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Revision – What is an Isotope?

GEOCHRONOLOGY HONOURS 2006 Lecture 01 Introduction to Radioactive Decay and Dating of Geological Materials. Revision – What is an Isotope?. Protons, Neutrons and Nuclides. The mass of any element is determined by the protons plus the neutrons.

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Revision – What is an Isotope?

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  1. GEOCHRONOLOGY HONOURS 2006Lecture 01Introduction to Radioactive Decay and Dating of Geological Materials

  2. Revision – What is an Isotope?

  3. Protons, Neutrons and Nuclides • The mass of any element is determined by the protons plus the neutrons. • Where the element has different numbers of neutrons these are called isotopes • Any element can have isotopes that have the same proton number but different numbers of neutrons and hence a different mass number. • The mass of any element is made up of the sum of the mass of each isotope of that element multiplied by its atomic abundance. • Various combinations of N and Z are possible, although all combinations with the same Z number are the same element.

  4. Stable versus Unstable Nuclides • Not all combinations of N and Z result in stable nuclides. • Some combinations result in stable configurations • Relatively few combinations • Generally N ≈ Z • However, as A becomes larger, N > Z • For some combinations of N+Z a nucleus forms but is unstable with half lives of > 105 yrs to < 10-12 sec • These unstable nuclides transform to stable nuclides through radioactive decay

  5. Radioactive Decay • Nuclear decay takes place at a rate that follows the law of radioactive decay • Radioactive decay has three important features • The decay rate is dependent only on the energy state of the nuclide • The decay rate is independent of the history of the nucleus • The decay rate is independent of pressure, temperature and chemical composition • The timing of radioactive decay is impossible to predict but we can predict the probability of its decay in a given time interval

  6. Radioactive Decay • The probability of decay in some infinitesimally small time interval, dt, is ldt, where l is the decay constant for the particular isotope • The rate of decay among some number, N, of nuclides is therefore dN / dt = -lN [eq. 1] • The minus sign indicates that N decreases over time. • Essentially all significant equations of radiogenic isotope geochronology can be derived from this expression.

  7. Types of Radioactive Decay • Beta Decay • Positron Decay • Electron Capture Decay • Branched Decay • Alpha Decay

  8. Beta Decay • Beta decay is essentially the transformation of a neutron into a proton and an electron and the subsequent expulsion of the electron from the nucleus as a negative beta particle. • Beta decay can be written as an equation of the form 19K40 -> 20Ca40 + b- +  + Q Where b- is the beta particle, n is the antineutrino and Q stands for the maximum decay energy. _ _

  9. Positron Decay • Similar to Beta decay except that now a proton in the nucleus is transformed into a neutron, positron and neutrino. • Only possible when the mass of the parent is greater than that of the daughter by at least two electron masses. • Positron decay can be written as an equation of the form 9F18 -> 8O18 + b+ +  + Q Where b+ is the positron, n is the neutrino and Q stands for the maximum decay energy.

  10. Positron VS Beta Decay The atomic number of the daughter isotope is decreased by 1 while the neutron number is increased by 1. The atomic number of the daughter isotope is increased by 1 while the neutron number is decreased by 1. Therefore in both cases the parent and daughter isotopes have the same mass number and therefore sit on an isobar.

  11. Electron Capture Decay • Electron capture decay occurs when a nucleus captures one of its extranuclear electrons and in the process decreases its proton number by one and increases its neutron number by one. • This results in the same relationship between the parent and the daughter isotope as in positron decay whereby they both occupy the same isobar.

  12. Alpha Emission • Represents the spontaneous emission of alpha particles from the nuclei of radionuclides. • Only available to nuclides of atomic number of 58 (Cerium) or greater as well as a few of low atomic number including He, Li and Be. • Alpha emission can be written as: 92U238 -> 90Th234 + 2He4 + Q Where 2He4 is the alpha particle and Q is the total alpha decay energy

  13. Alpha Emission A daughter isotope produced by alpha emission will not necessarily be stable and can itself decay by either alpha emission, or beta emission or both.

