Geoscience Reference
In-Depth Information
argon from spots within individual minerals. At each heating step, the
40
Ar
39
Ar
ratio of the gas given off is measured in a mass spectrometer. Laser techniques
have the advantage that, since individual minerals (or parts of minerals) can be
dated, minerals of differing ages in a sample can be distinguished. Argon-39 is
an unstable isotope and decays back to potassium-39, but its half-life of 269 yr
is long enough (compared with the time taken to make the analysis) for it to be
treated as though it were stable.
The amount of
39
Ar present in the sample after it has been irradiated is pro-
portional to the amount of
/
39
K present before it was irradiated in the nuclear
reactor:
[
39
Ar]
now
=
c
[
39
K]
now
(6.44)
where
c
is the constant of proportionality (a function of the length of time for
which the sample was irradiated, the neutron energies and the capture cross section
for the reaction).
The number of radiogenic
40
Ar atoms present in the sample is given by
Eq. (6.40). Therefore, by combining Eqs. (6.44) and (6.40), we can write the
40
Ar
39
Ar ratio as
40
Ar
39
Ar
/
40
K
39
K
e
(
λ
A
+
λ
C
)
t
−
1
1
c
λ
A
λ
A
+
λ
C
now
=
now
e
(
λ
A
+
λ
C
)
t
−
1
=
(6.45)
J
where
c
39
K
40
K
λ
A
+
λ
C
λ
A
If a standard sample of known age
t
s
is irradiated at the same time as the sample
to be studied, the term
J
can be determined. Measurement of the
40
Ar
J
=
now
39
Ar ratio
/
for this standard sample gives
40
Ar
39
Ar
s
now
=
e
(
λ
A
+
λ
C
)
t
s
−
1
(6.46)
J
where the superscript s refers to measurements on the standard. Rearranging
Eq. (6.46)gives
−
1
39
Ar
40
Ar
s
e
(
λ
A
+
λ
C
)
t
s
J
=
(6.47)
now
On substituting this value for
J
back into Eq. (6.45), we obtain
40
Ar
39
Ar
40
Ar
39
Ar
s
e
(
λ
A
+
λ
C
)
t
−
1
now
=
(6.48)
e
(
λ
A
+
λ
C
)
t
s
−
1
now
An age
t
can now be calculated from this equation. Corrections for the presence
of atmospheric
40
Ar can be made to Eq. (6.48).
As already mentioned, the isotope ratios are measured at each step, so an age
can be calculated for every temperature or power. If the sample has been closed
