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Showing 1–30 of 324 reference entries

Physics · Earth & cosmosNewtonian gravitation

An inverse-square force models attraction between point masses.

ModelEarth & cosmosRock cycle and geological transformation

Rock materials can change through multiple geological pathways.

ModelEarth & cosmosPlate tectonics

Moving lithospheric plates organize many large-scale geological processes.

ModelEarth & cosmosEarth's water cycle

Water moves among reservoirs above, on and below Earth's surface.

ModelEarth & cosmos · Biology · ChemistryEarth's carbon cycle

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

ModelEarth & cosmosPlanetary radiative energy balance

Earth's energy storage changes when incoming and outgoing energy differ.

ModelEarth & cosmosAtmospheric greenhouse effect

Infrared absorption and emission affect how Earth loses heat to space.

ModelEarth & cosmosWeather, climate and their time scales

Weather describes short-term conditions; climate describes their longer-term patterns.

DefinitionEarth & cosmosOrbits as gravitational motion

An orbiting body can remain in continuous gravitational free fall.

ModelEarth & cosmosStellar fusion and evolution

Main-sequence stars release energy by fusing hydrogen into helium.

ModelEarth & cosmosHot Big Bang and the cosmic microwave background

Expansion and relic radiation support an earlier hot, dense Universe.

ModelPhysics · Earth & cosmosFriedmann cosmological evolution

Homogeneity and isotropy reduce gravitational expansion to two balances.

ModelPhysics · Earth & cosmosNuclear binding energy

A bound nucleus has less rest mass than its separated nucleons.

ModelPhysics · Earth & cosmosExponential radioactive decay

A fixed decay probability per time gives a population timescale.

ModelPhysics · Earth & cosmosFission, fusion and reaction energy

Nuclear rearrangement can release or require energy.

ModelEarth & cosmosMinerals, structure and diagnostic properties

Mineral identification combines structural and physical evidence.

MethodEarth & cosmosRadiometric ages and sample history

Isotopic measurements estimate an age only with a suitable geological model.

MethodEarth & cosmosSeismic constraints on Earth's interior

Wave travel, refraction and transmission constrain an interior model.

MethodEarth & cosmosThe geodynamo model

Fluid motion in the outer core maintains much of Earth's magnetic field.

ModelEarth & cosmosWater budgets and storage change

A defined area's water storage changes with total inflow and outflow.

ModelEarth & cosmosDarcy flux and hydraulic conductivity

Groundwater flow is often approximately linear in hydraulic-head gradient.

ApproximationEarth & cosmosOcean circulation and overturning

Wind, buoyancy changes and mixing contribute to ocean transport.

ModelEarth & cosmosGlobal atmospheric circulation

Unequal heating and rotation organize broad circulation patterns.

ModelEarth & cosmosClimate forcing and energy-budget perturbations

External changes can disturb climate's radiation budget.

DefinitionEarth & cosmosClimate feedback mechanisms

Climate responses can amplify or damp a change.

ModelEarth & cosmosClimate detection and attribution methods

Attribution compares observed changes with plausible drivers and variability.

MethodEarth & cosmosStellar evolution and fuel stages

Stellar structure changes as core fuel and conditions change.

ModelEarth & cosmosWhite dwarfs, neutron stars and stellar black holes

Different evolutionary outcomes leave different compact remnants.

ModelEarth & cosmosAnnual stellar parallax and distance

Changing observing position permits geometric distance inference.

MethodEarth & cosmosCosmological redshift and distance inference

Spectral stretching carries expansion information but is not one universal distance ruler.

Method
ModelSource checked

Nuclear binding energy

PhysicsEarth & cosmos

A bound nucleus has less rest mass than its separated nucleons.

Key knowledge

For a specified nucleus, binding energy B = [Z m_p + (A−Z)m_n − m_nucleus]c² is the energy needed to separate it into free protons and neutrons.

Values and equations

B = [Z m_p + (A−Z)m_n − m_nucleus]c²

B
Nuclear binding energy J
Z, A
Proton number and nucleon count
m_p, m_n, m_nucleus
Proton, neutron and bare nuclear rest masses kg
c
Vacuum light speed m s⁻¹

Conditions and scope

  • Use bare nuclear and nucleon rest masses consistently; atomic masses require electron accounting.
  • Ground-state binding and excited-state energy must be distinguished; no tabulated isotope values are supplied.
Sources · 1

References

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

  1. University Physics 3: Nuclear Binding EnergySamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source

Evidence and review

Equations 10.4–10.5: nucleon mass deficit and binding energy.

2026-10-10 · Rest-mass binding definition only; no universal stability threshold or nuclear-mass model asserted.

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

    • For a specified nucleus, binding energy B = [Z m_p + (A−Z)m_n − m_nucleus]c² is the energy needed to separate it into free protons and neutrons.

    Rest-energy release and supplied dissociation energy use consistent total-energy accounting; not the nonrelativistic heat/work formula alone.

  2. Related to
    Relationship sources · 1

    Linked statements

    • For a single nuclide with constant decay constant λ > 0, expected undecayed population is N(t) = N₀e^(−λt), activity is λN and half-life is ln 2/λ.

    Nuclear energy differences constrain decay channels, while λ is separate decay-dynamics information.

  3. Uses definition
    Relationship sources · 2

    Linked statements

    • Fission splits a nucleus into smaller products; fusion combines nuclei. Reaction Q = (Σm_initial − Σm_final)c² measures rest-energy release: Q > 0 is exothermic and Q < 0 requires energy input.

    Changes in binding/rest energies determine the reaction Q under consistent mass accounting.

  4. Approximates
    Relationship sources · 1

    Linked statements

    • A liquid-drop binding parameterization combines a positive volume term with surface, proton Coulomb and neutron–proton asymmetry penalties, plus an even–odd pairing term: B≈a_vA−a_sA²ᐟ³−a_cZ(Z−1)A⁻¹ᐟ³−a_a(A−2Z)²/A+δa_pA⁻³ᐟ⁴. Here δ=+1 for even Z/even N, −1 for odd Z/odd N, and 0 for odd A; N=A−Z.

    Fitted bulk/surface/Coulomb/asymmetry/pairing terms approximate the same bare-nucleus ground-state binding quantity within a stated fit domain.

  5. Derived from
    Relationship sources · 2

    Linked statements

    • Removing one neutron or proton from a specified ground-state nucleus costs S_n=B(A,Z)−B(A−1,Z) or S_p=B(A,Z)−B(A−1,Z−1). Two-nucleon differences reduce some odd–even effects and changes across isotope/isotone sequences can reveal shell structure; a separation energy and total binding per nucleon answer different questions.

    A consistent ground-state binding difference cancels the free-nucleon rest energies for the stated removal channel.

  6. 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.

    Differences in nuclear rest energy underpin energy release.

Entry detailsPermanent link to this entry ↗
Record identity
physics-nuclear-binding-energy
Revision
university-reference.1
Structured reference record
University reference · University core expansion