Radioactive Decay
1. Due to radioactive decay, an igneous rock sample now contains one-fourth of the
amount of potassium-40 that it originally contained. The age, in years, of this rock
sample is approximately
A) 0.7 x 10 9 years
C) 2.6 x 10 9 years
B) 1.3 x 10 9 years
D) 5.2 x 10 9 years
2. Which radioactive element is used to determine the absolute age of late Pleistocene
animal remains?
A) rubidium-87
C) potassium-40
B) uranium-238
D) carbon-14
3. How much of an 800-gram sample of potassium-40 will remain after 3.9 × 10 9
years of radioactive decay?
A) 50 grams
B) 100 grams
C) 200 grams
D) 400 grams
4. Base your answer to the following question on the passage below.
Frozen Mammoth
A wooly mammoth was found in 1999 buried in the frozen soil of the Siberian
tundra. Carbon-14 dating indicated that it had died about 20,000 years ago. Many
fossils represent only the partial remains of organisms. However, a complete
mammoth with bones, skin, hair, and internal organs intact represented a unique
opportunity for scientists to investigate the lifestyle of this animal and the
environment in which it lived.
Identify both the period and epoch of geologic time during which the wooly
mammoth lived.
Radioactive Decay
5. The table below shows how the radioactive decay of potassium-40 can be used to
determine the age of a rock.
How old is a sample of granite that contains 8 grams of radioactive potassium-40
and 56 grams of its nonradioactive decay products?
A) 1.3 × 10 9
B) 2.6 × 10 9
C) 3.9 × 10 9
D) 5.2 × 10 9
6. The diagram below represents a sample of rubidium-87 ( 87 Rb).
Which diagram represents the correct proportion of
after two half-lives?
A)
B)
C)
87 Rb
D)
to its decay product,
87 Sr,
Radioactive Decay
7. The table below shows information about the radioactive decay of carbon-14.
What is the amount of carbon-14 remaining after 28,500 years?
A)
g
B)
g
C)
g
D)
g
Base your answers to questions 8 and 9 on the graph below, which shows the
generalized rate of decay of radioactive isotopes over 5 half-lives.
8. Which radioactive isotope takes the greatest amount of time to undergo the change
shown on the graph?
A) carbon-14
C) uranium-238
B) potassium-40
D) rubidium-87
Radioactive Decay
9. If the original mass of a radioactive isotope was 24 grams, how many grams would
remain after 3 half-lives?
A) 12
B) 24
C) 3
D) 6
10. How old is a fossil that has radioactively decayed through 4 half-lives of
carbon-14?
A) 5,700 years
C) 22,800 years
B) 17,100 years
D) 28,500 years
11. An igneous rock contains 10 grams of radioactive potassium-40 and a total of 10
grams of its decay products. During which geologic time interval was this rock
most likely formed?
A) Middle Archean
C) Middle Proterozoic
B) Late Archean
D) Late Proterozoic
Radioactive Decay
12. The diagram below represents a sample of a radioactive isotope.
Which diagram best represents the percentage of this radioactive isotope sample
that will remain after 2 half-lives?
A)
B)
C)
D)
13. A whalebone that originally contained 200 grams of radioactive carbon-14 now
contains 25 grams of carbon-14. How many carbon-14 half-lives have passed
since this whale was alive?
A) 1
B) 2
C) 3
D) 4
Radioactive Decay
14. The graph below shows the radioactive decay of a 50-gram sample of a
radioactive isotope.
According to the graph, what is the half-life of this isotope?
A) 100 years
B) 150 years
C) 200 years
D) 300 years
Radioactive Decay
15. The models below represent the decay of radioactive atoms to stable atoms after
their first and second half-lives.
Which model best represents the number of undecayed and decayed atoms after
three half-lives?
A)
B)
C)
D)
Radioactive Decay
16. The graph below shows the rate of decay of the radioactive isotope K-40 into the
decay products Ar-40 and Ca-40.
Analysis of a basalt rock sample shows that 25% of its radioactive K-40 remained
undecayed. How old is the basalt?
A) 1.3 billion years
C) 3.9 billion years
B) 2.6 billion years
D) 4.6 billion years
Base your answers to questions 17 and 18 on the diagram below, which represents
a model of a radioactive sample with a half-life of 5000 years. The white boxes
represent undecayed radioactive material and the shaded boxes represent the
decayed material after the first half-life.
17. Which radioactive isotope has a half-life closest in duration to this radioactive
sample?
A) carbon-14
C) uranium-238
B) potassium-40
D) rubidium-87
Radioactive Decay
18. How many more boxes should be shaded to represent the additional decayed
material formed during the second half-life?
A) 12
B) 6
C) 3
D) 0
19. A fossil shell contains 25% of the original amount of its carbon-14.
Approximately how many years ago was this shell part of a living organism?
