Quantum Theory and the Electronic Structure of Atoms (Chapter 7)

Vocabulary flashcards covering key terms from the lecture notes on waves, EM radiation, quantum theory, atomic orbitals, and electron configurations.

Wavelength

The distance between identical points on successive waves.

Amplitude

The vertical distance from the midline of a wave to its crest (maximum) or trough (minimum).

Frequency

The number of waves that pass a fixed point per second (Hz).

Speed of a wave

The product of its frequency and wavelength (u = νλ).

Electromagnetic radiation

Energy emitted and transmitted as electromagnetic waves; includes visible light; travels at the speed of light in vacuum.

Speed of light (c)

c = 3.00 × 10^8 m/s in vacuum; relates wavelength and frequency via c = λν.

Photon

A quantum of light energy; a particle of light with energy E = hν.

Planck's constant

h = 6.63 × 10^-34 J·s; constant in quantum energy equations.

Quantum

The smallest discrete unit of energy that can be emitted or absorbed.

Threshold frequency

Minimum frequency of light required to eject electrons in the photoelectric effect.

Photoelectric effect

Ejection of electrons from a metal surface when irradiated with light above threshold frequency.

Energy of a photon

E = hν; energy carried by a single photon.

Bohr model

Electrons occupy quantized energy levels; emission occurs when electrons move to lower levels; explains line spectra of hydrogen.

Balmer series

Hydrogen visible-line emission series from ni = 3 to nf = 2.

Rydberg formula

Relates hydrogen emission wavelengths to energy level transitions; 1/λ = RH(1/nf^2 − 1/n_i^2).

Rydberg constant

R_H ≈ 2.18 × 10^-18 J (or ≈ 1.097 × 10^7 m^-1, depending on units).

Hydrogen emission spectrum

Line spectrum produced by electron transitions in hydrogen atoms.

Schrödinger equation

Wave equation describing electron behavior; yields wavefunction ψ and electron energy; exact for hydrogen.

Wavefunction (ψ)

Mathematical function describing the energy and probability distribution of an electron.

Principal quantum number

n; determines energy and average distance of the electron (n = 1, 2, 3, …).

Angular momentum quantum number

l; determines subshell type (l = 0 to n−1; s, p, d, f, …).

Magnetic quantum number

ml; orientation of the orbital in space (ml = −l to +l).

Spin quantum number

m_s; electron spin: +1/2 or −1/2.

Pauli exclusion principle

No two electrons in an atom can have the same set of four quantum numbers.

Aufbau principle

Electrons fill the lowest-energy orbitals first.

Hund's rule

Electrons fill orbitals to maximize the number of parallel spins in a subshell.

Orbital

Region in space with high probability of finding an electron; labeled by n, l, m_l.

Subshell

Group of orbitals with the same n and l (e.g., 2p, 3d).

Shell

Principal energy level; all subshells with the same n.

Orbital capacity

An orbital can hold 2 electrons (with opposite spins).

Electron configuration

Distribution of electrons among orbitals; notation such as [Ne] 3s^2 for magnesium.

Spdf notation

Notation using letters s, p, d, f to indicate orbital types corresponding to l = 0, 1, 2, 3.

Ground-state electron configuration

The arrangement of electrons in the lowest-energy state for an atom.

Diamagnetism

Material with all electrons paired; weak repulsion to magnetic fields.

Paramagnetism

Material with unpaired electrons; attracted to magnetic fields.

Periodic table blocks

s-block, p-block, d-block, f-block correspond to the types of orbitals being filled.

Hydrogen spectral series (overview)

Lyman (UV), Balmer (visible), Paschen (IR) are series of hydrogen emission lines.

Degeneracy in hydrogen

For hydrogen, energy levels depend only on n (in the simple model), leading to degenerate orbitals within the same n.

Hydrogen energy level transitions

Electron transitions between energy levels produce photons with specific wavelengths.

Electron configuration notation example

[Ne] 3s^2 represents the noble-gas core plus outer electrons for an element.

Orbital types (s, p, d, f)

s (l=0), p (l=1), d (l=2), f (l=3); define shapes and number of orbitals per subshell.

Electron spin orientation

Two possible spin states: up (+1/2) and down (−1/2).

Spdf notation basics

Subshells are designated by n and l (e.g., 3p, 4d); electrons fill these with appropriate ml and ms.

λ-ν-c relation (electromagnetic waves)

Wavelength and frequency relate to the speed of light by c = λν.

Visible light range

Approximately 400–700 nm.

1/λ form of Rydberg equation

1/λ = RH(1/nf^2 − 1/n_i^2); used to calculate hydrogen spectral lines.

Photon energy (alternative form)

E = hc/λ; energy of a photon expressed in terms of wavelength.

Electron configuration practice (example)

For Mg: [Ne] 3s^2, illustrating filling after noble-gas core.