CHAPTER 18 Geologic Time
452
three half-lives, the ratio of parent atoms to
daughter atoms is 1:7 (one parent for every
seven daughter atoms).
If the half-life of a radioactive isotope
is known and the parent/daughter ratio can
be measured, the age of the sample can be
calculated. For example, assume that the
half-life of a hypothetical unstable isotope
is 1 million years and the parent/daughter
ratio in a sample is 1:15. Such a ratio
indicates that four half-lives have passed
and that the sample must be 4 million
years old.
Radiometric Dating
Notice that the percentage of radioactive
atoms that decay during one half-life is
always the same: 50 percent. However, the
actual number of atoms that decay with
the passing of each half-life continually
decreases. Thus, as the percentage of
radioactive parent atoms declines, the
proportion of stable daughter atoms rises,
with the increase in daughter atoms just
matching the drop in parent atoms. This
fact is the key to radiometric dating.
Of the many radioactive isotopes that
exist in nature, five have proved particularly useful in providing radiometric
ages for ancient rocks (TABLE 18.1).
Rubidium-87, thorium-232, and the two
isotopes of uranium are used only for dating rocks that are millions of years old, but
potassium-40 is more versatile.
POTASSIUM-ARGON. Although the halflife of potassium-40 is 1.3 billion years,
analytical techniques make possible the
detection of tiny amounts of its stable
daughter product, argon-40, in some rocks
that are younger than 100,000 years.
Another important reason for its frequent
use is that potassium is an abundant
constituent of many common minerals,
particularly micas and feldspars.
Although potassium (K) has three
natural isotopes—
39 K,
40 K, and
41 K—
only
40 K is radioactive. When
40 K decays,
it does so in two ways. About 11 percent
changes to argon-40 (
40
Ar) by means of
electron capture (see Figure 18.15C). The
remaining 89 percent of
40 K decays to
calcium-40 (
40 Ca) by beta emission (see
Figure 18.15B). The decay of
40 K to
40 Ca
however, is not useful for radiometric
dating, because the
40 Ca produced by
radioactive disintegration cannot be
distinguished from calcium that may
have been present when the rock formed.
The potassium-argon clock begins
when potassium-bearing minerals crystallize from a magma or form within a metamorphic rock. At this point the new
minerals will contain
40 K but will be free
of
39 Ar because this element is an inert gas
that does not chemically combine with
other elements.
As time passes, the
40 K steadily decays
by electron capture. The
40 Ar produced by
this process remains trapped within the
mineral’ s crystal lattice. Because no
40 Ar
was present when the mineral formed, all
of the daughter atoms trapped in the mineral must have come from the decay of
40 K.
To determine a sample’ s age, the
40 K/
40 Ar
ratio is measured precisely and the known
half-life for
40 K applied.
SOURCES OF ERROR. It is important
to realize that an accurate radiometric
date can be obtained only if the mineral
remained a closed system during the entire
period since its formation. A correct date
is not possible unless there was neither
addition nor loss of parent or daughter
isotopes, and this is not always the case.
In fact, an important limitation of the
potassium-argon method arises from the
fact that argon is a gas and it may leak
from minerals, throwing off measurements.
Indeed, losses can be significant if the
rock is subjected to relatively high
temperatures.
Of course, a reduction in the
amount of
40 Ar leads to an
underestimation of the rock’ s age.
Sometimes temperatures are high enough
for a sufficiently long period that all argon
escapes. When this happens, the potassiumargon clock is reset, and dating the sample
will give only the time of thermal resetting,
not the true age of the rock. For other
radiometric clocks, a loss of daughter
atoms can occur if the rock has been
subjected to weathering or leaching. To
avoid such a problem, one simple safeguard
is to use only fresh, unweathered material
and not samples that may have been
chemically altered.
Dating with Carbon-14
To date very recent events, carbon-14 is
used. Carbon-14 is the radioactive isotope
of carbon. The process is often called
radiocarbon dating. Because the half-life of
carbon-14 is only 5730 years, it can be
used for dating events from the historic
past as well as those from very recent
geologic history. In some cases carbon-14
can be used to date events as far back as
70,000 years.
Carbon-14 is continuously produced in the upper atmosphere as a
consequence of cosmic-ray bombardment. Cosmic rays, which are highenergy particles, shatter the nuclei of
gas atoms, releasing neutrons. Some
of the neutrons are absorbed by
nitrogen atoms (atomic number 7),
causing their nuclei to emit a proton.
As a result, the atomic number
decreases by 1 (to 6), and a different
element, carbon-14, is created
D I D Y O U K N O W ?
Numerical dates of the fossil record
show that life began in the ocean
approximately 3.8 billion years ago.
TABLE 18.1
Radioactive Isotopes Frequently Used in Radiometric Dating
Radioactive Parent
Stable Daughter Product
Currently Accepted Half-Life Values
Uranium-238
Lead-206
4.5 billion years
Uranium-235
Lead-207
713 million years
Thorium-232
Lead-208
14.1 billion years
Rubidium-87
Strontium-87
47.0 billion years
Potassium-40
Argon-40
1.3 billion years
452
three half-lives, the ratio of parent atoms to
daughter atoms is 1:7 (one parent for every
seven daughter atoms).
