GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 61–90 of 1709 reference entries

Physics · MeasurementElectric current

Current measures charge crossing a chosen surface per unit time.

DefinitionPhysicsElectric field and force

An electric field assigns force per unit test charge.

DefinitionPhysicsMagnetic force on a moving charge

Magnetic force depends on charge motion relative to the field.

ModelPhysicsOhm's law and its domain

A linear current-voltage relation requires suitable conditions.

Empirical findingPhysicsFirst law of thermodynamics

Keep the heat and work sign convention explicit in an energy balance.

ModelPhysicsSecond law: isolated-system entropy

Apply entropy increase to the whole isolated system.

ModelPhysics · ChemistryIdeal-gas equation of state

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

ModelPhysicsPhoton energy and frequency

One photon's energy is proportional to its frequency.

ModelPhysics · Mathematics & logicInvariant spacetime interval

Lorentz transformations preserve a combined space-time separation.

ModelPhysicsNewton's third law

Interaction forces act on different bodies in equal and opposite pairs.

ModelPhysicsAngular momentum and torque

Torque changes angular momentum about a specified origin.

ModelPhysicsHydrostatic pressure

Static fluid pressure rises with depth under gravity.

ModelPhysicsArchimedes' buoyancy principle

The hydrostatic upward force equals displaced-fluid weight.

ModelPhysicsMaxwell equations in free space

Four field equations connect electric and magnetic fields with charge and current.

ModelPhysicsSchrödinger time evolution

A quantum wavefunction evolves according to its Hamiltonian.

ModelPhysicsBorn position probability

A normalized wavefunction assigns probabilities to position intervals.

ModelPhysics · MeasurementElementary charge

The elementary charge has an exact SI numerical value.

DefinitionPhysics · MeasurementBoltzmann constant

The Boltzmann constant has an exact SI numerical value.

DefinitionMeasurement · Chemistry · PhysicsAvogadro constant

The mole is linked to a specified number of entities.

DefinitionMeasurement · PhysicsSI defining luminous efficacy

A specified frequency fixes the photometric SI reference.

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.

Model
DefinitionSource checked

Isotopes and mass number

Chemistry

Isotopes share a proton count but have different neutron counts.

Key knowledge

Isotopes are atoms of the same element with different numbers of neutrons. Their atomic number is the same, while their mass number A, the total number of protons and neutrons, differs.

Values and equations

A = Z + N

A
Mass number: total nucleon count
Z
Number of protons
N
Number of neutrons

Conditions and scope

  • Mass number counts nucleons; it is not an atomic mass measured in kilograms.
  • A change in electron count changes ionic charge, not isotope identity.
  • Counts for one specified atomic nucleus; all three quantities are dimensionless integers.
Sources · 2

References

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

  1. Chemistry 2e (2019), §2.3 Atomic structure and symbolismPaul Flowers, Klaus Theopold, Richard Langley and William R. Robinson · OpenStax/Rice UniversityTextbook chapteropenstax.orgRead source
  2. Physical Sciences 10: IsotopesSiyavulaTextbook chaptersiyavula.comRead source

Evidence and review

Source definitions and magnesium isotope examples; isotope abundances and nuclear lifetimes are outside this record.

2026-10-10 · English isotope identity and mass-number distinction checked against Atomic Structure and Symbolism.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Scope or convention differs

Same proton number, different neutron counts and mass numbers.

A mass number counts nucleons; it is not an exact measured atomic mass.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–6 of 6 relationships

Scientific relationships · 6 / 6

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • Isotopes are atoms of the same element with different numbers of neutrons. Their atomic number is the same, while their mass number A, the total number of protons and neutrons, differs.
    • An atom has a nucleus surrounded by electrons. Its atomic number Z is the number of protons in the nucleus and identifies the element. A neutral atom has the same number of electrons as protons; gaining or losing electrons forms an ion of that element.

    Isotope identity uses the shared atomic number of an element.

  2. Related to
    Relationship sources · 1

    Linked statements

    • Radiometric dating combines isotope measurements with a decay model to estimate elapsed time. Interpretation requires accounting for initial daughter material and subsequent isotope gain or loss. A mineral's isotopic age can record formation or later resetting, rather than every event in the rock's history.

    A stated isotope system and sample-retention history underlie an age interpretation.

  3. Related to
    Relationship sources · 2

    Linked statements

    • An isotope delta compares a specified sample isotope ratio with the same ratio in a stated reference. Equilibrium and kinetic fractionation can change isotope partitioning between substances; mixing also changes measured ratios. A delta is a relative ratio difference, not an absolute isotope abundance or a unique process diagnosis.

    Isotope identities define the amount ratio.

  4. Related to
    Relationship sources · 1

    Linked statements

    • The proton–proton chains and CNO cycles convert hydrogen into helium through different reaction sequences; CNO nuclei participate in a catalytic cycle. Helium burning can form carbon through the triple-alpha sequence. Rates and pathway contributions depend on temperature, density and composition, and neutrinos carry away part of the released energy.

    Isotope identities and nuclear counts specify each pathway.

  5. Related to
    Relationship sources · 1

    Linked statements

    • A mass spectrometer ionizes material, separates ions by mass-to-charge ratio and detects their abundance. Ionization and fragmentation produce method-dependent spectral patterns. A molecular ion, isotope pattern and fragments can constrain composition and connectivity, but the measured m/z is not automatically a neutral molecular mass.

    Isotope composition contributes to spectral patterns.

  6. Uses definition
    Relationship sources · 2

    Linked statements

    • The atomic mass constant mu is one twelfth of the mass of a free carbon-12 atom at rest in its ground state. A sample's relative atomic mass is its mean atomic mass divided by mu. Isotope fractions determine the mean; this is distinct from an isotope's integer mass number. Standard atomic weights describe specified normal terrestrial materials and may have intervals because isotope abundances vary.

    The average is over isotopes of one element; isotope mass number and dimensionless relative atomic mass remain distinct.

Entry detailsPermanent link to this entry ↗
Record identity
chem-isotopes
Revision
core.1
Structured reference record
Essential core · first collection