Geoscience Reference
In-Depth Information
Using Eq. (6.16)toeliminate
P
0
,wecan finally express the ratio of the numbers
of atoms of
40
Ar to
40
Kattime
t
in terms of the decay rates:
D
A
P
=
e
(
λ
A
+
λ
C
)
t
−
1
λ
A
λ
A
+
λ
C
(6.22)
The age of the sample
t
is therefore given by
λ
A
+
λ
C
log
e
1
λ
A
+
λ
C
λ
A
D
A
P
1
t
=
+
(6.23)
If the decay to
40
Ca were used, Eqs. (6.19)-(6.23)would have the same form
but with
D
C
and the rate of decay to calcium,
λ
C
, replacing
D
A
and the rate
λ
A
. The decay of
40
Kto
40
Ca is little used in geochronology
because calcium is so common that the
of decay to argon
40
Ca resulting from
40
K decays cannot
be accurately determined.
Other important factors
The choice and application of these radioactive dating methods to actual samples
require knowledge of a number of factors concerning both the methods and the
samples.
The choice of a particular dating method depends on the probable age of
the sample. Ideally, the decay scheme used should have a half-life of about the
same order of magnitude as the age of the sample. This ensures that the number
of daughter atoms is of the same magnitude as the number of parent atoms
(see Eq. (6.11)). If the half-life is very much greater or smaller than the age of
the sample, the ratio of daughter to parent atoms is either very small or very
large, which, in either case, may be difficult to measure accurately. Hence, in
this respect, the uranium-lead method appears to be the best radioactive dating
method for younger rocks. Very small quantities of the daughter atoms have to be
measured, and careful analysis is required in all isotope work. For recent samples,
particularly archaeological samples, short-half-life methods involving isotopes
such as carbon-14 are used.
Two other important factors affect the choice of dating method: the amounts of
parent and daughter elements present in the rock; and whether or not the sample
wasaclosed system. Clearly a sample that had never contained any rubidium
could not be a candidate for rubidium-strontium dating (rubidium is a trace
element). The advantage of potassium-argon dating is that it can be used on most
rocks because potassium is a widespread element. Table 6.3 gives rough estimates
of the concentrations of radioactive elements in average rocks.
In the formulation of Eqs. (6.1)-(6.23), we have assumed that there has been
no loss or gain of parent or daughter atoms except by radioactive decay. In other
words, we have assumed that our sample was a closed system. For most rocks
this is clearly a false assumption. For example, radioactively derived lead (termed
radiogenic
lead) is sometimes deposited together with uranium in cooling rocks
(both are transported in circulating hydrothermal water). The extra amount of