A) 5,700 years ago
C) 17,100 years ago
B) 11,400 years ago
D) 22,800 years ago
20. Which graph best shows the radioactive decay of carbon-14?
A)
B)
C)
D)
21. A sample of wood that originally contained 100 grams of carbon-14 now contains
only 25 grams of carbon-14. Approximately how many years ago was this sample
part of a living tree?
A) 2,850 years
C) 11,400 years
B) 5,700 years
D) 17,100 years
Radioactive Decay
22. Uranium-238 that crystallized at the same time Earth formed has undergone
approximately how many half-lives of radioactive decay?
A) one half-life
C) three half-lives
B) two half-lives
D) four half-lives
23. Fossil pollen has been recovered from sediments deposited in late-Pleistocene
lakes. The pollen’s geologic age can most accurately be measured by using
A) rubidium-87
C) oxygen-18
B) potassium-40
D) carbon-14
24. The characteristic of the radioactive isotope uranium-238 that makes this isotope
useful for accurately dating the age of a rock is the isotope’s
A)
B)
C)
D)
organic origin
constant half-life
common occurrence in sediments
resistance to weathering and erosion
Radioactive Decay
25. The table below gives information about the radioactive decay of carbon-14. Part
of the table has been deliberately left blank for student use.
After how many years will
A) 22,800 yr
B) 28,500 yr
gram of the original carbon-14 reamins?
C) 34,200 yr
D) 39,900 yr
26. A sample of wood found in an ancient tomb contains 25% of its original
carbon-14. The age of this wood sample is approximately
A) 2,800 years
C) 11,400 years
B) 5,700 years
D) 17,100 years
27. A student filled a graduated cylinder with 1,000 milliliters of water to represent a
radioactive substance. After 30 seconds, the student poured out one-half of the
water in the cylinder to represent the decay occurring within the first half-life.
The student repeated the process every 30 seconds. How much water did the
student pour from the cylinder at the 2-minute mark?
A) 12.5 mL
B) 62.5 mL
C) 125.0 mL
D) 250.0 mL
Radioactive Decay
28. The diagram below represents the present number of decayed and undecayed
atoms in a sample that was originally 100% radioactive material.
If the half-life of the radioactive material is 1,000 years, what is the age of the
sample represented by the diagram?
A) 1,000 yr
B) 2,000 yr
C) 3,000 yr
D) 4,000 yr
29. Which radioactive isotope is most useful for determining the age of mastodont
bones found in late Pleistocene sediments?
A) uranium-238
C) potassium-40
B) carbon-14
D) rubidium-87
30. The absolute age of a rock is the approximate number of years ago that the rock
formed. The absolute age of an igneous rock can best be determined by
A) comparing the amounts of decayed and undecayed radioactive isotopes in
the rock
B) comparing the sizes of the crystals found in the upper and lower parts of the
rock
C) examining the rock's relative position in a rock outcrop
D) examining the environment in which the rock is found
31. Carbon-14, an isotope used to date recent organic remains, would most likely be
useful in determining the age of a fossil
A) trilobite
C) armored fish
B) Coelophysis
D) Beluga whale
Radioactive Decay
32. Why are radioactive substances useful for measuring geologic time?
A) The ratio of decay products to radioactive substances remains constant in
rocks.
B) The half-lives of radioactive substances are short.
C) Samples of radioactive substances are easy to collect from rocks.
D) Radioactive substances undergo decay at a predictable rate.
33. A bone sample contains only
the bone sample?
A) 1 C 14 half-life
C) 9 C 14 half-lives
of its original radioactive C 14 content. How old is
B) 2 C 14 half-lives
D) 4 C 14 half-lives
Base your answers to questions 34 through 38 on the graph below, which
represents the decay of radioactive material X into a stable decay product.
34. If radioactive material X were heated, the length of its half-life period would
A) decrease
C) remain the same
B) increase
Radioactive Decay
35. Each of the objects below has different amounts remaining of the original
radioactive material X. Which object is most likely the oldest?
A)
B)
C)
D)
36. Which graph best represents the relative percentages of radioactive material X
and its stable decay product after 15,000 years? (The shaded region represents
radioactive material while the non-shaded region represents stable decay
products.)
A)
B)
C)
D)
37. Radioactive material X can only be used to date young geologic material because
radioactive material X
A)
B)
C)
D)
has only recently become radioactive
has a relatively short half-life
never existed in older rocks
has only recently been discovered
Radioactive Decay
38. What is the approximate half-life of radioactive material X?
A) 5,000 yr
B) 10,000 yr
C) 50,000 yr
D) 100,000 yr
39. Which process could be indicated by the expression below?
U 238 ® Pb 206
A)
B)
C)
D)
crystallization of minerals in basalt
chemical weathering of marble
radioactive decay in granite
ozone depletion in the atmosphere
40. The half-life of a radioactive substance is mainly controlled by the
A)
B)
C)
D)
amount of the substance
composition of the substance
pressure acting on the substance
temperature of the substance
41. Samples of plant pollen are preserved in sediment deposited by the last glacial ice
sheet. Which radioactive isotope is best for determining the age of the samples?
