earthjay science | Course Material and Educational …€¦ · Web viewRadiocarbon age control is a method of determining the time that something died. Living organisms absorb many

GEOL 460 Lab 8: Radioactive Decay and CRB Ages

Name: __________________________________________ Date: ________________

I. RadiocarbonRadiometric age control is based on three primary assumptions.

(1) There is a known initial concentration of parent and daughter isotopes.(2) There is a closure time, when the material no longer increases in concentration of a

given isotope.(3) That the isotope decays at a known rate.(4) That there is no contamination (remains a closed system following the closure time).

The mathematical expression, the age equation that relates radioactive decay to geologic time is:

D = D0 + N(t) (eλt − 1)

Where,

t is age of the sample,

D is number of atoms of the daughter isotope in the sample,

D0 is number of atoms of the daughter isotope in the original composition,

N is number of atoms of the parent isotope in the sample at time t (the present), given by N(t) = Noe-

λt, and

λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the

parent isotope[15] times the natural logarithm of 2.

Radiocarbon age control is a method of determining the time that something died. Living organisms absorb many isotopes during their lifetime. Relevant isotopes for this exercise include 12C and 14C. 12C is a stable isotope, but 14C is radioactive and decays to a daughter isotope at a known rate called the half-life. Once an organism dies, it generally ceases to absorb Carbon. 14C is formed in the atmosphere when cosmogenic nuclides bombard 14N. These 14N isotopes lose neutrons and turn into 14C isotopes. The rate of incoming nuclides varies with (1) the strength of Earth’s magnetosphere and (2) the rate that these nuclides are formed in the Sun. The rate that 14C decays proceeds with a half-life of 5730 years.

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Modern analytical techniques of estimating the amount of 14C in a sample is made by using accelerator mass spectrometry (AMS). AMS counts the atoms of 14C and 12C in a given sample, determining the 14C/12C ratio directly. The sample, often in the form of graphite, is made to emit C− ions (carbon atoms with a single negative

charge), which are injected into an accelerator. The ions are accelerated and passed through a stripper, which removes several electrons so that the ions emerge with a positive charge. The C3+ ions are then passed through a magnet that curves their path; the heavier ions are curved less than the lighter ones, so the different isotopes emerge as separate streams of ions. A particle detector then records the number of ions detected in the 14C stream, but since the

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volume of 12C (and 13C, needed for calibration of the instrument) is too great for individual ion detection, counts are determined by measuring the electric current created in a Faraday cup. Farraday cups are located where the isotope labels are placed in Figure 1.

When an AMS facility produces results from a set of samples, they calculate the time since the object died based on the half life of 14C. This age is called the “Lab Age” and is reported in “radiocabon years before present.” “Present” is defined as 1950 A.D. (Stuiver and Polach, 1977). The lab age is also presented as a normaly distributed data set with 1 σ and 2 σ uncertainty ranges.

Figure 1. Simplified schematic layout of an accelerator mass spectrometer used for counting carbon isotopes for carbon dating. Aitken (1990)

Because the rate of incoming nuclides has varied through time, we cannot simply apply the half-life to the measured quantity of 14C isotopes to determine the time since that object died. Radiocarbon geochronologists have constructed an empirical calibration curve based upon comparisons between tree ring radiocarbon ages and the count of years back based upon these tree rings (Fairbanks, 2005). The dendrochronologic based calibration curve extends to about 13,000 years before present (1950). Researchers have extended the calibration curve further back using 14C ages paired with high precision Th/U age determinations, back to ~50 ka (Fairbanks, 2005).

There are a number of radiocarbon calibration software applications that one may use to convert a “Lab Age” to a “Calendar Age.” These include Calib, OxCal, and Calibrate (Bronk Ramsey, 1995). There are others. These software applications have been developed to also include additional information to help model the age results (Bronk Ramsey, 2008). Some of the information that we can use in these depositional models includes: (1) the stratigraphic depth of the samples (2) the superposition of the samples, (3) sedimentation rates, (4) ages from other radiometric techniques (e.g. optically stimulated luminescence, Argon-Argon, etc.), and other information.

