Lab exercise02

Exercise 2
Relative and absolute dating of geologic events

Introduction
The study of Earth history involves determining the sequence of geologic
events over immense spans of time. In most cases the correct order of
events can be determined without knowing their actual ages: that is, we
simply establish that event B occurred before event C, but after event A.
Such dating, in which the occurrence of events is determined relative to one
another, is known as relative dating.

Of course it is always useful to know the actual ages of rocks and events, if
possible. Actual ages are determinied by means of radiometric dating
techniques. Although several techniques exist, all rely on the fact that
radioactive “parent” isotopes decay into stable “daughter” isotopes at a
constant rate. With knowledge of the decay rate, ratios of parent and
daughter isotopes then can be used to derive an absolute date, in years, for
the age of a given mineral sample.

The purpose of this lab is to introduce the principles and concepts
associated with both relative and absolute dating.

Relative dating
The relative order of geologic events can be established in most cases by
applying four or fewer basic principles. (1) The Principle of Original
Horizontality states that sedimentary rocks are deposited as horizontal or
nearly horizontal layers. Any marked deviation from horizontality indicates
that some movement or deformation of the Earth’s crust occurred after
deposition of the inclined layer. (2) The Principle of Superposition states
that in an ordinary vertical sequence of sedimentary rocks, the layer at the
bottom of the sequence is oldest, and successively higher layers are
successively younger. (3) The Principle of Cross-cutting relationships
states that geologic features such as faults and igneous intrusions, which cut
through rocks, must be younger than the rocks through which they cut. (4)
The Principle of Inclusion states that if rocks or rock fragments are
included within another rock layer, the rock fragments must be older than

2–1

the layer in which they are included. Examples of the application of these
principles are given in the following block diagrams (Figure 1).

Figure 1—(A) Sedimentary beds 1–3 were deposited as horizontal layers. Sometime later, a normal fault occurred. (B) Sedimentary beds 1–7
were deposited as horizontal layers. Later, these beds were folded into an anticline. Later still, the anticline was truncated by an erosional
unconformity, and finally, an eighth sedimentary bed was deposited as a horizontal layer. Inclusions of older rock fragments (derived from beds
1–7) are found at the base of bed 8.

Unconformities are especially useful in reconstructing Earth history. An
unconformity is a surface that corresponds with a gap in sedimentation,
either nondeposition or erosion. Rocks above an unconformity are younger
than those below it. Three main types of unconformities are recognized
(Figure 2): (1) angular unconformity, in which beds above and below the
surface are not parallel; (2) nonconformity, in which sedimentary layers
overly crystalline rocks (either igneous or metamorphic); and (3)
disconformity, in which beds above and below the surface are parallel, but
the surface itself is irregular, exhibiting evidence of erosional relief. In
geologic block diagrams and cross-sections, unconformities are usually drawn
as a wavy line.

Figure 2—Three types of unconformities (from Stanley, 1998).

2–2

Relative dating exercises
For each of the following five block diagrams (A–E), label with letters and/or
numbers each sedimentary rock layer, igneous rock body, fault, and
unconformity, and then determine the correct order in which the various
rock units and other features occurred.

2–3

F. Repeat the ordering procedure for the block diagram below, which is
already labeled.

2–5

Absolute dating
As mentioned, determination of the actual age, in years, of minerals is
accomplished by radiometric dating techniques. Radiometric dating is
possible because certain naturally occurring isotopes are radioactive and
their decay rates are constant. The half-life of a radioactive isotope is the
length of time required for one-half of a given number of “parent” atoms to
decay into stable “daughter” atoms. The relationship among parents,
daughters and half-life is illustrated below in Figure 3.

100

90

80

70

60

50

40

30

20

10

0
0 1 2 3 4 5 6 7 8 9
half-life

parent atoms daughter atoms
Figure 3—In a closed system, the number of radioactive parent atoms decreases by 50% each half-life,
and the number of daughter atoms increases correspondingly.

