Excelet

Radiometric Dating

A variety of long-lived radioactive isotopes can be used

to determine the age of geological materials.

Click on the tabs to navigate !!! time passes ----->

Place cursor in cell above!

Let's examine how this is done for the parent nuclide, P, decaying to the daughter nuclide, D!

, decaying to the daughter nuclide, D!

Parent Decay to Daughtert = 0.0 0 increase the time (click up arrow)

P D

number, N, of: 100 0 0.00

time line

0 100

0 0

half-life intervals

-50.0 0

-50.0 100

-50 0

-50 100

-50

-50

At time t = 0, only parent isotope is present.

This starts the clock! 0

x y y time time

3 4.5 4.5 -1 0 0 100

At time t = 0, P = Po = 100

D/P

Sinex 2010

P -----> D

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

time

N

add half-life intervals on graph

10.5 5 5 -1 1 10 90.48374

box 2 2 2 -1 2 20 81.87308

1 1 1.5 5 5 -1 3 30 74.08182

11 1 6.5 9.5 9.5 -1 4 40 67.032

11 11 4 6 6 -1 5 50 60.65307

1 11 3 8.5 8.5 -1 6 60 54.88116

1 1 2 8 8 -1 7 70 49.65853

8 2 2 -1 8 80 44.9329

7 3 3 -1 9 90 40.65697

9 2.5 2.5 -1 10 100 36.78794

10 2 2 -1 11 110 33.28711

7 6 6 -1 12 120 30.11942

9 4 4 -1 13 130 27.25318

10 10 10 -1 14 140 24.6597

3.5 8 8 -1 15 150 22.31302

4 10 10 -1 16 160 20.18965

7 6 6 -1 17 170 18.26835

8 9 9 -1 18 180 16.52989

7.5 4.5 4.5 -1 19 190 14.95686

9 10.5 10.5 -1 20 200 13.53353

5 5 5 -1 21 210 12.24564

9 7 7 -1 22 220 11.08032

5.5 2 2 -1 23 230 10.02588

2 10 10 -1 24 240 9.071795

6.5 8 8 -1 25 250 8.2085

9.5 8.5 8.5 -1 26

5.5 4.5 4.5 -1 27

1.67 1.4 1.4 -1 28

1.6 3.65 3.65 -1 29

6.76 10.69 10.69 -1 30

3.6 5.52 5.52 -1 31

6.03 9.95 9.95 -1 32

8.43 3.15 3.15 -1 33

4.71 6.34 6.34 -1 34

7.33 9.95 9.95 -1 35

6.03 3.86 3.86 -1 36

5.97 2.55 2.55 -1 37

6.13 9 9 -1 38

8.12 5 5 -1 39

5.94 7.6 7.6 -1 40

3.28 6.73 6.73 -1 41

7 8.78 8.78 -1 42

8.12 6.23 6.23 -1 43

2.46 3.22 3.22 -1 44

4.23 8.92 8.92 -1 45

4.48 1.66 1.66 -1 46

7.07 1.95 1.95 -1 47

10.23 6.73 6.73 -1 48

4.55 3.5 3.5 -1 49

8.37 1.52 1.52 -1 50

10.64 1.24 1.24 -1 51

8.12 8.28 8.28 -1 52

8.27 6.83 6.83 -1 53

8.12 3.75 3.75 -1 54

10.6 10.69 10.69 -1 55

8.34 9.77 9.77 -1 56

2.6 9.2 9.2 -1 57

10.45 2.87 2.87 -1 58

9.51 5.7 5.7 -1 59

6.8 7.04 7.04 -1 60

3.2 2.83 2.83 -1 61

9.73 4.5 4.5 -1 62

5.5 5.7 5.7 -1 63

10 3.82 3.82 -1 64

2.08 4.2 4.2 -1 65

7.83 5.63 5.63 -1 66

1.77 6.34 6.34 -1 67

3.82 2.34 2.34 -1 68

8 2.55 2.55 -1 69

6.57 2.83 2.83 -1 70

10.23 7.36 7.36 -1 71

