GEOL 1404 HISTORICAL GEOLOGY EXTRA CREDIT (12 pts) RADIOMETRIC AGE DATINGHAND IN WORKSHEETS AND GRAPHS ONLY!!You are NOT to work together on this… DUE: This Exercise is modified from Chapter 8 – Rock Units and Time-Rock Units in Levin & Smith’s Laboratory Studies in Earth History. See “Absolute Age Determination” for diagrams of decay curves and isochron illustrations. Absolute dating by the use of radioactive decay provides a natural “clock” that starts when certain types of rocks are formed. Radioactive decay is the spontaneous nuclear disintegration of isotopes of certain chemical elements into their stable daughter isotopes. As disintegration occurs, energy is released and can be detected by a Geiger counter or similar device. THE DECAY CONSTANT The rate of for isotopes is stated in terms of half-life: the amount of time it takes for a given amount of a radioactive parent isotope to be converted to its non-radioactive daughter. By comparing the amount of a radioactive parent isotope in a particular rock with its daughter product, the geologist can determine how much time has elapsed since the rock formed. The half-life gives an impression of the rate of change of a parent into its daughter, but to utilize the decay characteristics in a calculation of age, the decay rate () must be determined. (1) THE DECAY EQUATION Although the decay rate is unique for every parent-daughter pair, every radioactive decay follows the same decay curve known as the exponential decay curve. It is expressed by the following equation: Where: t = number of years that have elapsed P = number of parent atoms measured in the rock today P0 = number of parent atoms at time t (when the rock formed) exp = natural log of e (don’t worry about this for now) = decay constant for the parent atom The problem with this approach is that it is not possible to determine P0 without first knowing t. But, we can determine the number of daughter atoms present today. And if we assume that every daughter atom in the rock was created by the decay of a parent atom then the sum of the current number of parent atoms and daughter atoms will represent the number of parent atoms at time t, or P0 = P + D. The equation below reflects this relationship: Where: D = number of daughter atoms measured today P = number of parent atoms measured today But we have to other problems. First, we cannot assume that every daughter in the rock was created by the decay of a parent in the rock. It is very possible that some daughter isotopes were incorporated in the rock during formation and were not formed by decay after the rock formed. Second, it is very difficult to measure the actual number of daughter (and parent) atoms directly. It is much easier to measure the ratio of the parent isotope to an isotope of the daughter element but one NOT created through radioactive decay of the parent. We can address these uncertainties by deriving a more complicated equation: .

1. GEOL 1404 HISTORICAL GEOLOGY EXTRA CREDIT (12
pts) RADIOMETRIC AGE DATINGHAND IN WORKSHEETS
AND GRAPHS ONLY!!You are NOT to work together on this…
DUE:
This Exercise is modified from Chapter 8 – Rock Units and
Time-Rock Units in Levin & Smith’s Laboratory Studies in
Earth History. See “Absolute Age Determination” for diagrams
of decay curves and isochron illustrations.
Absolute dating by the use of radioactive decay provides a
natural “clock” that starts when certain types of rocks are
formed. Radioactive decay is the spontaneous nuclear
disintegration of isotopes of certain chemical elements into
their stable daughter isotopes. As disintegration occurs, energy
is released and can be detected by a Geiger counter or similar
device.
THE DECAY CONSTANT
The rate of for isotopes is stated in terms of half-life: the
amount of time it takes for a given amount of a radioactive
parent isotope to be converted to its non-radioactive daughter.
By comparing the amount of a radioactive parent isotope in a
particular rock with its daughter product, the geologist can
determine how much time has elapsed since the rock formed.
The half-life gives an impression of the rate of change of a
parent into its daughter, but to utilize the decay characteristics
in a calculation of age, the decay rate () must be determined.
(1)