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Figure 2. Sediment cores 01HB01 and 01HB02. Marsh deposits (dark gray) are overlain by muds (light gray). Sample locations are numbered, but not every sample location has a radiocarbon result.

Part A. OxCal CalibrationLog on to OxCal and calibrate some ages. Enter the results in Table 1 below. The samples that we will calibrate are the ones that have lab ages, but no calendar ages. e.g. >>>>>>

https://c14.arch.ox.ac.uk/oxcal/OxCal.html

Part B. Sedimentation Rate CalculationsWe will now calculate the sedimentation rates for each samples that have a direct radiocarbon age estimate. Use the sample depth as a proxy for the amount of sediment overlying each radiocarbon age, along with that radiocarbon age, to calculate a sedimentation rate at those depths. Then, calculate the mean sedimentation rate by using the sedimentation rate calculated at each radiocarbon age. Fill in the answers in the table below.

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https://c14.arch.ox.ac.uk/oxcal/OxCal.html


Part C. Calculated Age EstimatesWe could use a statistical age model to perform this task. If people know how to do this, feel free to attempt this. Otherwise, we will simply use the mean sedimentation rate and the sample depths to calculate an age estimate for some of the deposits interpreted to be marsh soils buried during earthquakes.

Part D. Correlation Finally, we would like to correlate the buried marsh deposits between each core. First, write the radiocarbon ages next to each sample number on the core diagram. Next, draw correlation tie-lines between the tops of the buried marsh deposits that you interpret to correlate with each other, based upon the radiocarbon ages. Label the tie-lines with buried horizon numbers, increasing sequentially, beginning with BH-1 for the uppermost buried marsh deposit. Enter the total number of buried marsh deposits here: ____________

Table 1. Radiocarbon age determination results for cores 01HB01 and 01HB02.

Core 01BR01

Sample Number

Depth

(cm)Lab Age

2 σ Error

Calendar Age

95.4%

ErrorSedimentation Rate (cm/yr)

Calculated Age

1 20 220 40 210 220 2 50 880 40 820 100 3 120 4 150 5 180 1570 40 6 220 7 270 2770 40

Mean Rate:

Core 01BR02

Sample Number

Depth

(cm)Lab Age

2 σ Error

Calendar Age

95.4%

Error Sedimentation Rate (cm/yr)

Calculated Age

1 10 2 35 3 40 890 40 830 100 4 80 1020 40 930 140 5 120 6 170 1920 40 7 200 2200 40

Mean Rate:References:

Aitken, M.J. 1990. Science-based Dating in Archaeology; London: Longman; ISBN 0-582-49309-9, 296 pp.

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Bronk Ramsey, C., 1995, Radiocarbon calibration and analysis of stratigraphy: The OxCal program: Radiocarbon v. 37, no. 2, p. 425-430.

Bronk Ramsey, C., 2008. Deposition models for chronological records: Quaternary Science Reviews, v. 27, no. 1-2, p. 42-60

Bronk Ramsey, C., 2009. Bayesian Analysis of Radiocarbon Dates: Radiocarbon, v. 51, no. 1, p. 337-360 Fairbanks, R.G., et al., 2005. Radiocarbon calibration curve spanning 0 to 50,000 years BP based on paired 230Th/

234U/ 238U and 14C dates on pristine corals in Quaternary Science Reviews, v. 24, p. 1781-1796. Stuiver, M., and Polach, H. A., 1977. Discussion: Reporting of 14C data: Radiocarbon, v. vol. 19,

II. Potassium-ArgonThe Columbia River Flood Basalts (CRB) geologic province is a region of eastern Washington, eastern Oregon, the extreme northwest Nevada, and western Idaho where continental flood basalts erupted from fissure eruptions that eventually flowed westward toward the ocean via the ancient Columbia River Valley. The region through which they flowed is now called the Columbia River Gorge. These eruptions span from ~17 through ~5.5 million years.

