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ADDITIONAL EXERCISES FOR CHAPTER 21
EXAMPLE (TO ACCOMPANY ARRANGING
EVENTS IN ORDER SECTION)
EXAMPLE (TO ACCOMPANY GEOLOGIC
PERIODS AND TYPICAL FOSSILS SECTION)
A piece of sedimentary rock with almost parallel stratified layers was
recovered from a site. The dimensions of a cross section of the rock are
shown in the figure below. Assuming the absence of chemical weathering
or erosion, how many years were required to form the rock specimen
shown if the rate of sediment deposition is 4.0 millimeters per year?
What are the minimum and maximum age differences between the fossil records of trilobites that were dated to the Silurian period and the
ammonites of the Triassic period?
SOLUTION
Triassic period: 208–245 million years before present
Silurian period: 408–438 million years before present
Direction of parallel striations
49 cm
maximum age difference = 4.38 × 108 − 2.08 × 108
= 2.20 × 108 or 220 million years
minimum age difference = 4.08 × 108 − 2.45 × 108
28 cm
= 1.63 × 108 or 163 million years
54 cm
SOLUTION
The useful dimension for calculating the years required to form the
rock should be 49 cm, which is the maximum length measured in a
direction perpendicular to the parallel striations. By applying the principles of original horizontality and superposition, we can estimate the
required time of formation for this rock sample as
49 cm
= 1.2 × 102 years
0.40 cm/year
EXAMPLE (TO ACCOMPANY GEOLOGIC
PERIODS AND TYPICAL FOSSILS SECTION)
How many years of time span were associated with the Paleozoic era
during which both plant and animal life flourished before the PermianTriassic Extinction Event ended the era? What percentage of Earth’s
geologic time was represented by the Paleozoic era?
SOLUTION
Paleozoic era: 245–551 million years before present
years spanned = 5.51 × 108 − 2.45 × 108
= 3.06 × 108 or 306 million years
EXAMPLE (TO ACCOMPANY MODERN
TECHNIQUES SECTION)
3.06 × 10
percentage of geologic time = _
× 100 = 6.80%
9
8
4.50 × 10
A lab specializing in carbon-14 radiometric dating techniques has
determined that the useful age range of specimens that can be dated
reliably corresponds to one-fifth to 10 half-lives of the C-14 radioisotope.
What is the range of the geologic time scale that corresponds to the
useful span of C-14 dating?
SOLUTION
Half-life of C-14: 5,730 years
earliest specimen that can be dated by C-14 = 5,730 years × 10
= 5.73 × 105 years
latest specimen that can be dated by C-14 = 5,730 years/5
= 1.15 × 104 years
21-1
CHAPTER 21 Geologic Time
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PARALLEL EXERCISES
Group B
Group A
1. A piece of sedimentary rock with almost parallel stratified layers
was recovered from a site. The dimensions of a cross section of
the rock are shown in the figure below. Assuming the absence of
chemical weathering or erosion, how many years were required
to form the rock specimen shown if the rate of sediment
deposition is 3.0 millimeters per year?
Direction of parallel striations
49 cm
Direction of parallel striations
49 cm
28 cm
28 cm
54 cm
2. Uranium-235 radiometric dating technique has a very useful
range of dating rock specimens corresponding to one-fifth to
10 half-lives of the U-235 radioisotope. What is the chronological
range of the geologic time scale that corresponds to the useful
span of U-235 dating and what is the age range of rocks that can
be measured with U-235 dating?
3. Thorium-230 and protactinium-231 are decay products of
uranium-234, and they are selectively precipitated into ocean floor
sediments. The half-lives of Th-230 and Pa-231 are 80,000 years
and 34,300 years, respectively. For marine sediments with these
two radioisotopes, what is the range of geologic time scale that
can be dated assuming that one-tenth and 10 half-lives of both
isotopes can be measured with acceptable accuracy?
4. Dinosaurs first appeared in the mid-Triassic to late-Triassic
period and became extinct at the end of the Cretaceous period.
For how long did the dinosaurs roam Earth?
5. On the geologic time scale, what is the average time span of an
epoch in the Tertiary period?
6. Human-like creatures first appeared in the Pleistocene epoch
1.6 million years ago. What is the fraction of Earth’s geologic time
that is occupied by human-like creatures?
2
1. A piece of sedimentary rock with almost parallel stratified layers
was recovered from a site. The dimensions of a cross section of
the rock are shown in the figure below. Assuming the absence of
chemical weathering or erosion, how many years were required
to form the rock specimen shown if the rate of sediment
deposition is 3.5 millimeters per year?
