Geologic Time: Concepts and Principles - The Changing Earth: Exploring Geology and Evolution - page 451

of the previous parent atoms, which is equivalent
to one-fourth of the original parent atoms) and
750,000 daughter atoms. After three half-lives, it
will have 125,000 parent atoms (one-half of the
previous parent atoms, or one-eighth of the origi-
nal parent atoms) and 875,000 daughter atoms,
and so on, until the number of parent atoms re-
maining is so few that they cannot be accurately
measured by present-day instruments.
By measuring the parent-daughter ratio and
knowing the half-life of the parent (which has
been determined in the laboratory), geologists
can calculate the age of a sample that contains the
radioactive element. The parent-daughter ratio is
usually determined by a mass spectrometer , an in-
strument that measures the proportions of atoms
of different masses.

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Figure 17.18 Three Types of Radioactive Decay

Parent
nucleus

Alpha
particle

Daughter
nucleus

Changes in atomic number
and atomic mass number

Atomic number = -2
Atomic mass number = -4

Proton Neutron Electron

Alpha decay, in which an unstable parent nucleus emits 2 protons
and 2 neutrons.

a

Parent
nucleus

Daughter
nucleus

Beta
particle

Sources of Uncertainty
The most accurate radiometric dates are obtained
from igneous rocks. As magma cools and begins to
crystallize, radioactive parent atoms are separated
from previously formed daughter atoms. Because
they are the right size, some radioactive parent
atoms are incorporated into the crystal structure
of certain minerals. The stable daughter atoms,
though, are a different size from the radioactive
parent atoms and consequently cannot fi t into the
crystal structure of the same mineral as the parent
atoms. Therefore, a mineral crystallizing in cool-
ing magma will contain radioactive parent atoms
but no stable daughter atoms (

Atomic number = +1
Atomic mass number = 0

Proton Neutron Electron

Beta decay, in which an electron is emitted from the nucleus.

b

Parent
nucleus

Daughter
nucleus

Figure 17.21).
Thus, the time that is being measured is the time
of crystallization of the mineral that contains the
radioactive atoms and not the time of formation
of the radioactive atoms.
Except in unusual circumstances, sedi-
mentary rocks cannot be radiometrically dated
because one would be measuring the age of a par-
ticular mineral rather than the time that it was
deposited as a sedimentary particle. One of the
few instances in which radiometric dates can be
obtained on sedimentary rocks is when the min-
eral glauconite is present. Glauconite is a greenish
mineral containing potassium 40, which decays to argon 40
(Table 17.1). It forms in certain marine environments as a re-
sult of chemical reactions with clay minerals during the con-
version of sediments to sedimentary rock. Thus, glauconite
forms when the sedimentary rock forms, and a radiometric
date indicates the time of the sedimentary rock's origin. Be-
ing a gas, however, the daughter product argon can easily
escape from a mineral. Therefore, any date obtained from
glauconite, or any other mineral containing the potassium
40 and argon 40 pair, must be considered a minimum age.
To obtain accurate radiometric dates, geologists must
be sure that they are dealing with a closed system , meaning
that neither parent nor daughter atoms have been added or

◗

Atomic number = -1
Atomic mass number = 0

Proton Neutron Electron

Electron capture, in which a proton captures an electron and is thereby
converted to a neutron.

c

When we discuss decay rates, it is convenient to refer to
them in terms of half-lives. The half-life of a radioactive ele-
ment is the time it takes for half of the atoms of the origi-
nal unstable parent element to decay to atoms of a new, more
stable daughter element. The half-life of a given radioactive
element is constant and can be precisely measured. Half-
lives of various radioactive elements range from less than a
billionth of a second to 49 billion years.
Radioactive decay occurs at a geometric rate rather than
a linear rate. Therefore, a graph of the decay rate produces a
curve rather than a straight line ( Figure 17.20). For exam-

ple, an element with 1,000,000 parent atoms will have 500,000
parent atoms and 500,000 daughter atoms after one half-life.
After two half-lives, it will have 250,000 parent atoms (one-half

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