2. THE DECAY EQUATION
Although the decay rate is unique for every parent-daughter
pair, every radioactive decay follows the same decay curve
known as the exponential decay curve. It is expressed by the
following equation:
Where:
t = number of years that have elapsed
P = number of parent atoms measured in the rock today
P0 = number of parent atoms at time t (when the rock formed)
exp = natural log of e (don’t worry about this for now)
= decay constant for the parent atom
The problem with this approach is that it is not possible to
determine P0 without first knowing t. But, we can determine
the number of daughter atoms present today. And if we assume
that every daughter atom in the rock was created by the decay
of a parent atom then the sum of the current number of parent
atoms and daughter atoms will represent the number of parent
atoms at time t, or P0 = P + D. The equation below reflects
this relationship:
Where:
D = number of daughter atoms measured today
P = number of parent atoms measured today
But we have to other problems. First, we cannot assume that
every daughter in the rock was created by the decay of a parent
in the rock. It is very possible that some daughter isotopes
were incorporated in the rock during formation and were not

3. formed by decay after the rock formed. Second, it is very
difficult to measure the actual number of daughter (and parent)
atoms directly. It is much easier to measure the ratio of the
parent isotope to an isotope of the daughter element but one
NOT created through radioactive decay of the parent.
We can address these uncertainties by deriving a more
complicated equation:
(2)
Where:
K = isotope of the daughter element that is not created by
radioactive decay
Although this equation looks ugly, it is actually in the slope-
intercept format of y = mx +b. In this case:
· y = D/K (Daughter ratio measured by analyzing the rock)
· x = P/K (Parent ratio measured by analyzing the rock)
· m= the slope of a line when x is plotted vs. y; in the equation,
it is (expλt-1)
· b = the y-intercept when x = 0 (in this equation, it is D0/K)
THE ISOCHRON
To determine the radiometric age of a rock, multiple samples
would be collected and the appropriate ratios of parent and
daughter would be determined. These ratios would then be
plotted versus each other. This will produce a line known as an
isochron. The slope of the isochron line (expλt-1) reflects the
age of the rock; the steeper the isochron, the older the rock.
Also, the y-intercept of the isochron will provide the original
ratio of daughter isotope at time = 0 (D0/K). Plotting the data

4. from multiple samples provides another piece of information. If
when plotted, the parent and daughter ratios from the rock do
not form a straight line, then it can be assumed that some parent
or daughter escaped since the time the rock was formed.
Therefore, it is important to plot the data to verify that the
samples appear to be unaltered.
We can plot the data on a graph, but we want to figure out the
age of the rock (t). Once the slope of the isochron is
determined, we can use the slope to calculate the age of the rock
using (expλt-1). We can solve this expression for t:
(3)
So by determining the slope of the isochron and the decay
constant of the parent isotope, we can determine the age of the
rock. The natural log function is represented on a scientific
calculator as “ln”.
EXERCISE – RADIOMETRICALLY AGE DATING

5. You have been studying the relationship between two rock units
in the Piedmont physiographic province of North Carolina.
The stratigraphic relationship between the intrusive igneous
complex known as the Salisbury Pluton and the surrounding
Whitewater Greywacke is poorly exposed, but initial field data
suggests that the pluton is older than the greywacke, suggesting
that the contact between the units is nonconformity. However,
it is possible that the pluton intruded into the greywacke,
making their relationship an intrusive contact. The goal of this
exercise is to determine the radiometric ages of each unit, and
thus confirming the stratigraphic relationship between the units.
Seven samples of the clay-rich graywacke and 13 samples from
the pluton have been collected for mass spectrometer analysis to
determine the ratios of parent 87Rb/86Sr and daughter
87Sr/86Sr for the purposes of determining the absolute age of
the units. The results of the analyses are in the table on the
worksheet.
The range of the ratios simply reflects that when the rocks
formed, different minerals in the rock incorporated different
amounts of rubidium. Samples with higher 87Rb/86Sr ratios
suggest that the minerals in that sample had a greater amount of
rubidium in them at the time of their formation. For the
greywacke, it is believed that during diagenesis, the radiometric
“clock” was re-set, meaning that the clay minerals “locked” in
an amount of rubidium that would allow the rock to be dated
radiometrically.
PART I: SALSBURY PLUTON
TASK 1– CALCULATE THE 87Rb DECAY CONSTANT
The half-life of 87Rb is 4.88 x 1010 years or 48.8 billion years.
From this value and using Equation 1, calculate the decay
constant λ and record the value in the table on the worksheet.

