Laboratory Manual for Introductory Geology 4e

FIGURE 12.9 Changing parent:daughter ratios during
radioactive decay.
Parent
Daughter
Parent (%)
100
75
50
25
0
Daughter (%)
0
25
50
75
100
Parent:daughter
ratio
— 3:1 1:1 1:3 —
The radiometric “clock” begins when a mineral containing the parent element
crystallizes during igneous or metamorphic processes. Over time, the amount of
the parent element decreases and the amount of the daughter element increases
(FIG. 12.9), in a pattern much like that of sand draining from the upper half of an
hourglass into the lower half. An isotope’s half-life is the amount of time it takes for
half of the parent atoms in a mineral sample to decay to an equal number of daughter
atoms (the center hourglass in Fig. 12.9).
How long the half-life of an isotope is depends on the rate at which that particular
isotope decays. The faster the decay rate, the shorter the half-life; the
slower the decay rate, the longer the half-life (FIG. 12.10). Generally, after only
4 half-lives have gone by, fewer than 10% of the parent atoms will be left. After
10 half-lives, there won’t be enough parent atoms left to measure accurately, so
a particular isotope is useful for determining dates only within time spans up
to 10 times its half-life. Logically, isotopes with short half-lives are used to date
relatively young rocks, whereas those with very long half-lives are used to date
relatively old rocks.
TABLE 12.1 lists the isotopes commonly used in radiometric dating, their halflives,
and the minerals in which they can be found. Many people who have heard of
carbon-14 dating may be surprised to learn that this isotope has such a short half-life
that it can be used to date only relatively recent materials. It is therefore a valuable
tool for archeologists studying cultures tens of thousands of years old, but not for
geologists studying rocks millions, hundreds of millions, and billions of years old.
FIGURE 12.10 Radioactive decay curves.
Parent atoms remaining (%)
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4
Number of half-lives
(a) The radioactive decay curve for an isotope.
Parent atoms remaining (%)
100
80
60
40
Slow decay rate
Moderate decay rate
Fast decay rate
20
0 Start Today
Time
(b) Decay curves for isotopes with different decay rates.
316 CHAPTER 12 INTERPRETING GEOLOGIC HISTORY