CHAPTER 21 Geologic Time
54 cm
2. Samarium-147 radiometric dating technique has a very useful
range of dating rock specimens corresponding to one-fifth to
10 half-lives of the Sm-147 radioisotope. What is the chronological
range of the geologic time scale that corresponds to the useful
span of Sm-147 dating and what is the age range of rocks that
can be measured with Sm-147 dating?
3. What is the chronological range that can be dated for a meteorite
sample containing the two radioisotopes of U-235 and U-238
which have half-lives of 7.04 × 108 and 4.5 × 109 years,
respectively? Assume that one-tenth and 10 half-lives of both
isotopes can be measured with acceptable accuracy.
4. Insects such as flies, beetles, dragonflies, and cockroaches
emerged at various times during the Permian period. For how
long have these insects survived on Earth?
5. On the geologic time scale, what is the average time span of a
period in the Paleozoic era in North America?
6. Vertebrate land animals appeared on Earth about 350 million
years ago and have evolved into many vertebrate species today.
What is the fraction of Earth’s geologic time for the existence of
these vertebrate land animals?
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SOLUTIONS TO ADDITIONAL GROUP A & B PARALLEL EXERCISES FOR CHAPTER 21
Group A
Group B
1. The useful dimension for calculating the years required to form
the rock should be 28 cm, which is the maximum length
measured in a direction perpendicular to the parallel striations.
By applying the principles of original horizontality and
superposition, we can estimate the required formation time for
this rock sample as
28 cm
__
= 93 years
0.30 cm/year
2. Half-life of U-235: 704 million years
54 cm
_
= 1.5 × 102 years
0.35 cm/year
2. Half-life of Sm-147: 106 billion years
oldest rocks that can be dated by U-235
upper age limit for Sm-147 dating
= 7.04 × 10 years × 10 = 7.04 × 10 years
8
9
youngest rocks that can be dated by U-235
= 1.06 × 1011 years × 10 = 1.06 × 1012 years
lower age limit for Sm-147 dating
= 7.04 × 10 years/5 = 1.41 × 10 years
8
1. The useful dimension for calculating the years required to
form the rock should be 54 cm, which is the maximum length
measured in a direction perpendicular to the parallel striations.
By applying the principles of original horizontality and
superposition, we can estimate the required time of formation
for this rock sample as
8
= 1.06 × 1011 years/5 = 2.12 × 1010 years
3. Half-life of U-235: 7.04 × 108 years
3. Half-life of Th-230: 80,000 years
Half-life of U-238: 4.5 × 109 years
Half-life of Pa-231: 34,300 years
The lower limit of the geologic time scale is determined by 1/10
of the Pa-231 half-life whereas the upper limit is determined by
10 times the half-life of the Th-230.
The lower limit of the chronological range is determined by 1/10
of the U-235 half-life whereas the upper limit is determined by
10 times the half-life of the U-238.
lower age limit for Pa-231dating
lower age limit for U-235 dating
= 3.43 × 104 years/10 = 3.43 × 103 years
upper age limit for Th-230
= 7.04 × 108 years/10 = 7.04 × 107 years
upper age limit for U-238 dating
= 8.00 × 10 years × 10 = 8.00 × 10 years
4
5
Therefore, the geologic time scale that can be dated for the
sediment samples is from 3.43 × 103 years to 8.00 × 105 years.
4. Triassic period: 208–245 million years before present
Mid-Triassic period: The midpoint or average
of 208–245 million years
End of Cretaceous period: 65 million years before present
years of dinosaur existence
= 4.5 × 109 years × 10 = 4.5 × 1010 years
Therefore, the chronological range that can be dated for the
meteorite sample is from 7.04 × 107 years to 4.5 × 1010 years.
4. Permian period: 245–286 million years before present
These insects survived several “mass extinction” events and
continue to live today
years of insect existence = 2.45 × 108 − 2.86 × 108 years
2.45 × 10 + 2.08 × 10
= __
− 6.5 × 107 = 1.6 × 108 years
8
8
2
5. Tertiary period: 1.6 to 65 million years before present
There were five epochs in the Tertiary period.
time span per epoch
time span per period
6.5 × 107 − 1.6 × 106
= __
= 1.3 × 107 years
5
2.45 × 10 − 5.51 × 10
= __
= 4.37 × 107 years
6. Pleistocene epoch: 1.6 million years before present
age of Earth = 4.50 × 10 years old
9
fraction of geologic time with human-like life-forms
1.6 × 10
=_
= 3.5 × 10−4
9
6
4.50 × 10
21-3
5. Paleozoic era: 245–551 million years before present
There were 7 periods in the Paleozoic era.
8
8
7
6. First vertebrate land animals appeared about 350 million years
ago.
age of Earth = 4.50 × 109 years old
fraction of geologic time with vertebrate land animals
3.5 × 10
=_
= 7.8 × 10−2
9
8
4.50 × 10
CHAPTER 21 Geologic Time
3