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===Decay constant determination=== {{See also|Radioactive decay law}} The radioactive decay constant, the probability that an atom will decay per year, is the solid foundation of the common measurement of radioactivity. The accuracy and precision of the determination of an age (and a nuclide's half-life) depends on the accuracy and precision of the decay constant measurement.<ref>{{cite journal|last1=Begemann|first1=F.|last2=Ludwig|first2=K.R.|last3=Lugmair|first3=G.W.|last4=Min|first4=K.|last5=Nyquist|first5=L.E.|last6=Patchett|first6=P.J.|last7=Renne|first7=P.R.|last8=Shih|first8=C.-Y.|last9=Villa|first9=I.M.|last10=Walker|first10=R.J.|date=January 2001|title=Call for an improved set of decay constants for geochronological use|journal=Geochimica et Cosmochimica Acta|volume=65|issue=1|pages=111–121|doi=10.1016/s0016-7037(00)00512-3|bibcode=2001GeCoA..65..111B}}</ref> The in-growth method is one way of measuring the decay constant of a system, which involves accumulating daughter nuclides. Unfortunately for nuclides with high decay constants (which are useful for dating very old samples), long periods of time (decades) are required to accumulate enough decay products in a single sample to accurately measure them. A faster method involves using particle counters to determine alpha, beta or gamma activity, and then dividing that by the number of radioactive nuclides. However, it is challenging and expensive to accurately determine the number of radioactive nuclides. Alternatively, decay constants can be determined by comparing isotope data for rocks of known age. This method requires at least one of the isotope systems to be very precisely calibrated, such as the [[lead–lead dating|Pb–Pb system]].{{Citation needed|date=October 2022}}
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