The principle of radiometric dating can be expressed by the following
relationship:
Nd
T= Nλ (formula 1)
p
Where T = time in years, Nd = amount of daughter atoms, Np = amount of
parent atoms, and λ = decay constant. The decay constant, λ, is defined as

2–6

0.693/half-life. Table 1 lists some commonly used radioactive parents /
daughters, their half-lives, λ’s, and effective dating ranges.

Table 1—Isotopes commonly used in radiometric dating.
Isotopes Half-life λ Effective dating
range
238
U / 206Pb 4.46 × 109 years 1.55 × 10-10 > 100 m.y.
40
K / 40Ar 1.25 × 109 years λε = 0.581 × 10-10 > 100,000 years
λβ = 4.96 × 10-10
87
Rb / 87Sr 4.88 × 1010 years 1.42 × 10-11 > 100 m.y.
14
C 5730 years ~50,000–70,000
years

Radiometric dates reflect the time that has elapsed since a mineral formed
and its chemical composition was set. Because the dating procedure requires
measuring the existing amounts of parent and daughter isotopes, it is
critically important to analyze only those mineral grains that have remained
closed systems since their time of origin. A key requirement in radiometric
dating is that there has been no loss or gain of parent or daughter atoms
through partial melting, metamorphism, weathering, or any other agent.

Another requirement in radiometric dating is that no daughter atoms were
originally present in the grain to be analyzed. If some daughter atoms were
originally present, then they must be corrected for.

For 238U/206Pb dating, the general relationship in formula 1 (above) can be
rewritten as follows:
(Dp – Di)
T=
1
λ
× loge [ Pp +1 ] (formula 2)

Where Dp = present amount of daughter
Di = initial amount of daughter
Pp = present amount of parent
T = time in years since crystallization of the grain

Formula 2 must be modified for 40K/40Ar dating, because 40K decays into two
daughter products, 40Ca and 40Ar. The modified equation is:

T=
1
(λε + λβ)
× loge [[ 40

40
Ar
K
×
λε + λβ
λε
] +1 ] (formula 3)

2–7

Because of the extremely long half-life of 87Rb, the practical formula for
radiometric dating with the 87Rb/87Sr method is:

(formula 4)

87 87
Sr - Sr
86 86
Srmeasured Srinitial
T
= 87
Rb
86
× λ
Srmeasured

Finally, because 14C has a very short half-life, the 14C method is useful in
dating organic material only as old as about 70,000 years. Laboratory work
using very precise, Geiger counter-like instruments established a
relationship between the “specific activity” of an organic substance and its
age. Specific activity is a measure of the amount of remaining 14C,
expressed in counts/min/gm of material. This relationship is given in the
graph in Figure 4.

2–8

Figure 4—Empirical relationship between specific activity of
14C in organic material and age of the material.

2–9

Absolute dating exercises
Examine the block diagram in Figure 5. Five samples have been collected
from various rocks and sediments in this area. Sample A is a contact
metamorphic rock with datable zircon grains that can be used to establish
the timing of metamorphism. Sample B contains datable biotite from an
igneous dike. Sample C contains biotite from a separate dike. Sample D is a
fragment of wood from ancient sediments now preserved on top of a mesa.
And Sample E is wood from sediments along the shore of a modern lake.

Figure 5—Block diagram showing collecting localities of five samples for radiometric dating.

2–10

a. Use information in Table 1 and formulae 2–4 to help you calculate the
absolute age of each sample. Complete Table 2 by filling in the “Age” column.

Sample Analysis Age (in years)
238
A U and 206Pb were measured. Of the total of
(zircon) these two isotopes, 78% are 238U and the
remaining 22% are 206Pb. Assume there was no
206
Pb originally
40
B Ar/40K ratio = 0.030
(biotite)
87
C Sr/86Srmeasured = 0.75
87
(biotite) Sr/86Srinitial = 0.70
87
Rb/86Srmeasured = 5.0
D Specific activity = 1 ct/m/gm
(wood)
E Specific activity = 8 ct/m/gm
(wood)

b. Use your knowledge of relative dating to determine the correct sequence
of igneous, metamorphic and sedimentary rocks in this diagram. Do the
absolute ages you calculated in part a (above) agree with the relative ages of
the five samples?

2–11

Lab exercise02

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Lab exercise02