Geoscience Reference
In-Depth Information
which is already a far less restrictive condition. This method is employed for many short-
lived nuclides (
14
C,
10
Be,
210
Pb) created by solar or galactic radiation interacting with
the atmosphere or rocks (cosmogenic nuclides). In the case of the carbon-14 clock,
P
refers to the radioactive
14
C isotope, while
P
is the most abundant isotope
12
C of carbon,
and a hypothesis is made about the isotopic abundance of
14
C in the upper atmosphere.
The principle of standardization to a stable isotope is also utilized for radioactive nuclides
derived from the decay of uranium isotopes (
234
U,
230
Th,
231
Pa), but the equations are then
a little more complex.
the same element as the radiogenic nuclide. As the system is closed, the number of stable
nuclides remains constant and
D
=
D
0
. This yields:
D
D
t
=
D
D
0
+
P
D
e
λ
t
1
−
(4.13)
t
D
and
y
D
,
Equation
(4.13)
is known as the isochron equation: in a plot of
x
=
P
/
=
D
/
D
)
0
will
a set of sub-systems of the same age
T
and the same initial isotope ratio (
D
/
lie on a straight line of slope e
λ
t
D
ratio is usually referred to, somewhat
improperly, as the parent/daughter ratio. Writing this equation for two samples 1 and 2 that
formed at the same time with the same isotope composition (
D
−
1. The
P
/
D
)
0
and subtracting them
/
from one another, we obtain an expression for the time:
ln
D
D
2
−
D
D
1
/
/
1
λ
t
=
(4.14)
D
)
2
−
(
D
)
1
(
P
/
P
/
Thus, for the system
87
Rb-
87
Sr,
P
stands for
87
Rb,
D
for
87
Sr, and
D
for
86
Sr, and we
can write:
87
Sr
86
Sr
87
Sr
86
Sr
0
+
87
Rb
86
Sr
e
λ
87
Rb
t
1
t
=
−
(4.15)
t
This expression defines Nicolaysen's
(1961)
isochron. It has the familiar form of the
equation of a straight line
y
(
87
Rb
86
Sr)
t
,
y
(
87
Sr
86
Sr)
t
,
=
y
0
+
mx
, where
x
=
/
=
/
(
87
Sr
86
Sr)
0
and slope
m
e
λ
87Rb
t
with intercept
y
0
=
/
=
−
1. Time
t
is derived from the
expression:
ln
87
Sr
86
Sr
2
−
87
Sr
86
Sr
1
/
/
1
87
Rb
86
Sr
2
−
87
Rb
86
Sr
1
t
=
(4.16)
λ
/
/
87
Rb
(all the ratios measured today).
For an isolated sample with a high parent/daughter ratio, i.e. (
P
D
)
1
D
)
2
and
/
(
P
/
D
)
1
can be assumed, the age derived in this way is a
model age
.
Figure 4.3
shows two examples of isochron diagrams. A simple way of understanding
isochrons is to appreciate that the existence of an alignment in the isochron diagram, in
which relations between the quantities plotted change with time, cannot be fortuitous and
depend on us to observe it today: if the samples form an alignment at the present time, an
alignment must also have existed at each time since their formation. Since the
D
for which the (
D
/
D
ratio
/
