Copy of Assignment3_Spring23_Time_ResponseSheet-4
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Geology
Date
Dec 6, 2023
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EAS 1180: How to Build a Habitable Planet
Learning Assignment 3: Keeping Relative and Absolute Geologic Time Response
Sheet Due Wednesday March 8
th
at 11:59 pm (see late policy in syllabus)
35 points
total
Please upload only this sheet when you go to turn your assignment in on
Gradescope
Part 1: An Application of Stratigraphic Relations to
Planetary Geology
Lava
(all dark
gray areas)
Impact craters
Faults
Volcano
Figure 2
1. Which of the labeled features is the youngest? How do you know (i.e., what stratigraphic principle
tells you this)?
(2 pts)
Based on stratigraphic principles, the labeled feature that is the youngest is likely the Impact
Craters. The principle of cross-cutting relationships states that any geological feature that cuts
across another feature must be younger than the feature it cuts. In the case of impact craters, they
cut across the surface of the planet, indicating that they are the most recent geological event to
occur.
2. Which labeled feature is the oldest? How do you know (i.e., what stratigraphic principle tells you this)?
(2 pts)
According to the information given, the volcano is the labeled feature that is the oldest. Because
faults are younger than the rocks they cut through according to the stratigraphic principle of
cross-cutting relationships, the volcano must be the older feature since the faults are younger
than the rocks it cuts through. Additionally, the presence of lava from the volcano's eruptions
suggests that the volcano was formed prior to the eruption of the lava.
3. Put all four labeled features in order according to their relative ages from oldest to youngest.
(2 pts)
Volcanoes, Lava, Faults, and Impact Craters
1
Part 2: Basic Principles of Radioisotopes
4. Copy and paste your scatter graphs 1 and 2 from the Excel workbook tab “Part 2” below. For full
credit, make sure your graphs have the correctly formatted x and y axes.
(2 pts)
5. What amount of radioactive potassium remains after 5 billion years?
(1 pt)
0.055
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6. What amount of radioactive uranium remains after 1 billion years?
(1 pt)
0.86
7. What amount of radioactive carbon remains after 20,000 years?
(1 pt)
0.089
8. Describe the shape of the
40
K-
40
Ar curve, the
238
U-
206
Pb curve and the shape of the
14
C-
14
N curve in
scatter plot 1
(1 pt)
Potassium has the most of a curve, with a faster decay than uranium's curve. Uranium almost
looks like a straight line. Radioactive carbon does not look like a curve, and is displayed as an
angle.
9. Which system shows the fastest decrease in the parent isotope in scatter plot 1?
(2 pts)
Radiocarbon has the fastest decrease.
10. Describe the shapes of the
238
U-
206
Pb curve and the
14
C-
14
N curve on scatter plot 2. (The
40
K-
40
Ar
curve will be hidden beneath the
238
U-
206
Pb curve.)
(1 pt)
The curve of uranium is similar to a straight line with no curve in plot 2. Radiocarbon has a
steep curve, and shows a linear decrease afterwards.
11. Based on these views of scatter plot 2, does the parent isotope decrease faster or slower as the
decay constant decreases?
(2 pts)
As the decay constant decreases, the isotope decreases as well with a slower rate of decay.
12. In general, would an isotopic system with a smaller decay constant be more useful for
dating younger or older rocks? Explain your answer.
(4 pts)
A smaller decay constant would be useful for dating older rocks, since it would cause
the
rate of decay to be slower, providing a longer time interval to study the rock accurately
and the differences between the parent and daughter isotope. A large decay constant with
a faster rate of decay would cause the isotope to reach its final decay state quicker, making
it difficult to study the rock over its billion years of existence.
2
Part 3: Determining Absolute Ages
Copy and paste the data tables and plots you generated for each isotope system below to receive full
credit for each question.
13. A Precambrian metamorphic rock from the Canadian Shield contains abundant plagioclase feldspar
and mica minerals. One mica crystal contains 2.43
⋅
10
-5
grams of radioactive
40
K and 8.00
⋅
10
-5
grams
of stable
40
Ar; another mica contains 2.30
⋅
10
-5
grams of radioactive
40
K and 7.12
⋅
10
-5
grams of stable
40
Ar. A plagioclase feldspar contains 2.19
⋅
10
-5
grams of radioactive
40
K and 6.80
⋅
10
-5
grams of stable
40
Ar What is the age of the crystal? Express your answer in Ga (giga-annum = billions of years).
(3 pts)
3 Ga old
14. A sample of basalt is retrieved from the bottom of the Atlantic Ocean approximately 1000 km east of
New York City. The sub-samples of basalt are analyzed with a mass spectrometer are found to contain
4.27
⋅
10
-5
grams of radioactive
238
U and 1.15
⋅
10
-6
grams of stable
206
Pb; 5.22
⋅
10
-5
grams of radioactive
238
U and 2.1
⋅
10
-6
grams of stable
206
Pb; and 4.80
⋅
10
-5
grams of radioactive
238
U and 1.63
⋅
10
-6
grams of
stable
206
Pb, respectively. What is the age of the basalt? Express your answer in Ma (mega annum =
millions of years).
(3 pts)
612 Ma old
15. A piece of a tree trunk found in glacial till from the Ice Age is cored three times. Each core is found
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to contain 9.8
⋅
10
-3
grams of radioactive
14
C and 3.17
⋅
10
-2
grams of
14
N; 1.02
⋅
10
-2
grams of radioactive
14
C and 4.01
⋅
10
-2
grams of
14
N; and 1.10
⋅
10
-2
grams of radioactive
14
C and 5.1
⋅
10
-2
grams of
14
N,
respectively. Approximately how old is the tree? Express your answer to the nearest hundred years
. (3
pts)
About 23 hundred years old.
3
Part 4: The Geologic Time Scale
16. For what percentage of Earth’s history have humans been present?
(2 pts)
2 Ma / 4.6 Ga
2000000 / 4600000000 = 0.000434783 or 0.0435 %
17. The innermost part of the zircon shown in Fig. 3 has an isotopic age of 4.4 Ga. During which eon of
the Geologic Time Scale did the zircon’s core form?
(1 pt)
The Hadean eon
18. What percent of Earth’s history passed before the earliest life forms appeared roughly 3 billion years
ago?
(2 pts)
34.78%
4
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