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Evolution__3rd_Edition

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528 PART 5 / Macroevolution<br />

N = N 0 e −lt , where l is the decay constant and t is the age of<br />

the rock. Take logs and t = (1/l)ln N 0 /N. It is practically easier to<br />

measure the quantity of the isotope generated by decay. Therefore,<br />

let N R equal the number of 87 Sr atoms generated by radioactive<br />

decay up to any time. Because each 87 Sr atom has been generated<br />

by the decay of one 87 Rb atom, N R = N 0 − N. This can be substituted<br />

into the formula for time:<br />

t<br />

1 N + N<br />

= ln<br />

l N<br />

For example, if 3% of the original 87 Rb in a rock has decayed into<br />

87 Sr, then the age of the rock is calculated as:<br />

Fossils are dated by radioisotopes,<br />

...<br />

. . . by the relative positions of<br />

rocks, ...<br />

R<br />

1<br />

t =<br />

ln( 100/ 97) = 2. 08 × 109<br />

years<br />

1.42 × 10−11<br />

Or about 2 billion years.<br />

(The decay constant and half-life of a radioisotope are simply<br />

related. When half the original 87 Rb has decayed into 87 Sr, the<br />

number of 87 Sr atoms formed must equal the number of 87 Rb<br />

atoms that have decayed. N = N R . Substitute that into the formula<br />

for time, and t 1/2 = ln 2/l = 0.693/l.)<br />

In summary, if we know the isotope ratio in the rock when it was<br />

formed and in a modern sample, and if we can reasonably assume<br />

that the change in the ratio between then and now was only caused<br />

by radioactive decay, we can estimate the absolute age of the rock.<br />

In practice, the dating of fossils by the radioisotope method usually requires a combination<br />

of absolute and relative dating. The reason is that the radioisotope method<br />

can only be used for rocks that contain radioisotopes. Some fossils contain 14 C, because<br />

carbon is found in living material, and these can be dated directly if they are not too old.<br />

Some other radioisotopes are found in corals or shells. However, most of the radioisotopes<br />

used to find geological dates are not found in fossils. These isotopes (such as<br />

87 Rb or 40 K) are only found in igneous rocks. In order to date a deposit of fossils, we<br />

need to find some associated igneous rocks that we can infer to have been deposited at<br />

about the same times as the fossils.<br />

For instance, if some fossiliferous sediments are laid down on top of an igneous<br />

rock, we can infer that the fossils are no older than the date of the igneous rock (on the<br />

principle that younger rocks lie on top of older ones). If an igneous rock has been<br />

intruded into a sedimentary rock, we can infer that the sediments are older than the<br />

igneous rock (because igneous rocks only intrude into existing sedimentary rocks). In<br />

the best case, a fossiliferous sediment will lie on top of one, older set of igneous rocks,<br />

and have another younger igneous rock intruded in it. Then the fossils can be dated to a<br />

time between the age of the two igneous rocks.<br />

The inference of the age of fossils from that of surrounding igneous rocks is an<br />

example of relative time measurement. If we know the relative date of a rock, or fossil,<br />

it means we know its date relative to that of another rock, or fossil: we have a statement<br />

of the form “rock A was laid down before/at the same time as/after rock B.” Some of<br />

the procedures for finding relative times are as follows. At any one site, more recent<br />

sediments are deposited on top of older sediments. Fossils lower down a sedimentary<br />

column are therefore likely to be older (sometimes a large geologic convulsion, such as<br />

a volcanic explosion, may turn a sedimentary column upside down, but it is obvious<br />

when this has happened). The date of any one fossil deposit relative to those at different<br />

sites can also usually be estimated. It is done by comparing the fossil composition of<br />

the site, for some common fossils such as ammonites or foraminifers, with a standard<br />

reference collection. For these reference fossils, the fossils deposited at one place and<br />

time will be much the same as those being deposited at another place. They show that<br />

..

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