radiometric_dating

radiometric_dating - Radiometric Dating EENS 2120 Tulane...

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This document last updated on 12-Apr-2011 EENS 2120 Petrology Tulane University Prof. Stephen A. Nelson Radiometric Dating Prior to 1905 the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state. Although we now recognize lots of problems with that calculation, the age of 25 my was accepted by most physicists, but considered too short by most geologists. Then, in 1896, radioactivity was discovered. Recognition that radioactive decay of atoms occurs in the Earth was important in two respects: 1. It provided another source of heat, not considered by Kelvin, which would mean that the cooling time would have to be much longer. 2. It provided a means by which the age of the Earth could be determined independently. Principles of Radiometric Dating Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential (Energy) barrier which bonds them to the nucleus. The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. T and P) cannot affect the rate of decay. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e. Note that dN/dt must be negative. The proportionality constant is λ , the decay constant. So, we can write Rearranging, and integrating, we get or ln(N/N o ) = - λ (t - t o ) If we let t o = 0, i.e. the time the process started, then (1) Radiometric Dating 4/12/2011 Page 1 of 14
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We next define the half-life, τ 1/2 , the time necessary for 1/2 of the atoms present to decay. This is where N = N o /2. Thus, or -ln 2 = - λ t, so that The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope. Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left. After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc. Knowledge of τ 1/2 or λ would then allow us to calculate the age of the material if we knew the amount of original isotope and its amount today. This can only be done for 14 C, since we know N 0 from the atmospheric ratio, assumed to be constant through time. For other systems we have to proceed further. Radiometric Dating 4/12/2011 Page 2 of 14
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Some examples of isotope systems used to date geologic materials. Parent Daughter τ 1/2 Useful Range Type of Material 238 U 206 Pb 4.47 b.y >10 million years Igneous & sometimes metamorphic rocks and minerals 235 U 207 Pb 707 m.y 232 Th 208 Pb 14 b.y 40 K 40 Ar & 40 Ca 1.28 b.y >10,000 years 87 Rb 87 Sr 48 b.y >10 million years 147 Sm 143 Nd 106 b.y. 14
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radiometric_dating - Radiometric Dating EENS 2120 Tulane...

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