10.4 8.64 8.64 -1 72

1.33 8.96 8.96 -1 73

7.67 10.37 10.37 -1 74

2.97 10.73 10.73 -1 75

1.52 7.4 7.4 -1 76

1.2 2.97 2.97 -1 77

2.6 7.12 7.12 -1 78

8.84 5.66 5.66 -1 79

9.22 1.4 1.4 -1 80

9.32 9.8 9.8 -1 81

2.75 2.48 2.48 -1 82

3.22 5.88 5.88 -1 83

7.77 7.5 7.5 -1 84

2.4 5.49 5.49 -1 85

6.03 1.31 1.31 -1 86

10 6.23 6.23 -1 87

10 3.4 3.4 -1 88

4.67 7.4 7.4 -1 89

6.8 4.11 4.11 -1 90

3.28 1.24 1.24 -1 91

5.05 9.49 9.49 -1 92

5.78 6.62 6.62 -1 93

5.18 2.76 2.76 -1 94

6.44 4.92 4.92 -1 95

5.5 10.37 10.37 -1 96

4 4.18 4.18 -1 97

5.5 3.47 3.47 -1 98

8.78 4.5 4.5 -1 99

increase the time (click up arrow)

0

100

0

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

time

N

9.516258

18.12692

25.91818

32.968

39.34693

45.11884

50.34147

55.0671

59.34303

63.21206

66.71289

69.88058

72.74682

75.3403

77.68698

79.81035

81.73165

83.47011

85.04314

86.46647

87.75436

88.91968

89.97412

90.9282

91.7915

Decay and the D/P ratio How does the D/P ratio vary over time? Decay reaction

9 k = 1.55E-10 4.47E+09 years 1

t P D

0.00E+00 1 0

1.00E+09 0.856386 0.143614

2.00E+09 0.733398 0.266602

3.00E+09 0.628072 0.371928 1.00E+09

4.00E+09 0.537872 0.462128

5.00E+09 0.460626 0.539374

6.00E+09 0.394474 0.605526 1.00E+09

7.00E+09 0.337822 0.662178

8.00E+09 0.289307 0.710693

9.00E+09 0.247758 0.752242

1.00E+10 0.212177 0.787823

1.10E+10 0.181705 0.818295

1.20E+10 0.15561 0.84439

1.30E+10 0.133262 0.866738

1.40E+10 0.114124 0.885876 daughter, D

1.50E+10 0.097734 0.902266

Setting the Clock decay mode

At t = 0, initial amount of parent,

age, t = 1.00E+09 10 adjust time to follow D/P ratio

What is the D/P at one half-life?

isotope half-life daughter decay mode

P ---> D

yr-1 t1/2 = select parent isotope

Po, is set and we assume Do = 0.

Sinex 2010

0E+00 1E+10 2E+100

0.2

0.4

0.6

0.8

1

1.2

age, t (years)

N/No

1 U - 238 4.47E+09 Pb-206 8a, 6b2 U - 235 7.07E+08 Pb-207 7a, 4b3 Th - 232 1.40E+10 Pb-208 6a, 4b Chapter 8 online

4 Rb - 87 4.80E+10 Sr-87 b http://www.geo.cornell.edu/geology/classes/Chapters/Chapter08.pdf

5 Sm - 147 1.06E+11 Nd-143 a6 K - 40 1.28E+09 Ar-40 EC

from: White, Geochemistry (2009)

P

0.856386

D

0.143614

D/P

0.167697

The

daughter, D

Pb-206

decay mode

8a, 6b

adjust time to follow D/P ratio

select parent isotope

http://www.geo.cornell.edu/geology/classes/Chapters/Chapter08.pdf

Using the D/P Ratio to Determine the Age How does the D/P ratio behave over time? select parent isotope

