Evolution__3rd_Edition

528 PART 5 / Macroevolution
N = N 0 e −lt , where l is the decay constant and t is the age of
the rock. Take logs and t = (1/l)ln N 0 /N. It is practically easier to
measure the quantity of the isotope generated by decay. Therefore,
let N R equal the number of 87 Sr atoms generated by radioactive
decay up to any time. Because each 87 Sr atom has been generated
by the decay of one 87 Rb atom, N R = N 0 − N. This can be substituted
into the formula for time:
t
1 N + N
= ln
l N
For example, if 3% of the original 87 Rb in a rock has decayed into
87 Sr, then the age of the rock is calculated as:
Fossils are dated by radioisotopes,
...
. . . by the relative positions of
rocks, ...
R
1
t =
ln( 100/ 97) = 2. 08 × 109
years
1.42 × 10−11
Or about 2 billion years.
(The decay constant and half-life of a radioisotope are simply
related. When half the original 87 Rb has decayed into 87 Sr, the
number of 87 Sr atoms formed must equal the number of 87 Rb
atoms that have decayed. N = N R . Substitute that into the formula
for time, and t 1/2 = ln 2/l = 0.693/l.)
In summary, if we know the isotope ratio in the rock when it was
formed and in a modern sample, and if we can reasonably assume
that the change in the ratio between then and now was only caused
by radioactive decay, we can estimate the absolute age of the rock.
In practice, the dating of fossils by the radioisotope method usually requires a combination
of absolute and relative dating. The reason is that the radioisotope method
can only be used for rocks that contain radioisotopes. Some fossils contain 14 C, because
carbon is found in living material, and these can be dated directly if they are not too old.
Some other radioisotopes are found in corals or shells. However, most of the radioisotopes
used to find geological dates are not found in fossils. These isotopes (such as
87 Rb or 40 K) are only found in igneous rocks. In order to date a deposit of fossils, we
need to find some associated igneous rocks that we can infer to have been deposited at
about the same times as the fossils.
For instance, if some fossiliferous sediments are laid down on top of an igneous
rock, we can infer that the fossils are no older than the date of the igneous rock (on the
principle that younger rocks lie on top of older ones). If an igneous rock has been
intruded into a sedimentary rock, we can infer that the sediments are older than the
igneous rock (because igneous rocks only intrude into existing sedimentary rocks). In
the best case, a fossiliferous sediment will lie on top of one, older set of igneous rocks,
and have another younger igneous rock intruded in it. Then the fossils can be dated to a
time between the age of the two igneous rocks.
The inference of the age of fossils from that of surrounding igneous rocks is an
example of relative time measurement. If we know the relative date of a rock, or fossil,
it means we know its date relative to that of another rock, or fossil: we have a statement
of the form “rock A was laid down before/at the same time as/after rock B.” Some of
the procedures for finding relative times are as follows. At any one site, more recent
sediments are deposited on top of older sediments. Fossils lower down a sedimentary
column are therefore likely to be older (sometimes a large geologic convulsion, such as
a volcanic explosion, may turn a sedimentary column upside down, but it is obvious
when this has happened). The date of any one fossil deposit relative to those at different
sites can also usually be estimated. It is done by comparing the fossil composition of
the site, for some common fossils such as ammonites or foraminifers, with a standard
reference collection. For these reference fossils, the fossils deposited at one place and
time will be much the same as those being deposited at another place. They show that
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