6. TASK 2– PLOT THE WHITEWATER GREYWACKE DATA
On the Whitewater Graywacke Graph, plot the 87Rb/86Sr vs.
87Sr/86Sr. The trend of the 7 points should approximate a
straight line.
TASK 3– DRAW THE ISOCHRON FOR THE WHITEWATER
GRAYWACKE DATA
Draw a single straight line through the data points that follows
the trend of the data – this is the isochron for the data. This
should be a single line that crosses the entire graph intersecting
the y-axis. Do NOT “connect the dots.”
TASK 4 – DETERMINE THE SLOPE OF THE ISOCHRON
Remember, the slope of the isochron reflects the age of the
rock. Slope can be determined by:
To determine your slope you must select x and y values from
the isochron. Pick two widely-separated points on your
isochronline to determine the age; it is best to find to places
where your isochron crosses a grid line intersection – this
makes it easy to determine a value of x and y. DO NOT
SIMPLY CHOOSE 87Rb/86Sr and 87Sr/86Sr VALUES FROM
THE TABLE!!!! Label the two points used for determining the
slope of the isochron on the graph.
(a) Determine the slope of the isochron and record the value in
the table on the worksheet.
(b) Add 1 to the slope and then take the natural log of this sum
and record it in the worksheet. It should be recorded without
scientific notation to four (4) decimal places.

7. TASK 5 – CALCULATE THE AGE OF THE SALSBURY
PLUTON
Calculate the age of the Salsbury Pluton using your slope, the
decay constant of 87Rb and Equation 3. Record the value of
“ln(slope)” on the worksheet.
Record this age value in scientific notation to two decimal
places in the table on the worksheet. Please review the Math
Practice posted on Blackboard if you need to brush up on
scientific notation.
---------------------------------------------------------------------------
---------------------------------------------------------
PART II: WHITEWATER GRAYWACKE – A DIFFERENT
APPROACH…
Another option for calculating ages of rocks using parent-
daughter ratios is to re-arrange Equation 2 to solve for t:
Re-arranged to solve for t:
(5)
This equation allows for the age of each sample that was part of
the isochron to be determined. The average of these ages
would provide an overall age of the rock unit.
Equation (5) looks worse that it is. We know all the terms
except one, and that one is easily obtained.

8. ; the ratio of current amount of parent isotope to the amount
non-radiogenic daughter isotope
; the ratio of the current amount of radiogenic daughter to the
amount of non-radiogenic daughter
D0/K can be easily determined. This value represents the y-
intercept of the isochron line. Once this intercept is
determined, an age of each sample can be calculated.
Equation (5) includes a natural log of the following:
(6)
It is a good practice to figure out the value of the above
expression separately; then take the natural log of it by using
the “ln” function button on the calculator.
TASK 1: PLOT THE WHITEWATER GRAYWACKE DATA

9. Follow the same procedures as Task 2 in Part I.
TASK 2: DRAW THE ISOCHRON FOR THE WHITEWATER
DATA
Again, follow the same procedures as Task 3 in Part I.
TASK 3– DETERMINE THE ORIGINAL RATIO OF 87Sr/87Sr
AT THE TIME OF DIAGENESIS
Record the value of the isochron’s y-intercept in the appropriate
location on Table 2. This value should be recorded without
scientific notation to 3 decimal places. Remember, this y-
intercept represents D0/K, or the original amount of 87Sr at the
time of diagenesis of the graywacke.
TASK 4 – CALCULATE THE AGE OF EACH WHITEWATER
GRAYWACKE SAMPLE
Calculate the age of each sample in Table 1 using Equation (5).
It should be accomplished in steps to avoid errors.
(a) For each P/K and D/K pair in Table 2 on the worksheet
calculate the value of Equation 6 below. Record this value on
the worksheet. This is an intermediate step for calculating the
age in Task 4(b) below. The value should be in non-scientific
notation format to four (4) decimal places.
(6)
(b) Calculate the age and record your age in the last column in
the table on the worksheet.To do this, you will use Equation (5)
below. NOTE, the calculations and age determination for
Sample A-2 have already been done for you as an example.

