Geology Reference
In-Depth Information
Table 10.1
Radiogenic isotope systems
Name
Reaction
Decay constant/y
-1
Half-life/y
Applications
†
K-Ar
λ
Ar
= 0.581 × 10
−10§
λ
Ca
= 4.962 × 10
−10§
Geochronology of K-bearing
minerals
40
K
→
40
Ar +
β
+
+
υ
40
K
→
40
Ca +
β
-
+
υ
1.250 × 10
9§
Geochronology, seawater evolution,
sediment correlation, magma
genesis
Rb-Sr
87
Rb
→
87
Sr +
β
-
+
υ
1.42 × 10
−11
4.88 × 10
10
Precambrian geochronology,
sediment provenance, crustal and
mantle evolution, stony meteorite
and lunar studies, magma genesis
Sm-Nd
147
Sm
→
143
Nd +
α
2+
6.54 × 10
−12
1.060 × 10
11
Geochronology, mantle evolution,
crustal growth models
Lu-Hf
176
Lu
→
176
Hf +
β
-
+
υ
1.94 × 10
-11
3.57 × 10
10
Geochronology including iron
meteorites, mantle and lithosphere
evolution
Re-Os
187
Re
→
187
Os +
β
-
+
υ
1.666 × 10
-11
4.16 × 10
10
U-Th-Pb
232
Th
→
208
Pb + 6
α
2+
+ 4
β
-
+ 4
υ
235
U
→
207
Pb + 7
α
2+
+ 4
β
-
+ 4
υ
238
U
→
206
Pb + 8
α
2+
+ 6
β
-
+ 6
υ
*
4.9475 × 10
-11
9.8485 × 10
-10
1.55125 × 10
-10
14.010 × 10
9
0.7038 × 10
9
4.468 × 10
9
Geochronology, crustal evolution,
meteorite studies, magma genesis
†
After Henderson and Henderson (2009).
§
The combined rate constant
λ
is the sum of the two individual rate constants = 5.543 × 10
-10
yr
-1
. The concept of half-life is applicable only
to the combined decay of
40
K.
* See Figure 3.3.1 for the full decay scheme.
potassium has therefore decreased through the 4.55 Ga
course of Earth history. Today
40
K makes up only
0.012% of present-day potassium (Figure 10.2).
40
K
decays in two alternative ways (Table 10.1; Figure 10.1.1),
one route leading to the calcium isotope
40
Ca, accounting
for 89% of decaying
40
K nuclei, and the other to
40
Ar,
an isotope of the
inert gas
argon (the remaining 11% of
decaying
40
K nuclei). The accumulation of
40
Ar in a crystal
of a K-bearing mineral from the decay of
40
K provides the
basis for the K-Ar dating technique.
From the moment that potassium is incorporated
into a newly formed mineral (Figure 10.3a), the pro-
portion of
40
K present begins to decline (Figure 10.3e,f).
Argon - a gas - is not incorporated during the initial
crystallization of a mineral (Figure 10.3a), but
40
Ar will
however form
in situ
in a K-rich crystal (Figure 10.3b,c,e,f)
as the product of
40
K decay. If none of it escapes, the
40
Ar/
40
K ratio (how much
40
Ar is present relative to
40
K) provides a measure of the time that has elapsed
since the mineral crystallized (Equation 10.1):
39
K 93.1%
41
K 6.88%
40
K 0.012%
Figure 10.2
Pie chart showing the isotopic composition
of potassium.
where
t
is the time in years since the mineral crystal-
lized (or - more accurately - cooled below the
closure
temperature
for Ar diffusion - see Chapter 3);
λ
Ar
is the
decay constant for the decay of
40
K to
40
Ar (y
−1
);
λ
is the
overall decay constant for both modes of
40
K decay (y
−1
,
Table 10.1); and
40
Ar/
40
K is the measured present-day
daughter/parent abundance ratio: the
40
Ar amount
in this ratio is determined by mass spectrometry
(Box 10.3), whereas the amount of
40
K is calculated
from the K-content of the mineral sample.
1
λ
λ
40
Ar
K
(10.1)
t
=
ln
1
+
λ
40
Ar
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