Geoscience Reference
In-Depth Information
of 5000-10,000 Bq as perfectly natural in origin. A granite cobblestone normally produces
a radioactivity of several thousand Bq.
In order to determine the age of a system using (4.2) from the measurement of the
number of parent atoms at the present time, we must also know P 0 . If we do, then we have
a chronometer based on the decay of a radioactive nuclide and the age will be given by:
1
λ
ln P 0
P
t
=
(4.3)
Dating using the 14 C decay gives a good example:
14 C 0
14 C
1
t
=
ln
(4.4)
λ
14 C
If we don't, a different solution is in order. For each parent atom, a daughter atom (or
radiogenic nuclide) is created, usually of a single element, whose number can be denoted
D . In a closed system and for a stable daughter nuclide D , the number of parent and
daughter atoms is constant. Therefore:
P e λ t
1
D
=
D 0 +
P 0
P
=
D 0 +
(4.5)
The term P (e λ t
1) is a measure of the accumulation of the radiogenic nuclide during
time t .Evenif D and P are measured, this equation is no more a timing device than the
previous one unless we know the number of daughter atoms D 0 at time t
0. A simple
case where this condition applies is when the initial number of daughter nuclides is small
enough so as to be negligible. We will refer to such chronometers as systems with high
parent/daughter ratios . This approximation is fairly generally valid for the potassium-
argon dating method and for uranium-lead dating of zircons described later, and the time
t will be given by:
=
ln 1
1
λ
D
P
t
=
+
(4.6)
For example, for the 238 U- 206 Pb chronometer:
ln 1
206 Pb
238 U
1
t
=
+
(4.7)
λ
238 U
When the previous methods fail (typically D 0 cannot be neglected with respect to D ),
a different assumption can often be used, which is the basis of the isochron method. This
method dates an event of isotopic homogenization, typically the precipitation of minerals
from the same melt or solution, and removes the ambiguity arising from our ignorance
of the initial state of the system. Isotopic homogenization results from the fact that the
chemical properties of different isotopes from the same element are very similar, though
as seen in Chapter 3 not identical. To help our understanding, this principle is illustrated
in Fig. 4.1 by a playful comparison. A fenced yard with a tree in the center represents
two crystalline sites with different energy levels. In the first case, we release a few dozen
cats and dogs into the yard-tree system and we can well imagine that after some brisk
movement among our elements, they will arrange themselves in appropriate sites, cats in
 
 
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