If the half-life of a radioactive isotope
is known and the parent/daughter ratio can
be measured, the age of the sample can be
calculated. For example, assume that the
half-life of a hypothetical unstable isotope
is 1 million years and the parent/daughter
ratio in a sample is 1:15. Such a ratio
indicates that four half-lives have passed
and that the sample must be 4 million
years old.
Radiometric Dating
Notice that the percentage of radioactive
atoms that decay during one half-life is
always the same: 50 percent. However, the
actual number of atoms that decay with
the passing of each half-life continually
decreases. Thus, as the percentage of
radioactive parent atoms declines, the
proportion of stable daughter atoms rises,
with the increase in daughter atoms just
matching the drop in parent atoms. This
fact is the key to radiometric dating.
Of the many radioactive isotopes that
exist in nature, five have proved particularly useful in providing radiometric
ages for ancient rocks (TABLE 18.1).
Rubidium-87, thorium-232, and the two
isotopes of uranium are used only for dating rocks that are millions of years old, but
potassium-40 is more versatile.
POTASSIUM-ARGON. Although the halflife of potassium-40 is 1.3 billion years,
analytical techniques make possible the
detection of tiny amounts of its stable
daughter product, argon-40, in some rocks
that are younger than 100,000 years.
Another important reason for its frequent
use is that potassium is an abundant
constituent of many common minerals,
particularly micas and feldspars.
Although potassium (K) has three
natural isotopes—
39 K,
40 K, and
41 K—
only
40 K is radioactive. When
40 K decays,
it does so in two ways. About 11 percent
changes to argon-40 (
40
Ar) by means of
electron capture (see Figure 18.15C). The
remaining 89 percent of
40 K decays to
calcium-40 (
40 Ca) by beta emission (see
Figure 18.15B). The decay of
40 K to
40 Ca
however, is not useful for radiometric
dating, because the
40 Ca produced by
radioactive disintegration cannot be
distinguished from calcium that may
have been present when the rock formed.
The potassium-argon clock begins
when potassium-bearing minerals crystallize from a magma or form within a metamorphic rock. At this point the new
minerals will contain
40 K but will be free
of
39 Ar because this element is an inert gas
that does not chemically combine with
other elements.
As time passes, the
40 K steadily decays
by electron capture. The
40 Ar produced by
this process remains trapped within the
mineral’ s crystal lattice. Because no
40 Ar
was present when the mineral formed, all
of the daughter atoms trapped in the mineral must have come from the decay of
40 K.
To determine a sample’ s age, the
40 K/
40 Ar
ratio is measured precisely and the known
half-life for
40 K applied.
SOURCES OF ERROR. It is important
to realize that an accurate radiometric
date can be obtained only if the mineral
remained a closed system during the entire
period since its formation. A correct date
is not possible unless there was neither
addition nor loss of parent or daughter
isotopes, and this is not always the case.
In fact, an important limitation of the
potassium-argon method arises from the
fact that argon is a gas and it may leak
from minerals, throwing off measurements.
Indeed, losses can be significant if the
rock is subjected to relatively high
temperatures.
Of course, a reduction in the
amount of
40 Ar leads to an
underestimation of the rock’ s age.
Sometimes temperatures are high enough
for a sufficiently long period that all argon
escapes. When this happens, the potassiumargon clock is reset, and dating the sample
will give only the time of thermal resetting,
not the true age of the rock. For other
radiometric clocks, a loss of daughter
atoms can occur if the rock has been
subjected to weathering or leaching. To
avoid such a problem, one simple safeguard
is to use only fresh, unweathered material
and not samples that may have been
chemically altered.
Dating with Carbon-14
To date very recent events, carbon-14 is
used. Carbon-14 is the radioactive isotope
of carbon. The process is often called
radiocarbon dating. Because the half-life of
carbon-14 is only 5730 years, it can be
used for dating events from the historic
past as well as those from very recent
geologic history. In some cases carbon-14
can be used to date events as far back as
70,000 years.
Carbon-14 is continuously produced in the upper atmosphere as a
consequence of cosmic-ray bombardment. Cosmic rays, which are highenergy particles, shatter the nuclei of
gas atoms, releasing neutrons. Some
of the neutrons are absorbed by
nitrogen atoms (atomic number 7),
causing their nuclei to emit a proton.
As a result, the atomic number
decreases by 1 (to 6), and a different
element, carbon-14, is created
D I D Y O U K N O W ?
Numerical dates of the fossil record
show that life began in the ocean
approximately 3.8 billion years ago.
TABLE 18.1
Radioactive Isotopes Frequently Used in Radiometric Dating
Radioactive Parent
Stable Daughter Product
Currently Accepted Half-Life Values
Uranium-238
Lead-206
4.5 billion years
Uranium-235
Lead-207
713 million years
Thorium-232
Lead-208
14.1 billion years
Rubidium-87
Strontium-87
47.0 billion years
Potassium-40
Argon-40
1.3 billion years