Geoscience Reference
In-Depth Information
Using
204
Pb, the non-radiogenic isotope of lead, in the same way as for the
uranium-lead method and including an initial amount of
208
Pb, we can write
Eq. (6.38)as
208
Pb
204
Pb
208
Pb
204
Pb
232
Th
204
Pb
(e
λ
t
now
=
0
+
−
1)
(6.39)
now
The construction of an isochron therefore allows
t
and [
208
Pb
204
Pb]
0
to be calcu-
lated (Fig. 6.4(a)). Alternatively, with an estimate for the initial lead-isotope ratio,
Eq. (6.39)gives a value for
t
directly with one sample. Thorium-lead isochrons
can be more successful than uranium-lead isochrons because thorium and lead
tend to be less mobile and so less easily lost than uranium.
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6.6 Potassium-argon
Potassium has three naturally occurring isotopes,
39
K,
40
K and
41
K. Their relative
abundances are 93%, 0.012% and 6.7%, respectively. Equation (6.22)gives the
amount of
40
Ar produced by
40
K decay:
e
(
λ
A
+
λ
C
)
t
−
1
λ
A
λ
A
+
λ
C
[
40
Ar]
now
=
[
40
K]
now
(6.40)
Including an initial amount of
40
Ar means that the amount of
40
Ar measured now
at time t is
e
(
λ
A
+
λ
C
)
t
−
1
λ
A
λ
A
+
λ
C
[
40
Ar]
now
=
[
40
Ar]
0
+
[
40
K]
now
(6.41)
←−
Figure 6.4.
Lead-lead, thorium-lead and uranium-lead whole-rock isochrons and
the concordia plot for a granite. (a) Thorium-lead isochron. The slight scatter in the
data indicates that the rocks may have lost or gained variable amounts of thorium.
However, since the points are not very scattered, the actual quantity of thorium lost
or gained was small. (b) Uranium-lead isochron. These isotope ratios are very
scattered due to loss of uranium. Had no uranium been lost, the points would fall on
the 2790-Ma reference isochron. However, loss of uranium causes the data to plot to
the left of their position on the reference isochron, as indicated by the arrow. The
amount of uranium lost by each rock can be estimated by assuming that the
206
Pb
204
Pb
ratio can then be compared with the actual value: this gives the fraction of uranium
retained by each rock. (c) Lead-lead isochron. The points fall on a straight line with
slope 0.1911, which corresponds to an age of 2790 Ma. Plots (a)-(c) show some of
the problems which are encountered when using the uranium and thorium decay
schemes and some of the ways in which information can be obtained despite the
mobility of uranium and thorium. (d) A concordia plot. The losses of uranium mean
that the data plot above the concordia curve. The data points lie on a straight line
(the discordia) which passes through the origin and intersects the concordia at
2800 Ma. This is consistent with the lead-lead isochron age and with the uranium
loss having occurred as the result of recent weathering. (From Faure (1986), after
Rosholt
et al
.(1973).)
204
Pb ratio and the reference isochron are correct. The reference
238
U
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