  14. Branched Decay • The difference in the atomic number of two stable isobars is greater than one, ie two adjacent isobars cannot both be stable. • Implication is that two stable isobars must be separated by a radioactive isobar that can decay by different mechanisms to produce either stable isobar. • Example 71Lu176 decays to 72Hf176 via negative beta decay 72Hf176 decays to 70Yb176 by positron decay or electron capture.

  15. Branched decay scheme for A=38 isobar

  16. Branched decay scheme for A=132 isobar

  17. Decay of 238U to 206Pb

  18. Radiogenic Isotope Geochemistry • Can be used in two important ways 1. Tracer Studies • Makes use of the differences in the ratio of the radiogenic daughter isotope to other isotopes of the element • Can make use of the differences in radiogenic isotopes to look at Earth Evolution and the interaction and differentiation of different reservoirs

  19. Radiogenic Isotope Geochemistry 2. Geochronology • Makes use of the constancy of the rate of radioactive decay • Since a radioactive nuclide decays to its daughter at a rate independent of everything, it is possible to determine time simply by determining how much of the nuclide has decayed.

  20. Radiogenic Isotope Systems • The radiogenic isotope systems that are of interest in geology include the following • K-Ar • Ar-Ar • Fission Track • Cosmogenic Isotopes • Rb-Sr • Sm-Nd • Re-Os • U-Th-Pb • Lu-Hf

  21. Table of the elements

  22. Radiogenic Isotope Systems • The radiogenic isotope systems that are of interest in geology include the following • K-Ar • Ar-Ar • Fission Track • Cosmogenic Isotopes • Rb-Sr • Sm-Nd • Re-Os • U-Th-Pb • Lu-Hf

  23. Geochronology and Tracer Studies Isotopic variations between rocks and minerals due to • Daughters produced in varying proportions resulting from previous event of chemical fractionation • 40K 40Ar by radioactive decay • Basalt  rhyolite by FX (a chemical fractionation process) • Rhyolite has more K than basalt • 40K  more 40Ar over time in rhyolite than in basalt • 40Ar/39Ar ratio will be different in each • Time: the longer 40K  40Ar decay takes place, the greater the difference between the basalt and rhyolite will be

  24. The Decay Constant • Over time the amount of the daughter (radiogenic) isotope in a system increases and the amount of the parent (radioactive) isotope decreases as it decays away. If the rate of radioactive decay is known we can use the increase in the amount of radiogenic isotopes to measure time. • The rate of decay of a radioactive (parent) isotope is directly proportional to the number of atoms of that isotope that are present in a system, ie Equation 1 that we have seen previously. • dN/dt = -lN, [eq. 1] • where N = the number of parent atoms and l is the decay constant • The -ve sign means that the rate decreases over time

  25. The Half Life • The half life of a radioactive isotope is the time it takes for the number of parent isotopes to decay away to half their original value. It is related to the decay constant by the expression • T1/2 = ln2/l • For 87Rb, the decay constant is 1.42 x 10-11y-1, hence, t1/287Rb = 4.88 x 1010years. In other words after 4.88 x 1010years a system will contain half as many atoms of 87Rb as it started off with.

  26. Geologically Important Isotopes and their Decay Constants

  27. Using the Decay Constant The number of radiogenic daughter atoms (D*) produced from the decay of the parent since date of formation of the sample is given by D* = No - N [eq. 2] Where D* is the number of daughter atoms produced by decay of the parent atom and No is the number of original parent atoms Therefore the total number of daughter atoms, D, in a sample is given by D = Do + D* [eq. 3]

  28. Using the Decay Constant The two equations can be combined to give D = Do + No – N [eq. 4] Generally, when rocks or minerals first form they contain a greater or lesser amount of the daughter atoms of a particular isotope system, i.e., not all the daughter atoms that we measure in a sample today were formed by decay of the parent isotope since the rock first formed.

