3,128,562,110
years
3.1286
Ga (billion years)
3,128.56
Ma (million years)
3,128,562,110
years
3.1286
Ga (billion years)
3,128.56
Ma (million years)
The Potassium-Argon Dating Calculator determines the age of geological samples using the decay of potassium-40 to argon-40. K-Ar dating is one of the most widely used geochronological methods, particularly valuable for dating volcanic and igneous rocks from thousands to billions of years old. It has been instrumental in establishing the geomagnetic polarity timescale, dating early human fossil sites in East Africa, and calibrating the geological time scale.
Potassium-40 undergoes branched decay: 89.28% decays by beta emission to calcium-40, and 10.72% decays by electron capture to argon-40. Only the electron capture branch produces the daughter isotope (Ar-40) used for dating. Since argon is a noble gas that escapes from molten rock, the K-Ar clock resets when a rock melts or is heated sufficiently, dating the last cooling event.
The age equation for K-Ar dating accounts for the branched decay of K-40:
$$t = \frac{1}{\lambda} \cdot \ln\left(1 + \frac{{}^{40}\text{Ar}}{{}^{40}\text{K}} \cdot \frac{\lambda}{\lambda_{ec}}\right)$$
where $$\lambda = 5.543 \times 10^{-10} \text{ yr}^{-1}$$ is the total decay constant, and $$\lambda_{ec}/\lambda = 0.1072$$ is the electron capture branch fraction. The full derivation starts from:
$${}^{40}\text{Ar}^* = \frac{\lambda_{ec}}{\lambda} \cdot {}^{40}\text{K} \cdot (e^{\lambda t} - 1)$$
Solving for $$t$$:
$$t = \frac{1}{\lambda} \cdot \ln\left(1 + \frac{{}^{40}\text{Ar}^*}{{}^{40}\text{K}} \cdot \frac{\lambda}{\lambda_{ec}}\right)$$
The method assumes all measured Ar-40 is radiogenic (produced by K-40 decay in situ) and that no argon was present when the rock formed or was lost after formation. Atmospheric argon corrections are applied using the Ar-40/Ar-36 ratio.
The calculated Age represents the time since the rock last cooled below the closure temperature for argon retention (typically 150-350°C depending on the mineral). For volcanic rocks, this closely approximates the eruption age. Ages are given in years, million years (Ma), and billion years (Ga). The method assumes a closed system — excess argon (inherited from magma or trapped fluid inclusions) can make ages appear too old, while argon loss from weathering or reheating makes ages too young.
Inputs
Results
An Ar-40/K-40 ratio of 0.0002 gives ~3.4 Ma, consistent with Pliocene volcanism. This is the age range of many East African hominin fossil sites.
Inputs
Results
A ratio of 0.5 yields ~2.93 Ga, placing this rock in the Late Archean eon, when early continental crust was forming.
K-40 in minerals decays to Ar-40 by electron capture. Since argon is a gas that escapes from molten rock, any Ar-40 in a solidified rock must have been produced by in-situ decay of K-40. Measuring the Ar-40/K-40 ratio and applying the branched decay equation gives the time since the rock solidified.
K-40 can decay by two competing processes: beta-minus emission to Ca-40 (89.28%) and electron capture to Ar-40 (10.72%). This occurs because both daughter nuclides have lower energy than K-40, making both pathways energetically allowed. The branching ratio is a fixed nuclear property determined by the relative transition probabilities.
Ar-Ar dating is a refinement of K-Ar that irradiates the sample with neutrons to convert K-39 to Ar-39. This allows measuring both parent (K via Ar-39) and daughter (Ar-40) as argon isotopes in the same mass spectrometer run. Ar-Ar dating enables step-heating experiments that can detect and correct for argon loss and excess argon.
Potassium-rich minerals are preferred: sanidine and orthoclase (K-feldspar), biotite, muscovite, hornblende, and leucite. Whole-rock basalt samples are also commonly dated. Each mineral has different argon closure temperatures, allowing thermochronological studies of cooling histories.
Excess argon is Ar-40 not produced by in-situ K-40 decay. It can be inherited from the magma source or trapped in fluid inclusions during crystallization. Excess argon makes K-Ar ages appear older than the true age. The Ar-Ar step-heating method can often identify and correct for excess argon.
K-Ar dating is effective from about 100,000 years to 4.5 billion years. The lower limit depends on the potassium content of the mineral and the sensitivity of the mass spectrometer. Very young samples may have too little radiogenic Ar-40 to measure accurately above atmospheric argon background.
Air contains Ar-40 (99.6%) and Ar-36 (0.334%) in a known ratio of 295.5. Any Ar-36 in the sample is assumed to be atmospheric, and the corresponding atmospheric Ar-40 (= 295.5 × Ar-36) is subtracted from the total Ar-40 to obtain the radiogenic component.
K-Ar dating of ocean floor basalts revealed that seafloor age increases symmetrically away from mid-ocean ridges, providing crucial evidence for seafloor spreading. Combined with magnetic polarity reversals recorded in basalt, K-Ar dates established the geomagnetic polarity timescale that underpins modern plate tectonics.
Generally not directly, because sedimentary minerals (clays, feldspars) are detrital grains with inherited ages from their source rocks. However, authigenic minerals (glauconite, illite formed during sedimentation) can provide approximate depositional ages. Volcanic ash layers interbedded with sediments are ideal K-Ar targets.
Closure temperature varies by mineral: hornblende ~530°C, muscovite ~350°C, biotite ~300°C, K-feldspar ~150-350°C. Below these temperatures, argon is retained in the crystal lattice. Above them, argon diffuses out, resetting the clock. This allows multi-mineral dating to reconstruct thermal histories (thermochronology).
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