There is a new brewery interested in developing a parcel that has access to a good supply of water. Interflow zones (top and bottom of CRB flows) and fault zones can form either barriers or pathways to subsurface water flow (read about hydrogeology). Your client needs to know the location of these basalts in order to better decide which land to purchase.

Your Geologic consulting company has been hired to do some drilling in search of a particular member of the CRB. Due to the local tectonics and faulting, the locations of different CRB members are poorly constrained in the region. You are tasked to determine which parcel has access to the Basalt of Lolo, part of the Priest Rapids member of the Wanapum Basalt. The drilling contractor has collected subsurface samples for you to analyze. Your coworker has already submitted the samples to the mass spectrometry lab and the results have been delivered to you electronically.

First we will review your knowledge of log scales and exponential functions. Then we will use the mass spectrometry results to determine the age of each sample. Finally, we will use these age estimates to determine which CRB member is accessed from each parcel. You will submit a report to your client listing the parcel(s) they should purchase.

Part A. Log Scale and Exponential FunctionsExponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent (or power) n. are ____. For example 102 = 10 X 10 = 100 and 103 = 10 X 10 X 10 = 1,000. Solve the following:

101 = _________ 102 = _________ 103 = _________ 104 = _________

105 = _________ 106 = _________ 107 = _________ 108 = _________

Plot on a Normal-Normal scaled grid sheet:

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- 10,000,000

20,000,000

30,000,000

40,000,000

50,000,000

60,000,000

70,000,000

80,000,000

90,000,000

100,000,000

- 10,000,000 20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 70,000,000 80,000,000 90,000,000

100,000,000 Chart Title

Plot of a Log-Log scaled grid sheet:

10

100

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000

10

100

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000 Chart Title

What is the benefit to plotting on a Log-Log scaled grid?

Exponents can be negative. In this case, they are placed in the denominator (the bottom of a fraction. For example 10-2 = 1 / 102 = 1 / 100 = 0.01 and 10-3 = 1 / 103 = 1 / 1000 = 0.001. Solve the following:

10-1 = _________ 10-2 = _________ 10-3 = _________ 10-4 = _________

10-5 = _________ 10-6 = _________ 10-7 = _________ 10-8 = _________

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The logarithm (Log) of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1,000 to base 10 is 3, because 10 to the power 3 is 1000. This is written like this: Log10100 = 2. Solve the following:

Log101,000 = _________ Log1010,000 = _________ Log10100,000 = _________

Log101,000,000 = _________ Log1010,000,000 = _________ Log10100,000,000 = _________

A special number used in science is “e.” e is an irrational and transcendental constant approximately equal to 2.718 281 828. Natural Logarithms use e as a base: ln = Loge. Calculators and computer programs know how to solve calculations of natural logs.

Part B. Radioactive DecayUse the Data in the table at the right to fill the first three rows in the table below. Then follow the instructions for rows 4 – 6.

Row 4—determine the fraction of parent isotope remaining at time (in half-lives) =x, where x=0, 1, 2, 3, 4, 5, or 6 by placing the amount of the parent isotope (Row 2) at time=x in the numerator, and the sum of isotopes (Row 3) at time=x, which is equivalent to the initial abundance of the parent isotope, in the denominator. Simplify your fractions. Show your work.

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Row 5—calculate the percentage of the parent isotope remaining at time (in half-lives) = x, where x = 0, 1, 2, 3, 4, 5, or 6 by multiplying the value in Row 4 at time = x by 100 or by converting the fraction to a decimal and multiplying by 100.

Row 6—determine the daughter-to-parent ratio at time (in half-lives) = x, where x = 0, 1, 2, 3, 4, 5, or 6 by dividing Row 1 by Row 2 for time = x.

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Plot the information in Row 1 on the graph below to show the change in the abundance of the daughter isotope over time.

Plot the information in Row 6 on the graph below to show the change in the daughter-to- parent ratio over time.

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Compare the graph of daughter isotope abundance in Problem 2 with the graph of daughter-to-parent ratio in Problem 3. Describe the shape of the curves and their trajectories. If both graphs contain information about the daughter isotope, then why do they behave so differently?

