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Reference library Connections Sources University circle All areas of study / Earth & cosmos Topic All topics Earth's structure & history · 35 Rocks, minerals & geochemistry · 35 Water, surface & climate · 69 Geophysics & Earth models · 48 Astronomy & observation · 31 Stars & galaxies · 50 Orbits & planetary systems · 47 Cosmology · 18 Shared & other concepts · 17
Physics · Earth & cosmos Newtonian gravitation An inverse-square force models attraction between point masses.
Model → Earth & cosmos Rock cycle and geological transformation Rock materials can change through multiple geological pathways.
Model → Earth & cosmos Plate tectonics Moving lithospheric plates organize many large-scale geological processes.
Model → Earth & cosmos Earth's water cycle Water moves among reservoirs above, on and below Earth's surface.
Model → Earth & cosmos · Biology · Chemistry Earth's carbon cycle Carbon moves through biological, oceanic, atmospheric and geological reservoirs.
Model → Earth & cosmos Planetary radiative energy balance Earth's energy storage changes when incoming and outgoing energy differ.
Model → Earth & cosmos Atmospheric greenhouse effect Infrared absorption and emission affect how Earth loses heat to space.
Model → Earth & cosmos Weather, climate and their time scales Weather describes short-term conditions; climate describes their longer-term patterns.
Definition → Earth & cosmos Orbits as gravitational motion An orbiting body can remain in continuous gravitational free fall.
Model → Earth & cosmos Stellar fusion and evolution Main-sequence stars release energy by fusing hydrogen into helium.
Model → Earth & cosmos Hot Big Bang and the cosmic microwave background Expansion and relic radiation support an earlier hot, dense Universe.
Model → Physics · Earth & cosmos Friedmann cosmological evolution Homogeneity and isotropy reduce gravitational expansion to two balances.
Model → Physics · Earth & cosmos Nuclear binding energy A bound nucleus has less rest mass than its separated nucleons.
Model → Physics · Earth & cosmos Exponential radioactive decay A fixed decay probability per time gives a population timescale.
Model → Physics · Earth & cosmos Fission, fusion and reaction energy Nuclear rearrangement can release or require energy.
Model → Earth & cosmos Minerals, structure and diagnostic properties Mineral identification combines structural and physical evidence.
Method → Earth & cosmos Radiometric ages and sample history Isotopic measurements estimate an age only with a suitable geological model.
Method → Earth & cosmos Seismic constraints on Earth's interior Wave travel, refraction and transmission constrain an interior model.
Method → Earth & cosmos The geodynamo model Fluid motion in the outer core maintains much of Earth's magnetic field.
Model → Earth & cosmos Water budgets and storage change A defined area's water storage changes with total inflow and outflow.
Model → Earth & cosmos Darcy flux and hydraulic conductivity Groundwater flow is often approximately linear in hydraulic-head gradient.
Approximation → Earth & cosmos Ocean circulation and overturning Wind, buoyancy changes and mixing contribute to ocean transport.
Model → Earth & cosmos Global atmospheric circulation Unequal heating and rotation organize broad circulation patterns.
Model → Earth & cosmos Climate forcing and energy-budget perturbations External changes can disturb climate's radiation budget.
Definition → Earth & cosmos Climate feedback mechanisms Climate responses can amplify or damp a change.
Model → Earth & cosmos Climate detection and attribution methods Attribution compares observed changes with plausible drivers and variability.
Method → Earth & cosmos Stellar evolution and fuel stages Stellar structure changes as core fuel and conditions change.
Model → Earth & cosmos White dwarfs, neutron stars and stellar black holes Different evolutionary outcomes leave different compact remnants.
Model → Earth & cosmos Annual stellar parallax and distance Changing observing position permits geometric distance inference.
Method → Earth & cosmos Cosmological redshift and distance inference Spectral stretching carries expansion information but is not one universal distance ruler.
Method → ← Back to entries Model Source checked
Exponential radioactive decay Physics Earth & cosmos
A fixed decay probability per time gives a population timescale.
Key knowledge 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.
Values and equations N(t) = N₀e^(−λt); activity = λN(t); t_½ = ln 2/λ
N, N₀ Expected undecayed population and initial population
λ Decay constant s⁻¹
t, t_½ Elapsed time and half-life s
activity Expected decay rate Bq Conditions and scope No production, daughter feeding, transport or competing changes to the stated population/model. Individual decay times are stochastic; dating requires additional isotope and closed-system assumptions. Sources · 1 Evidence and review Equations 10.10, 10.17–10.18: exponential population, half-life and activity.
2026-10-10 · Single constant-rate decay population model only; no geochronological date or exact individual lifetime claim.
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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.
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. Geological dating uses the decay model but additionally requires a sample-history model.
Derived from Relationship sources · 2 Linked statements
Independent constant decay channels have total rate λ=Σ_iλ_i and branching fractions b_i=λ_i/λ. For a closed parent–daughter chain with branch b, Ṅ₁=−λ₁N₁ and Ṅ₂=bλ₁N₁−λ₂N₂. Distinct rates give N₂(t)=N₂₀e^(−λ₂t)+bλ₁N₁₀(e^(−λ₁t)−e^(−λ₂t))/(λ₂−λ₁); equal rates give e^(−λt)(N₂₀+bλN₁₀t). Daughter activity is λ₂N₂, rather than the parent decay rate by default. Each constant-rate undecayed population supplies a source/loss term; channel sums and linear feeding extend the unproduced single-nuclide exponential.
Related to Relationship sources · 1 Linked statements
With depthz positive downward, constant conductivityk and uniform volumetric heat productionH, a stationary conductive slab obeys kT_zz+H=0. If T(0)=T_s and outward/upward surface heat flux is q_s=kT_z(0), then T(z)=T_s+(q_s/k)z−Hz²/(2k). At H=0 the gradient is constant; internal production makes upward flux decrease with depth in this model. Radiogenic heat is an internal source whose inventory evolves.
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