Measuring theAge of things (Astro 202 2/12/08)Nomenclature+ ProtonNeutronElectronCarbon 12 Carbon 14Nitrogen 146 protons6 neutrons6 electrons7 protons7 neutrons7 electrons6 protons8 neutrons6 electronsSame Element, Different IsotopesCarbon 126 protons6 neutrons6 electronsElement: Number of ProtonsIsotope: Number of Neutrons (Same No. of Protons)Note diagrams not toscale!Different ElementsThree Types of Nuclear Decay!"#electronneutrinoHelium NucleusphotonCarbon 14Nitrogen 14electronneutrinoCarbon 14 DecayHalf-Life Half-Life 1/2Half-Life 1/4Half-Life 1/8Half-Life 1/16Example: Buried Trees from theEnd of the Ice Age found at sitesaround the edge of the GreatLakes.Imagine we found a piece of wood which contains 100 nuclei ofCarbon-14, which has a half-life of 6000 years.Assuming the wood did not gain or lose atoms to itsenvironment, how many Carbon-14 nuclei would the objecthave:6000 years ago?Imagine we found a piece of wood which contains 100 nuclei ofCarbon-14, which has a half-life of 6000 years.Assuming the wood did not gain or lose atoms to itsenvironment, how many Carbon-14 nuclei would the objecthave:6000 years ago? 20012000 years ago?Imagine we found a piece of wood which contains 100 nuclei ofCarbon-14, which has a half-life of 6000 years.Assuming the wood did not gain or lose atoms to itsenvironment, how many Carbon-14 nuclei would the objecthave:6000 years ago? 20012000 years ago? 40018000 years ago?Imagine we found a piece of wood which contains 100 nuclei ofCarbon-14, which has a half-life of 6000 years.Assuming the wood did not gain or lose atoms to itsenvironment, how many Carbon-14 nuclei would the objecthave:6000 years ago? 20012000 years ago? 40018000 years ago? 800Imagine we found a piece of wood which contains 100 nuclei ofCarbon-14, which has a half-life of 6000 years.Assuming the wood did not gain or lose atoms to itsenvironment, how many Carbon-14 nuclei would the objecthave:6000 years ago? 20012000 years ago? 40018000 years ago? 800So, How old is this tree?To figure out how old an object is using an unstable nucleus,we need to know how many nuclei it contains now and howmany nuclei it contained originally.How can we do this reliably?Ancient Trees andModern trees obtainCarbon-14 from thesame place…..Carbon-14 isproduced bycosmic raysstriking theatmosphereCosmic rays are nucleithat move through spaceat speeds approachingthe speed of light.All living organisms acquire carbon-14 from the atmosphereIf the Carbon-14 content ofthe atmosphere hasremained constant, thenancient trees havecomparable amounts ofCarbon-14 as modern treesA 5,730 year old tree would have half the Carbon-14 of a modern tree A 11,460 year old tree would have one-quarter the Carbon-14 of a modern tree By comparing Carbon-14 dates with independent age measurements,we can confirm the Carbon-14 content of the atmosphere has remainedrather constant.Data from Libby’s 1960 Nobel Prize LectureCorrecting Carbon-14With Tree RingsDendrochronologyVariations in Carbon-14 content of the atmosphere canbe detected and accounted for….These variations can tell us something about the history ofEarth’s climate and solar system magnetic fieldsData from radiocarbon.org INTCAL04These trees haveroughly 1/4 of theiroriginal Carbon-14remaining, so thesetress are between10,000 and 12,000years old.These trees date to theend of the last Ice Age,and give uniqueinsights into theshifting climate…..Leavitt et al. 2007 in Radiocarbon 49(2) 855-864See alsowww.ltrr.arizona.edu/~sleavitt/YoungerDryasLinknew.htmHow do we date earlierevents, like theChicxulub Impact craterTopography from NASA RadarCarbon-12Potassium-39 Potassium-40Carbon-14There are many other types of unstable nuclei besides Carbon 14.Stable UnstableAluminum-27Aluminum-26Half-lives of different nuclei….Carbon-14 5,730 yearsAluminum-26 717,000 yearsPotassium-40 1,280,000,000 yearsRubidium-87 47,500,000,000 yearsUranium-235 704,000,000 yearsUranium-238 4,468,000,000 yearsNumbers from http://ie.lbl.govPotassium 40Argon 40electronneutrinoPotassium 40Calcium 40electronneutrinoPotassium-40 has two ways it can decay90%10%Potassium-40 can be used to measure the age ofmelted rocks…..Potassium-40Argon-40Calcium-40Potassium-40 decay in hot or molten rockPotassium-40Argon-40Calcium-40Potassium-40 decay in a cold, solid rockPotassium-40 Calcium-40The Rock TodayArgon-40Potassium-40 Argon-40 Calcium-40Potassium 40Calcium-40The Original RockThe Rock TodayPotassium-40 measurements of small particles of glass and meltfrom the impact date this event….Swisher et al. 1992 in Science, 257 (954)Potassium-40 measurements of small particles of glass and meltfrom the impact date this event to64.98 +/- 0.05 million years ago….Swisher et al. 1992 in Science, 257 (954)Comparing the dateof the impact withthose of fossildeposits confirmsthe impact occurredclose to the end ofthe age of thedinosaurs.Summary points:Unstable nuclei are potentially powerful tools fordetermining the age of things, because whether a givennucleus decays or not depends only on the interactionsbetween the protons and neutrons in individual nuclei andbecause groups of unstable nuclei decay in a predictable,regular way characterized by a parameter known as thehalf-lifeSummary points:In practice, to be able to use unstable nuclei to measurethe age of some, we need to know:(1) The half-life of the nucleus(2) The number of unstable nuclei in the object now(3) The number of unstable nuclei in the objectoriginallyCarbon-14 nuclei, which have a half-life of 5,730 years, areuseful for dating objects that used to be part of living thingsthat lived during the last ~50,000 years. This is because theoriginal Carbon-14 content of these organisms arecomparable to that of similar organisms living todayPotassium-40 nuclei, which have a half-life of 1.28 billionyears, are useful for measuring the age of ancient volcanicrocks that are millions or billions of years old. This is becausemolten rocks contain little Argon-40, so the amount of Argon-40 in a rock is a measure of how much Potassium-40decayed in the rock since it last