The initial abundance of the parent isotope at the formation of our sample was 16 parts per million (ppm). If modern mass spectrometers are capable of accurately measuring isotope abundance down to a level of 10 parts per billion (ppb), after how many half-lives will it no longer be possible to calculate an accurate age for the sample? [Hint: At time t=6, the remaining parent isotope equals ¼ ppm. There are 1000 ppb in 1 ppm. Calculate the amount of the parent isotope remaining in ppb for time t=x, where x=6, 7, 8, and so on until the quantity remaining is less than 10 ppb.] Show your work.

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Part C. Columbia River BasaltHow old are they?Using radioactive decay to determine the age of materials requires several geologically reasonable assumptions to be made. (1) The half-life has not changed through time. This is generally accepted. For example, tree rings have been counted back over 11,000 years to calibrate the radiocarbon curve. (2) The initial concentration of the parent isotope is known. This is also determinable for the various isotopes. (3) There was a closure time, when the radioactive clock began. There cannot be any contamination of “new” material to the system after this time (i.e. it is a “closed” system). This assumption is sometimes difficult to test and analyses may be cross checked with analyses with samples from different locations. (4) The sample was not contaminated and the measurement was taken with high precision.

Potassium–Argon dating, abbreviated K–Ar dating, is a radiometric dating method used in geochronology and archaeology. It is based on measurement of the product of the radioactive decay of an isotope of potassium (K) into argon (Ar). Potassium is a common element found in many materials, such as micas, clay minerals, tephra, and evaporites. In these materials, the decay product 40Ar is able to escape the liquid (molten) rock, but starts to accumulate when the rock solidifies (recrystallizes). Time since recrystallization is calculated by measuring the ratio of the amount of 40Ar accumulated to the amount of 40K remaining. The long half-life of 40K allows the method to be used to calculate the absolute age of samples older than a few thousand years.

To calculate the age of rocks in the 40K-40Ar system scientists use the following formula:

t = (1/λ) ln [(40Ar/40K) (correction factor) (λ/λe) + 1]

Where t is the time since the radioactive clock started, λ is the decay constant of 40K-40Ca-40Ar system (5.543x10-10/yr and λe is the decay constant for the 40K-40Ar system (0.581x10-

10/yr). And ln is the natural log. The ratio of 40Ar/40K must be adjusted for the difference in atomic weight. The correction factor is 0.97838 (adjustment to handle the difference of masses for 40Ar/40K or: 39.0983/39.9623).

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Calculate the ages for each of the seven samples. Show your work. Enter these ages in the table on the right. List the name of the Basalt that you interpret to be found in each parcel, based on your age determination and the table provided at the end of this packet. (From Reidel et al. (1989b) and Tolan et al. (1989).)

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Which parcel will work?Write a paragraph explaining your age determinations. List the age determination you made for the Basalt of Lolo, part of the Priest Rapids member of the Wanapum Basalt. Finally list the parcel number that you recommend that they purchase for their development.

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Stratigraphic nomenclature of the CRBG. From Reidel et al. (1989) and Tolan et al. (1989).

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III. Rubidium and Strontium

1. Six samples of granodiorite from a pluton in British Columbia, Canada, have strontium and rubidium isotopic compositions in the table at the right.

a. Find the age of the intrusionb. Find the initial 87Sr/86Sr ratio of the magma at

the time of the intrusion.c. Assuming an 87Sr/86Sr ratio of 0.699 and an

87Rb/86Sr ratio of 0.1 for the undifferentiated Earth 4550 Ma ago, comment on the possibility that this batholith originated in the mantle.

2. Whole rock rubidium-strontium isochrons for two plutons are shown in the two plots at the right. Calculate the age of each pluton and comment on the source of magma. >>>>>>>>>>>>

3. The single plot to the left shows a rubidium-strontium isochron for some unmetamorphosed sediments and clay

minerals, namely Illite and chlorite, found in the sediment. Calculate an age from this isochron and comment on its meaning.

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earthjay science | Course Material and Educational …€¦ · Web viewRadiocarbon age control is a method of determining the time that something died. Living organisms absorb many