10. (5)
i. Take the natural log (“ln” function on the scientific
calculator) of the 6 remaining values from 4(a).
ii. Then divide each of these by the decay constant (λ), which
was determined in Part I, Task 1 and is listed in Table 1.
iii. Record each of the 6 remaining ages in scientific notation to
two decimal places. Please review the Math Practice posted on
Blackboard if you need to brush up on scientific notation.
TASK 5 – CALCULATE THE AVERAGE AGE OF THE
WHITEWATER GRAYWACKE SAMPLES
Determine the average of the 7 ages from Task 4 and record the
value in Table 2. This is the age of the Graywacke.
GEOL 1404 EXTRA CREDIT NAME:
____________________________
RADIOMETRIC AGE DATING WORKSHEET
DUE:
PART I: SALSBURY PLUTON
87Rb half-life = 4.88 x 1010 yr
Task 1: 87Rb decay constant (λ)

11. Table 1 – Salsbury Pluton Spectrometer Results
Sample No.
87Rb/86Sr
87Sr/86Sr
R5945A
8.068
0.6562
R5946
1.199
0.5496
R5945
9.839
0.7034
R5945B
7.700
0.6587
R5948B
4.698
0.6143
R5949A
8.262
0.6607
R5943A
2.225
0.5659
R5939A
2.106
0.5672
R5942B
5.152
0.6110
R5947A
4.806
0.6120
R5948A
4.990

12. 0.6122
R5946A
6.080
0.6306
R5949B
6.912
0.6379
Task 4(a): isochron slope:
Task 4(b): ln (isochron slope+1):
Task 5: Age of rock
PART II: WHITEWATER GRAYWACKE
TABLE 2 – WHITEWATER GRAYWACKE MASS
SPECTROMETER RESULTS
TASK 3: Isochron y-intercept
Sample No.
87Rb/86Sr
87Sr/86Sr
TASK 4(a)

13. TASK 4(b)
Calculated age (yrs ago)
A-2
86.20
1.2569
1.0060
4.21 X 108 yr ago
C-2
7.22
0.7841
D-3
22.30
0.8758
F-3
50.20
1.0478
G-6
0.76
0.7467
I-1
1.28
0.7489
I-2

14. 3.40
0.7601
TASK 5 - Average Age =
QUESTIONS:
Determine the geologic Eon, Era and Period (if the rock is of
Paleozoic or younger) of the pluton.
Determine the geologic Eon, Era and Period (if the unit is of
Paleozoic age or younger) of the graywacke.
Based on the age relationship between the Whitewater
Greywacke and Salisbury Pluton, is the contact between them a
nonconformity or an intrusive contact? Explain/defend your
answer.
7
(

15. )
(
)
[
]
1
exp
-
=
t
P
D
l
(
)
(
)
[
]
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exp
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D
l
(
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t

16. exp
1
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;
)
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(
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×
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yrs
t
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1

17. ln(
1
2
1
2
x
x
y
y
slope
-
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(
)
(
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:
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Equation
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19. Sr
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87
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the
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of

20. ratio
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:
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22. ø
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T
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23. )
(
)
t
P
P
l
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=
exp
0
WHITEWATER GRAYWACKE
86.2 7.22 22.3 50.2 0.76 1.28 3.4 1.25685
0.78414000000000006 0.87580499999999994
1.047795 0.74665499999999996 0.74885999999999997
0.76009499999999997
87Rb/86Sr
87Sr/86Sr
SALSBURY PLUTON
changed rb/sr and sr/sr 8.0676000000000005
1.1988000000000001 9.8388000000000009
7.7004000000000001 4.6979999999999995
8.2620000000000005 2.2248000000000001
2.1059999999999999 5.1516000000000002
4.8060000000000009 4.9896000000000003 6.0804
6.9120000000000008 0.65617499999999995
0.54959999999999998 0.70342499999999997
0.658725 0.61432500000000001 0.66067500000000001

24. 0.56587499999999991 0.56722499999999998
0.61102499999999993 0.61199999999999999
0.61214999999999997 0.63060000000000005
0.63787499999999997
87Rb/86Sr
87Sr/86Sr