6.2 Electronic Structure & Quantum Numbers

Content category 4E also tests the quantum mechanical model of the atom — how electrons are organized into shells and orbitals, how they absorb and release energy, and the historical experiments that revealed light and matter both behave in quantized, wave-particle ways.

Orbital Structure of the Hydrogen Atom

Hydrogen, with a single proton and single electron, is the simplest atom to solve exactly using quantum mechanics, which is why the MCAT emphasizes it as the model system. An electron's location is described not as a fixed orbit but as an orbital — a three-dimensional region of space where there is a high probability of finding the electron. Each orbital is defined by a set of quantum numbers. The principal quantum number (n) is the most important for the MCAT: it is a positive integer (1, 2, 3, …) that specifies the electron's main energy shell and, roughly, its average distance from the nucleus — higher n means higher energy and generally greater distance from the nucleus. Within each shell, electrons occupy subshells (s, p, d, f) made of one or more orbitals of a specific three-dimensional shape; the s subshell has 1 orbital, p has 3, d has 5, and f has 7.

Every individual orbital, regardless of subshell type, can hold a maximum of two electrons, and those two electrons must have opposite spins. This limit is a direct consequence of the Pauli Exclusion Principle, which states that no two electrons in the same atom can share an identical set of all four quantum numbers. Because each shell n contains n² orbitals, a full shell holds a maximum of 2n² electrons — 2 electrons in shell 1, 8 in shell 2, 18 in shell 3, and so on.

Quantum numbers and orbital capacity (quick reference):

Ground State, Excited States, and Line Spectra

An atom's ground state is its lowest-energy, most stable electron configuration. When an electron absorbs exactly the right amount of energy, it can jump to a higher, less stable energy level, putting the atom in an excited state. Because atomic energy levels are quantized (only specific discrete energies are allowed), an electron can only absorb or emit a photon whose energy exactly matches the gap between two allowed energy levels — not just any amount of energy.

This quantization is why atoms produce line spectra instead of continuous rainbows of color. An absorption spectrum is produced when white light passes through a cool gas of a given element: electrons absorb photons of specific wavelengths to jump to higher energy levels, leaving dark lines at those exact wavelengths in an otherwise continuous spectrum. An emission spectrum is produced when excited electrons fall back down to lower energy levels, releasing the energy difference as photons of specific wavelengths — visible as bright, discrete colored lines. Because every element has a unique arrangement of energy levels, its line spectrum is a fingerprint used to identify it; this principle underlies flame tests and clinical flame photometry used to measure sodium and potassium concentrations in blood.

The Bohr Atom and the Heisenberg Uncertainty Principle

Before the full quantum mechanical model, Niels Bohr proposed that hydrogen's electron travels in fixed, circular orbits of specific allowed radii and energies, jumping between orbits only by absorbing or emitting a photon of exactly the right energy. For a hydrogen atom, the Bohr model predicts the allowed energies as Eₙ = −13.6 eV/n², where n is the principal quantum number of the orbit. This model successfully explains hydrogen's line spectrum (the Rydberg equation, 1/λ = R(1/n₁² − 1/n₂²) with R ≈ 1.097 × 10⁷ m⁻¹, describes the resulting spectral line wavelengths), but it breaks down for any atom with more than one electron because it ignores electron-electron repulsion.

The Bohr model's fixed orbits were eventually replaced by the modern probabilistic orbital picture, largely because of the Heisenberg Uncertainty Principle: it is fundamentally impossible to simultaneously know an electron's exact position and exact momentum with unlimited precision — the more precisely one is measured, the less precisely the other can be known (Δx·Δp ≥ h/4π). Since an electron's exact trajectory can never be pinned down, the quantum mechanical model describes electron location only in terms of probability regions (orbitals) rather than the neat circular paths Bohr imagined.

Electron Configuration, Magnetism, and Effective Nuclear Charge

Electrons fill orbitals following the Aufbau principle (lowest-energy orbitals fill first) and Hund's rule (electrons fill degenerate — equal-energy — orbitals within a subshell singly, with parallel spins, before any orbital gets a second electron). The result is written in conventional electron configuration notation, listing each occupied subshell with a superscript for its electron count, in order of filling: for example, iron (Z = 26) is 1s²2s²2p⁶3s²3p⁶4s²3d⁶, often abbreviated with the preceding noble gas core as [Ar]4s²3d⁶.

Whether an atom's electrons are paired determines its magnetic behavior. An atom or ion with one or more unpaired electrons is paramagnetic — it is weakly attracted into an external magnetic field because the unpaired electron spins can align with it. An atom or ion in which every electron is paired is diamagnetic — it is weakly repelled by an external magnetic field, since paired spins cancel each other's magnetic moments. (This is distinct from ferromagnetism, the strong, permanent magnetism of bulk iron, cobalt, and nickel, which requires cooperative alignment across many atoms, not just a property of a single ion.)

Finally, an electron in a multi-electron atom doesn't feel the full pull of the nucleus, because inner ("core") electrons partially block, or shield, the attraction between the nucleus and outer electrons. The net positive charge an outer electron actually experiences is the effective nuclear charge (Zeff), approximately equal to the actual nuclear charge Z minus the shielding contributed by inner electrons. Across a period, Zeff increases (protons are added, but shielding from the same inner shell barely changes), which is a major reason atomic radius shrinks and ionization energy rises moving left to right across the periodic table.

The Photoelectric Effect

When light of sufficiently high frequency strikes a metal surface, it can eject electrons — a phenomenon called the photoelectric effect. Classical wave theory predicted that a sufficiently intense beam of any frequency should eventually eject electrons, but experiments showed otherwise: below a metal-specific threshold frequency, no electrons are ejected no matter how bright the light is, while above that threshold, electrons are ejected instantly, even at very low intensity.

Einstein explained this by treating light as a stream of discrete energy packets, or photons, each carrying energy E = hf (h is Planck's constant, f is the light's frequency). Ejecting an electron from the metal requires overcoming the metal's work function (φ), the minimum energy needed to free an electron from its surface. If a photon's energy exceeds the work function, the excess energy becomes the ejected electron's kinetic energy: KEmax = hf − φ. Increasing light intensity above the threshold frequency increases the number of electrons ejected per second (more photons striking the surface), but it does not increase each electron's maximum kinetic energy — only increasing the frequency does that. This particle-like behavior of light was direct evidence for the quantization of light energy and helped establish wave-particle duality, the same duality that governs how electrons themselves are described in the quantum mechanical model of the atom.