Parent Isotope

7 k = 9.802E-10 7.07E+08 years 2

t D/P

1.00E+07 0.00985 ###

2.00E+07 0.019797 ###

3.00E+07 0.029843 ###

4.00E+07 0.039987 ###

5.00E+07 0.050231 ###

6.00E+07 0.060576 ###

7.00E+07 0.071023 ###

8.00E+07 0.081572 ###

9.00E+07 0.092226 ###

1.00E+08 0.102985 ###

1.10E+08 0.113849 ###

1.20E+08 0.124821 ###

1.30E+08 0.135901 ###

1.40E+08 0.147089 ###

1.50E+08 0.158388 ###

The D/P can be measured

by mass spectrometry.

0 as assumed

What happens if the initial amount of daughter is not zero as assumed?

isotope half-life

yr-1 t1/2 =

increase D

Sinex 2010

0E+00 1E+08 2E+080

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

age, t (years)

D/P

use approximation

1 U - 238 4.47E+09

2 U - 235 7.07E+08

3 Th - 232 1.40E+10

4 Rb - 87 4.80E+10

5 Sm - 147 1.06E+11

6 K - 40 1.28E+09

select parent isotope

D/P

0.01

Age

1.02E+07

years

is not zero.

Age

1.02E+07

years

%Error

0.0

0

0

as assumed

Suppose Do

increase Do

U-Pb Dating of Zircons D/P plot for each pair

7

time

1.0E+07 1.6E-03 9.9E-03

2.0E+07 0.0031068 0.0198933 Age of sample

3.0E+07 0.0046638 0.0299878 4.6E+07

4.0E+07 0.0062233 0.0401823 766

5.0E+07 0.0077851 0.0504777

6.0E+07 0.0093494 0.060875 If line goes off data,

7.0E+07 0.0109162 0.0713751 adjust the time scale.

8.0E+07 0.0124853 0.0819792

9.0E+07 0.0140569 0.0926883

1.0E+08 0.0156309 0.1035034 7.1E-03

The lower plot shows 4.6E-02

one isotope pair plotted

against the other isotope 4.6E+07 0 0 0.007115

pair. This plot is 4.6E+07 0.007115 0.046047 0.007115

4.6E+07 0.046047 0.046047 0

4.6E+07 6.0E-02

a closed system with

no lead loss from the

zircons.

206Pb/238U 207Pb/235U

206Pb/238U

207Pb/235U

called the concordia

diagram. This is for

Sinex 2010

0.0E+00 2.0E+07 4.0E+07 6.0E+07 8.0E+07 1.0E+08 1.2E+080.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

time, years

Pb/U

0 0.02 0.04 0.06 0.08 0.1 0.120

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

207Pb/235U

206Pb/238U

Age of sample

If line goes off data,

adjust the time scale.

It just is not that simple!

Sinex 2010

Examining the Rb-Sr Isochron Consider a rock as shown here.

k = 1.444E-11 4.80E+10 years

0.000 0.61 0 1.5 0.61 How does the age

0.500 0.6382 0.0282 1.415407 0.689822

1.000 0.6664 0.0564 2.5 0.61 intercept line influence the isochron?

1.500 0.6946 0.0846 2.359012 0.743037 0 0.61

2.000 0.7228 0.1128 3.5 0.61 5 0.61

2.500 0.7510 0.1410 3.302616 0.796252

3.000 0.7792 0.1692 4.5 0.61

3.500 0.8074 0.1974 4.246221 0.849467

4.000 0.8356 0.2256

4.500 0.8638 0.2538 points at t = 0 point at later time

5.000 0.8920 0.2820 1.5 0.61 1.415407 0.689822

2.5 0.61 2.359012 0.743037

3.5 0.61 3.302616 0.796252

graph are various mineral 4.5 0.61 4.246221 0.849467

separates of the rock. The slope of this plot

is the D/P corrected

From a plot of D/S as slope = 0.056 intercept = 0.61 for any D from

a function of P/S: yields the age other sources.

