Atomic Structure and Electron Configuration

From Billiard Balls to Probability Clouds

Chemistry's central story is the atom — and that story has been rewritten many times. Dalton's solid-sphere model (1803) explained mass ratios. Thomson's "plum pudding" model explained that atoms contain electrons. Rutherford's gold foil experiment (1911) shattered the plum pudding by showing atoms are mostly empty space with a dense nucleus. Then Bohr gave hydrogen a tidy planetary model with fixed orbits.

The quantum mechanical model goes further and stranger: electrons don't follow fixed paths. They occupy orbitals — regions of space where there is a high probability of finding an electron. This is not a limitation of our measurement tools; it is the actual nature of reality at the subatomic scale.

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Quantum Numbers and Orbital Types

Every electron in an atom is described by four quantum numbers:

• Principal quantum number (n): Energy level (n = 1, 2, 3…). Higher n = higher energy, farther from nucleus.
• Angular momentum quantum number (ℓ): Subshell shape. ℓ = 0 (s), 1 (p), 2 (d), 3 (f).
• Magnetic quantum number (mₗ): Orbital orientation. Values range from −ℓ to +ℓ.
• Spin quantum number (mₛ): Electron spin, either +½ or −½.

The Pauli Exclusion Principle states that no two electrons in an atom can share the same set of four quantum numbers. This means each orbital holds at most two electrons with opposite spins.

Hund's Rule tells us that when filling orbitals of equal energy, electrons occupy separate orbitals before pairing up — all with parallel spins before any pairing occurs.

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Writing Electron Configurations

Electron configurations are written by filling subshells in order of increasing energy. The Aufbau ("building up") principle guides this:

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

For iron (Fe, Z = 26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ or in abbreviated form [Ar] 4s² 3d⁶

Note two common exceptions: chromium ([Ar] 4s¹ 3d⁵) and copper ([Ar] 4s¹ 3d¹⁰) achieve extra stability through half-filled or fully filled d subshells.

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Concept Check

What is the abbreviated electron configuration of phosphorus (Z = 15)?

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[Ne] 3s² 3p³ — phosphorus has 15 electrons. After the [Ne] core (10 electrons), 5 remain: 2 fill 3s, and 3 occupy separate 3p orbitals (Hund's Rule).

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Photoelectron Spectroscopy (PES)

PES is an AP Chemistry experimental technique that provides direct evidence for electron configurations. High-energy photons eject electrons from an atom; the kinetic energy of ejected electrons reveals their binding energies. The result is a spectrum where:

• Peak position corresponds to binding energy (related to which subshell the electron came from)
• Peak height (relative area) corresponds to the number of electrons at that energy level

A PES spectrum for sodium would show three peaks: a small peak at very high binding energy (1s, 2 electrons), a medium peak (2s and 2p, 8 electrons total), and a small low-energy peak (3s, 1 electron). The AP exam frequently shows PES data and asks you to identify the element or confirm the configuration.

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Periodic Trends

Atomic structure explains why periodic trends exist — they are not arbitrary patterns but direct consequences of nuclear charge and electron shielding.

Atomic Radius decreases across a period (increasing nuclear charge pulls electrons closer) and increases down a group (additional energy levels push electrons farther out).

Ionization Energy (IE) is the energy required to remove one mole of electrons from one mole of gaseous atoms. IE increases across a period and decreases down a group. Notable exceptions: Be > B (removing from 2p vs 2s) and N > O (paired 2p electron in O is easier to remove).

Electronegativity follows the same trend as IE — highest near fluorine (upper right), lowest near francium (lower left).

Electron Affinity is the energy change when a gaseous atom gains an electron. Halogens have the most negative (most favorable) electron affinities — they are one electron away from a noble gas configuration.

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AP Exam Connection

The AP Chemistry exam tests atomic structure through:

• Multiple-choice: PES data interpretation, electron configuration writing, trend prediction
• Free-response: Explaining trend exceptions using nuclear charge and shielding arguments
• Lab skills: Understanding spectroscopic evidence for atomic models

When explaining trends on the AP exam, always connect your answer to effective nuclear charge (Zeff) — the net positive charge experienced by an electron, accounting for shielding by inner electrons.

$$Z_{eff}=Z-\sigma$$

where Z is the atomic number and σ is the shielding constant.

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Unit Summary

The quantum mechanical model describes electrons as waves occupying orbitals defined by four quantum numbers. Electron configurations are determined by the Aufbau principle, Hund's Rule, and the Pauli Exclusion Principle. PES provides experimental evidence for these configurations. Periodic trends in atomic radius, ionization energy, and electronegativity arise from competing effects of increasing nuclear charge and electron shielding — understanding these mechanistically, not just as patterns to memorize, is the key AP Chemistry skill.