EAS 302
Radioactive Decay, Isochrons and Geologic Time
Lab 2
Due Wednesday, February 8, 2006
Reading for this Lab: Stanley, Chapter 6, pp 164-169. Optional: White,
Geochemistry, Chapter 8
I. Radioactive Decay Experiment
I.1 Introduction
The purpose of this week’s lab is to understand how (absolute) geologic time is
determined. The age of geologic events is (usually) determined by radiometric
dating. Radiometric dating makes takes advantage of (1) the constant decay rate of
naturally occurring radioactive nuclides and (2) this radioactive decay produces a
new (daughter) nuclide. Simply put, by measuring the amount of the radioactive
parent and the amount of radiogenic daughter it has produced, the time elapsed can
be calculated since the rate of decay is constant. Let’s begin by considering the
mathematics of decay.
The basic equation of radioactive decay is:
dN = – !N
(1)
dt
where N is the number of radioactive atoms and l is the decay constant, which is
different for each radioactive nuclide. dN/dt is the change in the number of
radioactive atoms present per unit time or the rate of decay, also called the activity.
Activity is often measured in disintegrations per second or per minute.
Equation 1 can be integrated to yield:
N = e–! t
or
N = N0 e–! t
(2)
N0
where N0 is the number of nuclides present at the initial time (t = 0).
A radioactive isotope decays to produce a radiogenic daughter. The number of
daughters, D, produced over time t is just D = N0 - N. If D0 is the number of
daughters originally present (at t = 0), then equation 2 may be written as:
D = D0 + N(e!t – 1)
(3)
It is generally more convenient to work with a ratio rather than an absolute number
of atoms. So typically we measure the ratio of a radiogenic isotope, such as 87Sr, to
a non-radiogenic one, such as 86Sr. Taking the specific case of the decay of 87Rb to
87
Sr, we can write equation 3 as:
87
Sr = 87Sr + 87Rb e! t – 1
(4)
86
86
86
Sr
Sr 0
Sr
This is the form of the equation we generally use in calculating geologic ages.
I.2 “Virtual” Radioactive Decay Experiment
Image that we have created 2 radioactive nuclides by placing samples of
aluminum and copper in a nuclear reactor. Some of the 27Al and 65Cu atoms
captured neutrons to become 28Al and 66Cu. These nuclear configurations are not
stable, however, and they decay by b- decay to 28Si and 66Zn. They will also give off
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EAS 302
Radioactive Decay, Isochrons and Geologic Time
Lab 2
gamma radiation with energies of 1.779 Mev and 1.092 Mev (Mev is millions of
electron volts). We will use the gamma rays emitted to detect the decay.
A series of measurements of the activity (the number of decays per minute) of
each radioisotope over a 15 minute time period. The results are listed in the table
below.
(a) Make a plot of activity as a function of time.
#
Time
Activity Al
Activity Cu
1
1
388
2186
2
2
284
1910
3
3
209
1669
4
4
153
1455
5
5
113
1272
6
6
84
1111
7
7
60
972
8
8
45
848
9
9
32
740
10
10
22
645
11
11
18
566
12
12
12
493
13
13
9
431
14
14
7
376
15
15
5
329
(b) Using the data you obtained, calculate the decay constant of each isotope.
(Hint: linearized equation 2).
II. Geologic Time: Calculating Isochrons
The table below gives 87Sr/86Sr and 87Rb/86Rb ratios measured on minerals in the
meteorite Bholghati.
III.1 Isochrons
Plot the data on an isochron diagram (try using Excel or some other plotting
package). Do the data form an isochron?
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EAS 302
Radioactive Decay, Isochrons and Geologic Time
Lab 2
III.2 Calculating geologic ages
Use linear regression to calculate the slope and intercept. From the slope,
calculate the age and initial 87Sr/86Sr of this meteorite (the decay constant of 87Rb is
1.42 x 10-11y-1). Note: slope and intercept functions are available on many scientific
calculators. Alternatively, you may use the linear regression functions built into
Microsoft Excel™. The functions are "SLOPE(Ydata,Xdata)" and
"INTERCEPT(Ydata,Xdata). Or use another statistical or mathematical computer
program. If none of these are available to you, you may calculate slope and
intercept using the functions given in Appendix III of White Geochemistry.
Rb-Sr data from Bholghati
87
87
Rb/86Sr
Sr/86Sr
0.1751
0.710524
0.00373
0.699265
0.02166
0.700352
0.02082
0.700289
0.01015
0.69966
0.01391
0.699853
0.01545
0.699879
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