Why ratio to a stable nuclide? The value of k is a constant for any P-D system.

answer

The idea for this is from: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/clkroc.html

yr-1 t1/2 = 87Rb -----> 87Sr + b-

87Rb/86Sr 87Sr/86Sr

and 87Rbo/86Sr

A, B, C, and D on the

yields the Do/S

A line where the slope only depends on time, t, is called an isochron.

Sinex 2010

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00

0.3

0.6

0.9

1.2

1.5

87Rb/86Sr

87Sr/86Sr

How does the age

influence the isochron?

age, t (yr)

3.80E+09

38

0.610

61

The slope of this plot

is the D/P corrected

for any D from

other sources.

Rb -----> 87Sr + b-

and 87Rbo/86Sr

87Sro/86Sr

Plotting an Isochron Here are a variety of radiogenic isotopes used for dating.

Parent Isotope

k = 1.444E-11 4.80E+10 years 4 select parent isotope

P/S D/S

0.0000 1.4 How does the age

0.1000 1.400434

0.2000 1.400868 the isochron?

0.3000 1.401302 intercept line

0.4000 1.401736 0 1.4

0.5000 1.40217 1 1.4

0.6000 1.402604

0.7000 1.403038

0.8000 1.403473

0.9000 1.403907

1.0000 1.404341

Beware the y-axis, D/S

rescales with isotope

selected and age!

From a plot of D/S as slope = 0.004 intercept = 1.40 <----- Watch these!!!

a function of P/S: yields the age

Try solving the two examples on the assess and assess II tabs!

isotope half-life

yr-1 t1/2 =

and Do/S influence

yields the Do/S

Sinex 2010

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.001.397

1.398

1.399

1.4

1.401

1.402

1.403

1.404

1.405

P/S

D/S

1 U - 238 4.47E+09

2 U - 235 7.07E+08

3 Th - 232 1.40E+10

4 Rb - 87 4.80E+10

5 Sm - 147 1.06E+11

6 K - 40 1.28E+09

select parent isotope

How does the age

the isochron?

age, t (yr)

3.00E+08

3

1.4

14

Beware the y-axis, D/S

rescales with isotope

selected and age!

and Do/S influence

Do/S

Metagabbro from Cana Brava complex in central BrazilTwo different whole rock samples and mineral separates

P/S D/S were analzyed.

The Task:

pyroxene 0.1819 0.51235

plagioclase 0.0763 0.51185

whole rock 0.1691 0.51232 2. Perform a linear regression on the data. Report the equation.

whole rock 0.1678 0.51227

plagioclase 0.0609 0.51172 3. Determine the age of the volcanic rocks. Show the calculations.

biotite 0.1773 0.51232

Data from: http://www.geo.cornell.edu/geology/classes/Geo656/ProblemSets/656_05PS03Solution.pdf

147Sm/ 144Nd 143Nd/ 144Nd

1. Plot an isochron for the 147Sm - 143Nd data.

4. Was the 143Ndo = 0? Explain why or why not.

Sinex 2010

Volcanic rocks from the Ritter Range in CaliforniaSeven samples were collected and analyzed.

P/S D/SThe Task:

1.600 0.7071

2.230 0.7078

3.050 0.7093 2. Perform a linear regression on the data. Report the equation.

3.170 0.70914

4.250 0.7106 3. Determine the age of the volcanic rocks. Show the calculations.

4.340 0.711

4.410 0.7113

Data from: http://serc.carleton.edu/files/NAGTWorkshops/petrology/teaching_examples/rb-sr_isochrons.xls

87Rb/86Sr 87Sr/86Sr

1. Plot an isochron for the 87Rb - 87Sr data.

4. Was the 87Sro = 0? Explain why or why not.

Sinex 2010