Evolution__3rd_Edition

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CHAPTER 18 / The History of Life 527
Box 18.1
Radioactive Decay and the Dates of Geological History
Radioisotopes of chemical elements decay over time. For example,
the isotope of rubidium 87 Rb decays into an isotope of strontium,
87 Sr. The decay is very slow and has a half-life of about 48.6 billion
years; that is, half of an initial sample of 87 Rb will have decayed into
87 Sr in 48.6 billion years (about 10 times the age of Earth).
Radioactive decay proceeds at an exponentially constant rate.
Exponential decay means that a constant proportion of the initial
material decays in each time unit. For example, suppose we start
with 10 units and one-tenth of them decay per time interval; in the
first time interval 1 unit will decay, and we shall have 9 units left.
In the second time interval, a proportion equal to one-tenth of the
remaining nine units (i.e., 0.9 units) will decay; and we shall be
left with 8.1 units. In the third time interval, a further tenth of the
8.1 units will decay, leaving 7.29 units (8.1 − 0.81) at the beginning
of the fourth time interval, and so on. In radioactive decay, the
proportion of the isotope that decays each year is called the decay
constant (l), and for 87 Rb/ 87 Sr the decay constant is 1.42 × 10 −11 per
year. Therefore, whatever the amount of 87 Rb that is present at any
time, a proportion equal to 1.42 × 10 −11 of it will decay into 87 Sr in
the next year.
To estimate the age of a rock by the radioisotope technique,
we need to be able to make two measurements and validate one
assumption. The two measurements are the isotope composition
of the rock now and when it was formed. The proportions of 87 Rb
and 87 Sr are obviously measureable now. The composition of the
rock was originally fixed when it crystallized as an igneous rock
from liquid magma, and the ratios of 87 Rb and 87 Sr in modern
magma can be measured: the ratio is a good estimate of the
Table B18.1
Radioactive decay systems used in geochronology.
isotope ratio when the rock first formed. The isotope ratio will
slowly change from the original ratio as 87 Rb radioactively decays
into 87 Sr. In order to estimate the age of the rock from the change in
the isotope ratio, we must assume that all the change in the ratio is
due to radioactive decay. For the case of 87 Rb/ 87 Sr, the assumption
is probably valid. Neither isotope seeps into, or leaks out of, the
rock, and the ratios are therefore solely determined by time and
radioactive decay. For some other radioisotopes, the assumption is
less well met. Uranium, for example, can be oxidized into a mobile
form and move among rocks (though the problem in this case can
be dealt with by combining two uranium decay schemes, such that
the time is inferred from the ratio of two lead isotopes and the
concentration of uranium does not matter).
Table B18.1 lists the main radioisotopes used in geochronology.
The decay of 40 K, for example, is a geochronologically useful decay
scheme. When a volcano erupts the heat volatalizes all the 40 Ar out
of the volcanic lava and ash, but not the 40 K. When the volcanic dust
cools, therefore, it contains (of 40 K and 40 Ar) only 40 K. The 40 K then
decays into both 40 Ca and 40 Ar. In practice, there is so much 40 Ca in
the rock from other sources that it is not convenient to use it for
dating purposes, but all the 40 Ar in the rock will have been produced
by the decay of 40 K. The decay is so slow that it is not practical to
use it for rocks less than about 100,000 years old; but there are
other radioisotopes for shorter times. The decay of 14 C into
nitrogen, for example, has a half-life of only 5,730 years.
The exact age of a rock is calculated as follows. Take 87 Rb/ 87 Sr as
an example. Let N 0 be the number of 87 Rb atoms in the sample of
rock when it was formed, and N be the number today. Then
Radioactive Decay constant
isotope (× 10 −11 /year) Half-life (years) Radiogenic isotope
14 C 1.2 × 10 7 5.73 × 10 3 14 N
40 K 5.81 + 47.2 1.3 × 10 9 40 Ar + 40 Ca*
87 Rb 1.42 4.86 × 10 10 87 Sr
147 Sm 0.654 1.06 × 10 11 143 Nd
232 Th 4.95 1.39 × 10 10 208 Pb
235 U 98.485 7 × 10 8 207 Pb
238 U 15.5125 4.4 × 10 9 206 Pb
* 40 K decays into both 40 Ar and 40 Ca, with the two decay constants given; the half-life is for the sum of the two.