Glossary: Electronic Structure

Key terms from Chapter 7: Electronic Structure of the Atom. Terms are organized alphabetically for quick reference.

A

Absorption spectrum: Dark lines on a continuous background, produced when atoms absorb specific wavelengths from white light passing through them. The pattern is complementary to the emission spectrum.
Angular momentum quantum number (l): Quantum number that determines orbital shape. Values range from 0 to n − 1. Corresponds to subshell labels: l = 0 (s), l = 1 (p), l = 2 (d), l = 3 (f).
Antinode: Point of maximum displacement in a standing wave. In atomic orbitals, regions of maximum electron density.
Atomic orbital: A mathematical function describing the probability distribution of an electron around the nucleus. Each orbital has a characteristic shape determined by quantum numbers n, l, and m_l.
Aufbau principle: Electrons fill orbitals starting from the lowest energy and proceeding to higher energies, “building up” the electron configuration.

B

Balmer series: Spectral lines produced by electron transitions ending at n = 2 in hydrogen. These lines fall in the visible region (365–656 nm).
Black-body radiation: Electromagnetic radiation emitted by an object due to its temperature. The spectrum depends only on temperature, not composition.
Bohr model: Early quantum model of the atom (1913) in which electrons occupy specific allowed orbits with quantized angular momentum. Successfully explained hydrogen’s spectrum but failed for multi-electron atoms.
Boundary surface: A surface enclosing a specified percentage (typically 90%) of an orbital’s electron density. Used to visualize orbital shapes.

C

Complementarity: The principle that wave and particle descriptions of matter are mutually exclusive but both necessary for a complete picture. Observing wave behavior precludes observing particle behavior, and vice versa.
Core electrons: Inner-shell electrons that do not participate in bonding. Represented by noble gas notation in electron configurations.

D

de Broglie wavelength: The wavelength associated with a moving particle: λ = h/(mv). Shows that all matter has wave properties.
Degenerate orbitals: Orbitals with identical energy. In hydrogen, all orbitals with the same n are degenerate. In multi-electron atoms, shielding breaks this degeneracy.
Diamagnetic: Having no unpaired electrons. Diamagnetic substances are weakly repelled by magnetic fields.

E

Effective nuclear charge (Z_eff): The net positive charge experienced by an electron after accounting for shielding by other electrons.
Electromagnetic radiation: Energy that travels through space as oscillating electric and magnetic fields. Includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
Electron configuration: The arrangement of electrons among an atom’s orbitals, written using spdf notation (e.g., 1s²2s²2p⁶).
Electron density: The probability of finding an electron per unit volume at a given point, equal to |Ψ|².
Emission spectrum: Bright lines on a dark background, produced when excited atoms emit photons at specific wavelengths as electrons drop to lower energy levels.
Exchange energy: Stabilization that results when electrons with parallel spins occupy different orbitals. Arises from the Pauli exclusion principle and favors configurations with more unpaired electrons.
Excited state: Any energy state above the ground state. Atoms in excited states can emit photons and return to lower states.

F

Frequency (ν): The number of wave cycles passing a point per second. Measured in hertz (Hz = s⁻¹). Related to wavelength by c = λν.

G

Ground state: The lowest energy state of an atom. At room temperature, most atoms are in their ground state.

H

Hamiltonian operator (Ĥ): The quantum mechanical operator for total energy. Applying it to a wave function gives the energy times the wave function: ĤΨ = EΨ.
Heisenberg uncertainty principle: It is impossible to simultaneously know both the exact position and exact momentum of a particle. Mathematically: Δx · Δp ≥ ℏ/2.
Hund’s rule: When filling degenerate orbitals, electrons occupy them singly with parallel spins before pairing. Maximizes exchange energy.

I

Ionization energy: The minimum energy required to remove an electron from a gaseous atom in its ground state.

L

Line spectrum: A spectrum consisting of discrete wavelengths rather than a continuous range. Produced by atoms in low-pressure gases.
Lyman series: Spectral lines produced by electron transitions ending at n = 1 in hydrogen. These lines fall in the ultraviolet region.

