12 Half Lives for Radioactive Elements Radioactive ParentStable DaughterHalf lifePotassium 40Argon 401.25 billion yrsRubidium 87Strontium 8748.8 billion yrsThorium 232Lead 20814 billion yrsUranium 235Lead 207704 million yrsUranium 238Lead 2064.47 billion yrsCarbon 14Nitrogen 145730 years
13 Growth of Radioactive Daughter Products where decay of parent(original) nucleus:if it’s radioactiveitself!as we’ve seen beforetry:note:and if:
14 Growth of Radioactive Daughter Products so:so:and:Note: as 2→0as seen before.As N1(t)and N2(t)may reach the stateso that:
15 Note: some elements have both radioactive and non-radioactive isotopes.Examples: carbon, potassium.Just saw: 3 isotopes of uranium.238U the most abundant ( %)Radioactive elements tend to become concentratedin the residual melt that forms during the crystallizationof igneous rocks.More common inSIALIC rocks(granite, granite pegmatite)and continental crust.
16 Radioactive isotopes don't tell much about the age of sedimentary rocks (or fossils).radioactive minerals in sedimentary rocksderived from the weathering of igneous rocksThus: dating sedimentary rock givesthe time of cooling of the magmathat formed the original igneous rock.tells us nothing about when the sedimentary rock formed.
17 To date a sedimentary rock, it is necessary to isolate a few unusual minerals (if present) which formed onthe seafloor as the rock was cemented.Glauconite is a good example. It crystallizes under reducingconditions that cause precipitation of minerals into sedimentsGlauconite contains potassium,so it can be dated using thepotassium-argon technique.
18 Minerals you can dateMost minerals containing radioactive isotopes are in igneous rocks.The dates they give indicate the time the magma cooled.Potassium 40 is found in:potassium feldspar (orthoclase)muscoviteamphiboleglauconite (greensand; found in some sedimentary rocks; rare)Uranium may be found in:zirconurananitemonaziteapatitesphene
19 R = = 2 different rock samples have ratios of 238U to 206Pb atoms of 1.2 and 1.8.Compute the age of each sample.238U atoms remaining today:The number 238U atoms decayed number of 206Pb atoms today:number 238U atomsnumber of 206Pb atomsSo:R ==R=1.2: 109 yearsR=1.8: 109 years
20 If other (stable) isotopes of the daughter are also present What if there were initially some daughter productsalready there when the rock was formed?unknown!Remember: elements come in many isotopes(some even tag a specific decay series!)If other (stable) isotopes of the daughter are also presentThen look at the ratio:
21 Which we can rewrite as: N(t)=N0e-tN0=N(t)e+ty = x m b
22 Rb-Sr dating method Allows for the presence of initial 87Sr Age = 4.53 109 y2 = 0.04 109 yG.W. Wetherill, Ann. Rev.Nucl. Sci. 25, 283 (1975)
23 Some concentration ratios measured for Eagle Peak Pluton All samples lie along thesame line, so formed fromthe same batch of magmaSome concentration ratios measured for Eagle Peak Plutonof the Sierra Nevada Batholith=14
24 Rubidium half-life=48.8 By = 48,800,000,000 years The Sierra Nevada pluton was formed by subduction(one tectonic plate driven beneath another) remeltingcontinental crust and forming volcanic rock calledbasalt 8,530,000 years ago. Sure enough west ofthis fault (and deeper below the basalts) are 4.55 Bysamples of continental crust.
25 How does Carbon-14 dating work? Cosmic rays strike Nitrogen 14 atoms in the atmosphereand form (radioactive) Carbon 14 whichcombines with oxygen to form radioactive carbon dioxidewith a half-life of 5730 yearsThe steady barrage (for at least 10s of thousands of years) ofcosmic cays gives the atmosphere equilibrium concentrations12C %13C %14C 1 atom for every 1012 atoms of 12C
26 How does Carbon-14 dating work? radioactive carbon dioxide is absorbed and used by plants.enters the food chain & the carbon cycle.Living things are in equilibrium with the atmosphere.All living things contain a constant ratio of 14C to 12C(1 in a trillion).At death, 14C exchange ceases and any 14C in the tissues of the organism begins to decay to Nitrogen 14, and is not replenished by new 14C.The change in the 14C to 12C ratio is the basis for dating.
27 Assumes that the rate of Carbon 14 production The half-life is so short (5730 years) that this method can only be used on materials less than 70,000 years old. Archaeological dating uses this method.) Also useful for dating the Pleistocene Epoch (Ice Ages).Assumes that the rate of Carbon 14 production(and hence the amount of cosmic rays striking the Earth)has been constant (through the past 70,000 years).
29 What is the age of this fragment of wood? An old wood fragment is burned to release CO2which is collected in a cc vessel to apressure of 2.00104 Pa (N/m2) at 295 K.In one week, 1420 b- decays are counted.b) An atmospheric sample of carbon dioxide isplaced into the same size vessel under thesame P and T for comparison purposes.What is the age of this fragment of wood?What number of counts does sample (b) give us?
30 A = lN = A = 3.76 10-4/sec Only 1 in a trillion are radioactive: 5730 yr1 yr31,557,600 sec/yrA = lN=9.82 108A = 3.76 10-4/secIn 1 week expectBut the CO2 collected from the woodfragment is only 1420/2277 as active
33 Fission Track Dating Charged particles from radioactive decay (spontaneous fission of uranium)pass through mineral's crystal latticeleave trails of damage called FISSION TRACKS.Procedures to study: Enlarge tracks by etching in acid(so visible with light under microscope)More readily seen with electron microscopeCount the etched tracks (or note track density in an area)Useful in dating:Micas (up to 50,000 tracks per cm2)TektitesNatural and synthetic (manmade) glassReheating "anneals" or heals the tracks.The number of tracks per unit area is a function of age and uranium concentration.