 3$ is f.
• Magnetic quantum number ($m_l$): Specifies the orientation of the orbital in space. Values range from $-l$ to $+l$. For a p sublevel ($l = 1$), $m_l$ can be $-1, 0,$ or $+1$, giving three orbitals.
• Spin quantum number ($m_s$): Indicates the direction of electron spin, either $+\frac{1}{2}$ (spin-up) or $-\frac{1}{2}$ (spin-down).

Together, these four numbers act like an address for each electron. The Pauli exclusion principle guarantees that no two electrons share the exact same address.

Anomalous Configurations

Some elements don't follow the standard Aufbau filling order. This happens when the energy difference between two sublevels is very small, and a slight rearrangement produces a more stable arrangement.

The key idea: half-filled and fully filled d sublevels are unusually stable. This extra stability can be enough to pull an electron away from the 4s sublevel.

• Chromium (Z = 24): Expected configuration is $[Ar]\,3d^4\,4s^2$, but the actual configuration is $[Ar]\,3d^5\,4s^1$. One 4s electron moves to 3d, creating a half-filled d sublevel (5 electrons in 5 orbitals).
• Copper (Z = 29): Expected configuration is $[Ar]\,3d^9\,4s^2$, but the actual configuration is $[Ar]\,3d^{10}\,4s^1$. One 4s electron moves to 3d, completing a fully filled d sublevel.

For an intro course, you mainly need to recognize chromium and copper as the classic examples and understand why they deviate: the extra stability of half-filled or fully filled d sublevels outweighs the cost of leaving 4s with only one electron.

Configurations and Periodic Table Position

The periodic table is organized by increasing atomic number, and its structure directly reflects electron configurations.

Periods (rows) correspond to the principal quantum number ($n$) of the outermost electrons. Starting a new period means electrons begin filling a new shell. For example, Period 3 elements have their highest-energy electrons in the $n = 3$ shell.

Groups (columns) contain elements with similar valence electron configurations, which is why elements in the same group show similar chemical behavior.

The table is divided into blocks based on which sublevel is being filled:

• s-block (Groups 1 and 2): Valence electrons fill the s subshell. Includes hydrogen, helium, alkali metals, and alkaline earth metals.
• p-block (Groups 13–18): Valence electrons fill the p subshell. Includes nonmetals, metalloids, halogens, and noble gases.
• d-block (Groups 3–12): Often called the transition metals. Valence electrons fill the d subshell.
• f-block (lanthanides and actinides): The two rows pulled out below the main table. Valence electrons fill the f subshell.

This block structure is why the periodic table has its distinctive shape. The s-block is 2 columns wide (s orbitals hold 2 electrons), the p-block is 6 wide (3 orbitals × 2 electrons), the d-block is 10 wide (5 × 2), and the f-block is 14 wide (7 × 2). If you understand orbital capacity, the table's layout makes sense.