M

Madelung rule: Orbitals fill in order of increasing n + l; when equal, the orbital with lower n fills first. Correctly predicts ~80% of electron configurations.
Magnetic quantum number (m_l): Quantum number that specifies the orientation of an orbital in space. Values range from −l to +l.

N

Noble gas notation: Abbreviated electron configuration using the symbol of the preceding noble gas in brackets to represent core electrons. Example: Na = [Ne]3s¹.
Node: A region where the wave function (and therefore electron density) equals zero. Radial nodes are spherical; angular nodes are planar or conical.
Normalization: The requirement that the total probability of finding a particle somewhere equals 1: ∫|Ψ|²dV = 1.

O

Orbital: See Atomic orbital.

P

Pairing energy: The energy penalty for placing two electrons in the same orbital. Results from electron-electron repulsion and loss of exchange stabilization.
Paramagnetic: Having one or more unpaired electrons. Paramagnetic substances are attracted to magnetic fields.
Paschen series: Spectral lines produced by electron transitions ending at n = 3 in hydrogen. These lines fall in the infrared region.
Pauli exclusion principle: No two electrons in an atom can have the same set of four quantum numbers. Consequently, each orbital holds at most two electrons with opposite spins.
Penetration: The ability of an electron to get close to the nucleus through inner electron shells. s orbitals penetrate most effectively, making them lower in energy than p, d, or f orbitals of the same shell.
Photoelectric effect: Emission of electrons from a metal surface when light shines on it. Explained by Einstein using the photon concept.
Photon: A quantum (discrete packet) of electromagnetic radiation with energy E = hν.
Planck’s constant (h): Fundamental constant relating photon energy to frequency: h = 6.626 × 10⁻³⁴ J·s.
Principal quantum number (n): Quantum number that determines orbital size and energy. Values are positive integers: 1, 2, 3, …
Probability density: See Electron density.

Q

Quantization: The restriction of a physical quantity to discrete values rather than a continuous range. Energy levels in atoms are quantized.
Quantum number: An integer or half-integer that labels quantum states. The four quantum numbers for electrons are n, l, m_l, and m_s.

R

Radial probability distribution, P(r): The probability of finding an electron in a thin spherical shell at distance r from the nucleus: P(r) = 4πr²|R(r)|².
Radial wave function, R(r): The part of the wave function that depends on distance from the nucleus.
Rydberg constant (R_H): Constant appearing in the Rydberg equation: R_H = 1.0974 × 10⁷ m⁻¹.
Rydberg equation: Formula for wavelengths of hydrogen spectral lines: 1/λ = R_H(1/n_f² − 1/n_i²).

S

Schrödinger equation: The fundamental equation of quantum mechanics: ĤΨ = EΨ. Solutions give allowed wave functions and energies.
Shell: All orbitals with the same principal quantum number n. Also called an energy level.
Shielding: The reduction in effective nuclear charge experienced by outer electrons due to repulsion from inner electrons.
Spectral line: A specific wavelength in an emission or absorption spectrum, corresponding to a particular electronic transition.
Spherical harmonics, Y(θ, φ): The angular part of atomic wave functions. Determines orbital shape and orientation.
Spin quantum number (m_s): Quantum number specifying electron spin. Values are +½ (“spin up”) or −½ (“spin down”).
Standing wave: A wave pattern that oscillates in place with fixed nodes and antinodes. Electron orbitals are three-dimensional standing waves.
Stationary state: In the Bohr model, an allowed orbit in which an electron does not radiate energy.
Subshell: All orbitals with the same n and l values. Examples: 2p subshell (three orbitals), 3d subshell (five orbitals).

U

Ultraviolet catastrophe: The prediction of classical physics that a black body would emit infinite energy at short wavelengths. Resolved by Planck’s quantum hypothesis.

V

Valence electrons: Outermost electrons that participate in chemical bonding.

W

Wave function (Ψ): Mathematical function describing the quantum state of a system. |Ψ|² gives the probability density.
Wavelength (λ): The distance between consecutive peaks (or troughs) of a wave. Related to frequency by c = λν.
Wave-particle duality: The principle that all matter and radiation exhibit both wave and particle properties, depending on how they are observed.