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Showing 1–30 of 284 reference entries

Physics · ChemistryIdeal-gas equation of state

A simple gas model relates pressure, amount, volume and temperature.

ModelMeasurement · Chemistry · PhysicsAvogadro constant

The mole is linked to a specified number of entities.

DefinitionChemistryAtoms and elemental identity

The proton count of an atomic nucleus identifies its chemical element.

DefinitionChemistryIsotopes and mass number

Isotopes share a proton count but have different neutron counts.

DefinitionChemistryPeriodic organization of the elements

Atomic-number order reveals recurring patterns in electron structure and chemical properties.

ModelChemistryChemical bonds

Bonding describes interactions that bind atoms into molecules or extended structures.

DefinitionChemistry · MeasurementMole and amount of substance

The mole counts specified entities using the exact Avogadro constant.

DefinitionChemistryReaction stoichiometry

Balanced coefficients relate the amounts consumed and produced by a reaction.

MethodChemistryBalancing atoms and electric charge

A chemical equation must preserve each element's atom count and the total charge.

MethodChemistryDynamic chemical equilibrium

At equilibrium, opposing reactions continue without net composition change.

ModelChemistryBrønsted acids and bases

In the Brønsted description, an acid donates a proton and a base accepts it.

DefinitionChemistryGibbs energy and thermodynamic direction

Gibbs-energy change distinguishes thermodynamic favourability from reaction speed.

ModelChemistryReaction rates and empirical rate laws

Reaction rate measures change over time; a rate law describes its dependence under specified conditions.

MethodChemistryCatalysis and equilibrium

A catalyst changes the reaction pathway and rate, while preserving the equilibrium constant for the same reaction.

ModelBiology · ChemistryMetabolism and chemical pathways

Metabolism comprises the regulated chemical reactions of living systems.

DefinitionEarth & cosmos · Biology · ChemistryEarth's carbon cycle

Carbon moves through biological, oceanic, atmospheric and geological reservoirs.

ModelPhysics · ChemistryAtomic state labels and Pauli occupancy

Quantum labels specify orbitals and spin states.

ModelPhysics · ChemistryBloch states and electronic bands

A periodic crystal potential organizes energies by wavevector and band.

ModelPhysics · ChemistrySemiconductor electrons and holes

Band occupancy and doping control mobile carriers.

ModelChemistryElectron screening and effective nuclear attraction

Other electrons modify the attraction experienced by an electron in an atom.

ModelChemistryMultielectron ground-state configurations

Orbital occupations connect atomic electronic structure with valence chemistry.

ModelChemistryLocalized bonds and resonance descriptions

Localized orbital overlap and resonance are complementary chemical descriptions.

ModelChemistryMolecular orbitals and bonding occupation

A molecular orbital description distributes electronic states across a molecule.

ModelChemistryIntermolecular interactions

Dispersion, dipole interactions and hydrogen bonding influence molecular materials.

ModelChemistryBonding classes of solids

Ionic, metallic, molecular and network solids organize common bonding patterns.

DefinitionChemistryPolymers and macromolecular architecture

Polymers are substances composed of macromolecules with recurring structural units.

DefinitionChemistryCoordination compounds and ligands

Ligand donor atoms surround a central metal in a coordination sphere.

DefinitionChemistryActivities and chemical potentials

Activity expresses composition relative to a specified thermodynamic standard state.

DefinitionChemistrypH and hydrogen-ion activity

pH is an activity-based quantity realized through measurement conventions.

DefinitionChemistryBuffers and finite buffering capacity

An acid–base pair can resist limited changes in solution pH.

Model
ModelSource checked

Atomic state labels and Pauli occupancy

PhysicsChemistry

Quantum labels specify orbitals and spin states.

Key knowledge

Hydrogenic bound states use n ≥ 1, l = 0,…,n−1, m_l = −l,…,l and electron m_s = ±½. Pauli exclusion permits at most one electron per spin-orbital, hence two opposite-spin electrons per spatial orbital.

Conditions and scope

  • Integer n,l,m_l labels describe the Coulomb/central-field orbital model; multielectron orbital assignments are approximations.
  • A spatial orbital is a wavefunction, not a classical trajectory; chemical filling order is a separate entry.
Sources · 3

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Samuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice University3 sources
    1. University Physics 3: The Hydrogen AtomSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
    2. University Physics 3: Electron SpinSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
    3. University Physics 3: The Exclusion Principle and the Periodic TableSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source

Evidence and review

Sections 8.1, 8.3 and 8.4: orbital ranges, spin projection and four-label exclusion.

2026-10-10 · One-particle orbital labels and electron occupancy only; exact multielectron spectra and filling exceptions excluded.

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Scientific relationships · 1 / 1

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  1. Related to
    Relationship sources · 3

    Linked statements

    • Hydrogenic bound states use n ≥ 1, l = 0,…,n−1, m_l = −l,…,l and electron m_s = ±½. Pauli exclusion permits at most one electron per spin-orbital, hence two opposite-spin electrons per spatial orbital.

    Electron spin projection supplies the two m_s labels in the stated orbital basis.

Entry detailsPermanent link to this entry ↗
Record identity
physics-atomic-quantum-states
Revision
university-reference.1
Structured reference record
University reference · University core expansion