PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Closure temperatureSlide 13Isotope stabilitySlide 15Slide 16Slide 17Slide 18How do we quantify stable or not?Measuring radioactive decayWhat is geologically useful?Decay equationIntegrate from 0 to time “t”The # of radiogenic daughter atoms formed (D*) is equal to the # of parent atoms consumedGeneral geochronological equationSlide 26Isochron DiagramSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34U-PbMultiple simultaneous decay sequencesEquationsWhen initial Pb is insignificant and lots of U available….Concordia diagramsSlide 40Slide 41Table of Isotopic Masses and Natural Abudances Atomic weight element =Mi(abuni)+Mj(abunj) + …in amu, where 1amu = 1/12 mass 12CFour types of radioactive decay1) alpha () decay - 4He nucleus (2p + 2n) ejected2) beta () decay - change of nucleus charge, conserves mass3) gamma () decay - photon emission, no change in A or Z4) spontaneous fission - for Z=92 and above, generates two smaller nucleiSpontaneous fissionFission tracks from 238U fission in old zircon- heavy nuclides split into two daughtersand neutrons- U most common (fission-track dating)Decay chains- three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached238U --> radioactive daughters --> 206PbAlso 235U (t1/2) = 700 MaAnd 232Th (t1/2) =10 Ga234Th24dCounting Statistics and Error EstimationRadioactive decay process behaves according to binomial statistics.For large number of decays, binomial statistics approach a perfect Guassian.Observed # disintegrationsNumber of ObservationsEx: 100 students measure 14C disintegrations in 1g of modern coral (A = 13.56 dpm)with perfect geiger counters, for 10 minutes135.6Expected value (N)N+sqrt(N)N-sqrt(N)N+2sqrt(N)N-2sqrt(N)N+3sqrt(N)N-3sqrt(N)1=68.3%2=95%3=99%147.2124.0Since the students only counted 135.6 disintegrations, they will only achieve a 1 accuracyof ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5%In other words, your 1 relative error (in %) will be equal to (1/(sqrt(total counts)))*100Introduction to Mass SpectrometrySample introductionIonizationMinimize collisions, interferencesSeparatemassesCount ionsCollect resultsNier-type mass specDecay systems of interest for geologistsVarious isotopic systems start ticking the clock at different temperatures. Above these temperatures, parent and/or daughter isotopes move freely in and out of the systemK (radioactive parent) - Ar (daughter)ExampleKArAt T’s above a certain # (say, Tc), all or some Ar atoms are lost from the system considered the “chronometer”.K (radioactive parent) - Ar (daughter)ExampleKArWhen T is < than Tc, all Ar atoms remain within the system considered the “chronometer”, e.g. a K-spar grain.Closure temperature To a first approximation, there is one temperature below which diffusion is so slow that radiogenic parent or daughter atoms become static.The corollary is that every age we measure with an isotopic system records the time elapsed since the temperature cooled below that value.Stability of nuclei as a function of proton (Z) vs. neutron (N) numbersA (mass #)= Z+NIsotope stabilityHow many isotopes per element? The “stability” line is a thick one with some isotopes that are energetically stable and others that tend to “decay” into a different nuclear state.The Chart of the NuclidesZ (atomic number)N (neutron number)Isotopes of phosphorusHow many isotopes per elementNot all of these isotopes are stable as they depart from the idealized stability line. The isotopes that are not stable will tend to decay into more stable configurations.Let’s look at the element Rb and its various isotopes.Essentially there are only two isotopes that don’t decay away within short time scales, 87Rb and 85Rb. All others are not present in nature. Of these, one is stable (85Rb), and one is radiogenic (87Rb)How do we quantify stable or not?If isotopes decay away within laboratory time scales, that’s a no brainer - they are not stable.Slower decaying species - need to know their: A. Decay constant orB. Half lifeMeasuring radioactive decayHalf life (t1/2) = the time required for half of the parent atoms to decay, alternatively use:The decay constant () = ln2/t1/2What is geologically useful?Systems that have half lives comparable to or longer than the age of the planet. Fast decaying systems are evidently no good. E.g. 87Rb’s half life is ten times the age of the earth. Some super slow decaying systems have yet to be figured out. In the meantime, they count as “stable” isotopes.Decay equationLaw of decay- the rate of decay of an unstable parent is proportional to the number of atoms remaining at any time t. The proportionality constant is lambda — decay constant — units reciprocal of time.€ dndt= −λn-dndt= nIntegrate from 0 to time “t”€ dnn= −λ dt0t∫n 0n∫n0= atoms present at time 0, λ - decay constantlnnn0= −λtn = n0e−λtThe # of radiogenic daughter atoms formed (D*) is equal to the # of parent atoms consumed€ D* = n0− nGeneral geochronological equation€ D* = neλt− nD* = n(eλt−1)D = D0+ n(eλt−1)Decay curve of a radionuclide and growth curve of its stable daughter in linear coordinates.Decay curve of parentteNNλ−=0( )teNDλ−−= 10*Growth curve of daughterIsochron Diagram0.51260.51300.51340.51380.51420.51460.0 0.2 0.4 0.6 0.8147Sm/144Nd143Nd/144NdQuickTime™ and a decompressorare needed to see this picture.Age = 315±35 MaInitial 143Nd/144Nd =0.51273±0.00011MSWD = 0.0061data-point error ellipses are 2σK-Ar and 40Ar-39Ar Dating Hornblende thin sectionMany K-bearing minerals: biotite, muscovite, hornblende,K-feldspar, etc.Closed vs. Open System BehaviorThe K-Ar age is only accurate if the sample has remained a CLOSED SYSTEM:i.e. there has been no gain or loss of K or Ar through time.In reality, this is almost never the case, because Ar is a noble gas and is highly mobile.You will get an inaccurate K-Ar age if:1. Your initial Ar was not zero (the mantle contains appreciable 40Ar that may not have been completely degassed during rock formation).2. You lose Ar because of low-temperature alteration.3. Your sample is contaminated by atmospheric Ar (which is ~97% 40Ar).We can address #3 by monitoring 36Ar (~20,000 more abundant in air than in the mantle)Step-wise heating and