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More parent more daughter isotope how do we deal with

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Unformatted text preview: do not need to know this mathemaKcal sequence for exams or homework ∫ kdt (we integrate the equaKon) t0 (the soluKon of the integral) (aier taking the exponenKal of both sides) 8 Rates of Decay Nt = e− kt N0 € this is the basic equaKon of radioacKve decay Nt is the number of parent atoms at Kme t N0 is the original number of parent atoms k is called the ‘rate constant’ or ‘decay constant’ each radioacKve nuclide has a unique rate constant For 14C, k = 0.0001 . For 238U, k = 0.000000000155 An easier term to grapple with is the ‘half- life’, the Kme required for half of the radioacKve substance to decay For 14C, t1/2 = 5730 years . For 238U, t1/2 = 4470 million years 9 QuesKon: It seems like we need to know how much parent isotope originally existed in the mineral. More parent = more daughter isotope. How do we ‘deal’ with this problem? Nt = e− kt N0 The decay of each parent results in the formaKon of one daughter isotope. Therefore: € N0 = Nt + D where N0 is the iniKal number of parents, Nt is present- day number of parents, and D is present- day number of daughters. Thus, the radioacKve decay equaKon becomes: Nt = e− kt Nt + D € 10 40K à༎ 40Ar t 1/2 = 1,250,000 years P D Nt = e− kt Nt + D € 11 from “The Age of the Earth” by G. Brent Dalrymple There are many such radioisotope systems available for determining the ages of minerals and rocks 12 from “The Age of the Earth” by G. Brent Dalrymple How old is the Earth? One approach is to go out and age- date the oldest rocks we can find. The oldest ages will be a minimum esKmate of the age of the Earth 13 More old rocks. 14 More old rocks. The earliest- formed rocks on Earth no longer exi...
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