Table 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 (α) decay - 4He nucleus (2p + 2n) ejected2) beta (β) decay - change of nucleus charge, conserves mass3) gamma (γ) 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)1σ=68.3%2σ=95%3σ=99%147.2124.0Since the students only counted 135.6 disintegrations, they will only achieve a 1σ accuracyof ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5%In other words, your 1σ 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 differenttemperatures. Above these temperatures, parent and/ordaughter isotopes move freely in and out of the systemK (radioactive parent) - Ar (daughter)ExampleKArAt T’s above a certain # (say, Tc), all or some Aratoms are lost from the system considered the“chronometer”.K (radioactive parent) - Ar (daughter)ExampleKArWhen T is < than Tc, all Ar atoms remain withinthe system considered the “chronometer”, e.g. aK-spar grain.Closure temperatureTo a first approximation, there is onetemperature below which diffusion is soslow that radiogenic parent or daughteratoms become static.The corollary is that every age wemeasure with an isotopic system recordsthe time elapsed since the temperaturecooled 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 thickone with some isotopes thatare energetically stable andothers 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 asthey depart from the idealized stabilityline.The isotopes that are not stable willtend to decay into more stableconfigurations.Let’s look at the element Rb and itsvarious isotopes.Essentially there are only two isotopes that don’tdecay away within short time scales, 87Rb and 85Rb.All others are not present in nature. Of these, one isstable (85Rb), and one is radiogenic (87Rb)How do we quantify stable or not?If isotopes decay away withinlaboratory time scales, that’s a nobrainer - they are not stable.Slower decaying species - need toknow their:A. Decay constant orB. Half lifeMeasuring radioactive decayHalf life (t1/2) = the time required for half ofthe parent atoms to decay, alternativelyuse:The decay constant (λ) = ln2/t1/2What is geologically useful?Systems that have half livescomparable to or longer thanthe age of the planet. Fastdecaying systems areevidently no good.E.g. 87Rb’s half life is ten timesthe age of the earth.Some super slow decayingsystems have yet to be figuredout. In the meantime, theycount as “stable” isotopes.Decay equationLaw of decay- the rate of decay of an unstable parent isproportional to the number of atoms remaining at any time t.The proportionality constant is lambda — decay constant —units reciprocal of time.€ dndt= −λn-dndt= λnIntegrate from 0 to time “t”€ dnn= −λdt0t∫n 0n∫n0= atoms present at time 0, λ- decay constantlnnn0= −λtn = n0e−λtThe # of radiogenic daughter atomsformed (D*) is equal to the # ofparent atoms consumed€ D* = n0− nGeneral geochronologicalequation€ D* = neλt− nD* = n(eλt− 1)D = D0+ n(eλt− 1)Decay curve of a radionuclide and growth curve of its stabledaughter 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/144NdAge = 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 highlymobile.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 themantle)Step-wise heating and 40Ar-39Ar DatingvsPlot (40Ar*/39Ar) vs heating stepsOrPlot Apparent Age vs. fraction 39Ar releasedPlot (40Ar*/39Ar) vs heating stepsOrPlot Apparent Age vs. fraction 39Ar releasedStep-wise heating and 40Ar-39Ar Dating“plateau” gives most reliable crystallization agelow-temperature stepsreveal sample has lost 40Ar*higher T steps give consistent 40Ar*/39Ar ratios. . . or measure many grains and use isochron methodLaser applications in Ar-Ar datinglaser spotAllows for step-wise heating of different zones within grainsLee et al., 1991U-Pb• U-Pb is a special system…Why?• There are two independent isotopic clocksticking at the same time (actually three buttwo with U as a parent and Pb as daughter.Multiple simultaneous decay sequences• Decay route t1/2, Ga