  29. Dating of Rocks from Radioactive Decay Recalling that -dN/dt = lN [eq. 1] Integration of the above yields N=Noe-lt [eq. 5] We can substitute this into equation 4 to get D=Do + Nelt – N [eq. 6] which simplifies to D=Do + N(elt – 1) [eq. 7]

  30. The Radiogenic Decay Equation • Equation 7 is the basic decay equation and is used extensively in radiogenic isotope geochemistry. • In principle, D and N are measurable quantities, while Do is a constant whose value can be either assumed or calculated from data for cogenetic samples of the same age. • If these three variables are known then the above equation can be solved for t to give an “age” for the rock or mineral in question.

  31. Plotting Geochron Data • There are two methods for graphically illustrating geochron data • 1. The Isochron Technique • Used when the decay scheme has one parent isotope decaying to a daughter isotope. • Results in a straight line plot • 2. The Concordia Diagram • Used when more than one decay scheme results in the formation of the daughter isotopes • Results in a curved diagram (we’ll talk more about this later when we look at U-Th-Pb)

  32. The Isochron Technique • The Isochron Technique • Requires 3 or more cogenetic samples with a range of Rb/Sr • 3 cogenetic rocks derived from a single source by partial melting, FX, etc. • 3 coexisting minerals with different K/Ca ratios in a single rock • Let’s look at an example in the Rb/Sr system

  33. The Rb-Sr system • Strontium has four naturally occurring isotopes all of which are stable • 38Sr88, 38Sr87, 38Sr86, 38Sr84 • Their isotopic abundances are approximately • 82.53%, 7.04%, 9.87%, and 0.56% • However the isotopic abundances of strontium isotopes varies because of the formation of radiogenic Sr87 from the decay of naturally occurring Rb87 • Therefore the precise isotopic composition of strontium in a rock or mineral depends on the age and Rb/Sr ratio of that rock or mineral.

  34. Rb-Sr Isochrons • If we are trying to date a rock using the Rb/Sr system then the basic decay equation we derived earlier has the form Sr87 = Sr87i + Rb87(elt –1) • In practice, it is a lot easier to measure the ratio of isotopes in a sample of rock or a mineral, rather than their absolute abundances. Therefore we can divide the above equation through by the number of Sr86 atoms which is constant because this isotope is stable and not produced by decay of a naturally occurring isotope of another element.

  35. Rb-Sr Isochrons • This gives us the equation 87Sr/86Sr = (87Sr/86Sr)i + 87Rb/86Sr(elt – 1) • To solve this equation, the concentrations of Rb and Sr and the 87Sr/86Sr ratio must be measured. • The Sr isotope ratio is measured on a mass spectrometer whilst the concentrations of Rb and Sr are normally determined by XRF or ICPMS.

  36. Rb-Sr Isochrons • The concentrations of Rb and Sr are converted to the 87Rb/86Sr ratio by the following equation. 87Rb/86Sr = (Rb/Sr) x (Ab87Rb x WSr)/(Ab86Sr x WRb), where Ab is the isotopic abundance and W is the atomic weight. • The abundance of 86Sr (Ab86Sr) and the atomic weight of Sr (WSr) depend on the abundance of 87Sr and therefore must be calculated for each sample.

  37. What can we learn from this? • After each period of time, the 87Rb in each rock decays to 87Sr producing a new line • This line is still linear but is steeper than the previous line. • We can use this to tell us two important things • The age of the rock • The initial 87Sr/86Sr isotope ratio

  38. Determining the Age of a Rock

  39. Determining the Age of a Rock

  40. Let’s look now at the initial ratio

  41. The Fitting of Isochrons • After the 87Sr/86Sr and 87Rb/86Sr ratios of the samples or minerals have been determined and have been plotted on an isochron, the problem arises of fitting the ‘best’ straight line to the data points. • The fit of data points to a straight line is complicated by the errors that are associated with each of the analyses

  42. The Fitting of Isochrons

  43. Equations for Calculating the Best Slope and Intercepts of a Straight Line

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