Geoscience Reference
In-Depth Information
expulsion, become that number of
4
He atoms. The only stable reference isotope is
3
He.
The growth equation of the
4
He
3
He isotope ratio is therefore:
/
4
He
3
He
4
He
3
He
8
238
U
3
He
1
e
−
λ
238
U
t
t
=
0
+
−
0
7
235
U
3
He
6
232
Th
3
He
1
e
−
λ
235
U
t
1
e
−
λ
232
Th
t
+
−
+
−
0
0
(4.36)
which can be rearranged as:
4
He
3
He
4
He
3
He
238
U
3
He
1
e
−λ
238
U
t
t
=
0
+
−
0
8
7
235
U
238
U
6
232
Th
238
U
e
−
λ
232
Th
t
e
−
λ
235
U
t
1
−
1
−
×
+
+
e
−
λ
238
U
t
e
−
λ
238
U
t
1
−
1
−
0
0
(4.37)
At a given point in time
235
U
238
U
0
is indistinguish-
able from the nearly invariant Th/U ratio. The last expression therefore shows that
4
He
238
U
0
is a constant, while
232
Th
/
/
3
He
essentially reflects the evolution of the ratio of the incompatible refractory isotope
238
Uto
the volatile stable isotope
3
He in the system. The isotope geochemistry of helium is an
incomparable tool for investigating the outgassing of the mantle and also to model water
circulation in aquifers. Note that, by force of habit, many geochemists continue to use the
inverse
3
He
/
4
He ratios standardized to the value for atmospheric helium (1.4
10
−
6
)
/
×
instead of the
4
He
3
He ratios.
/
Exercises
1. What is the proportion of radiogenic
40
Ar
∗
in the total
40
Ar of a sample with a
40
Ar/
36
Ar ratio of (1) 50 000 (2) 2000 (3) 300? If the total
40
Ar content is known
to within 1%, what do you expect for the precision on the concentration of radiogenic
40
Ar
∗
in each case? Assume that atmospheric argon has a
40
Ar/
36
Ar ratio of
296.
2. Calculate the age of a basalt containing 1.7 wt% K
2
O and 6.0 10
−
11
mol g
−
140
Ar.
Assume that the atomic proportion of
40
K in natural potassium is 0.0117 %.
3. Two samples are irradiated with fast neutrons in the same vial. The K-Ar age of one
of them (the monitor) is known. It is observed that some of the
39
Kofthesamplesis
transformed into
39
Ar. Using the monitor to assess the yield of the nuclear reaction,
devise a method to infer the K-Ar age of the unknown sample from the age of the
monitor and the
40
Ar
∗
/
39
Ar ratios of the sample and the monitor (
∗
≈
labels radiogenic
argon).
4. A famous Rb-Sr isochron work: the Baltimore gneiss (Wetherill
et al.
,
1968
). Draw
the whole-rock (WR)
87
Sr/
86
Sr vs.
87
Rb/
86
Sr and the biotite-whole-rock isochrons for