A) potassium-40
C) uranium-238
B) carbon-14
D) rubidium-87
42. Which two elements are most useful for the radioactive dating of recent organic
remains?
A) C 14 and N 14
C) U 238 and Pb 206
B) K 40 and Ca 40
D) Rb 87 and Sr 87
Radioactive Decay
43. A graph of the radioactive decay of carbon-14 is shown below.
Which graph correctly shows the accumulation of nitrogen-14, the decay product
of carbon-14, over the same period?
A)
B)
C)
D)
44. If a sample of a radioactive substance is crushed the half-life of the substance will
A) decrease
C) remain the same
B) increase
Radioactive Decay
45. The table below gives information about the radioactive decay of carbon-14. [Part
of the table has been left blank for student use.]
What is the amount of the original carbon-14 remaining after 34,200 years?
A) g
B)
g
C)
g
D)
g
46. An archeologist found an ancient skeleton estimated to be 10,000 to 25,000 years
old. Which radioactive isotope would be most useful for finding the age of the
skeleton?
A) carbon-14
C) uranium-238
B) potassium-40
D) rubidium-87
47. What is the approximate age of an igneous rock that contains only one-fourth of
its original potassium-40 content due to radioactive decay?
A) 1.3 × 10 9 years
C) 3.9 × 10 9 years
B) 2.6 × 10 9 years
D) 5.2 × 10 9 years
Radioactive Decay
48. Base your answer to the following question on the map below, which shows an
area of the northwestern United States affected by a major volcanic eruption at
Crater Lake during the Holocene Epoch.
The age of this volcanic eruption was most accurately determined to be Holocene
by measuring the radioactive
A)
B)
C)
D)
potassium in the fine-grained volcanic rock
carbon in trees buried by the ash
uranium in the volcanic ash
rubidium in the igneous glass
49. An ancient bone was analyzed and found to contain carbon-14 that had decayed
for nearly two half-lives. Approximately how old is the bone?
A) 1,400 years
C) 5,600 years
B) 2,800 years
D) 11,000 years
Radioactive Decay
50. Which statement best explains why geologic materials from the Quarternary
Period must be dated by using radioactive isotopes different from the isotopes
used to date materials from the Cambrian Period?
A)
B)
C)
D)
All rocks contain radioactive substances.
Some isotopes decay faster than others.
Not all isotopes form stable decay products.
The decay of atoms occurs as a random event.
51. The diagram below represents the skull of a saber-toothed tiger that died 30,000
years ago.
The age of the skull could be determined most accurately by using
A) uranium-238
C) potassium-40
B) rubidium-87
D) carbon-14
52. If a sample of a radioactive substance is crushed, the half-life of the substance
will
A) decrease
C) remain the same
B) increase
Radioactive Decay
53. The table below gives information about the radioactive decay of carbon-14. [Part
of the table has been left blank for student use.]
What is the amount of the original carbon-14 remaining after 34,200 years?
A) 1/8 g
B) 1/16 g
C) 1/32 g
D) 1/64 g
54. Using radioactive dating methods and mathematical inferences, scientists have
estimated the date of Earth's formation to be approximately
A) 1.1 × 10 6 years ago
C) 3.3 × 10 9 years ago
B) 2.4 × 10 6 years ago
D) 4.6 × 10 9 years ago
55. Radioactive carbon-14 dating has determined that a fossil is 5.7 × 10 3 years old.
What is the total amount of the original C l4 still present in the fossil?
A) 0%
B) 25%
C) 50%
D) 75%
56. A rock contains uranium-238, which has a half-life of 4.5 × 109 years. If the rock
is crushed and heated, the half-life of the uranium-238 it contains will
A) decrease
C) remain the same
B) increase
Radioactive Decay
57. An igneous rock contains one-half of its original amount of potassium-40. The
age of the igneous rock is closest to
A) 0.7 × 10 9 years
C) 2.1 × 10 9 years
B) 1.4 × 10 9 years
D) 2.8 × 10 9 years
58. Which radioactive element would be used to determine the age of late Pleistocene
mastodont bones found in western Connecticut?
A) carbon-14
C) uranium-238
B) potassium-40
D) rubidium-87
59. Which radioactive isotope disintegrates to lead (Pb 206)?
A) C 14
B) K 40
C) Rb 87
D) U 238
Radioactive Decay
60. The diagram below represents the radioactive decay of uranium-238.
Shaded areas on the diagram represent the amount of
A)
B)
C)
D)
undecayed radioactive uranium-238 (U 238)
undecayed radioactive rubidium-87 (Rb 87 )
stable carbon-14 (C 14 )
stable lead-206 (Pb 206)
61. A marine fossil was found to contain one-half of its original quantity of
carbon-14. Approximately how old is this fossil?
A) 5,700 years
C) 17,100 years
B) 11,400 years
D) 22,800 years
62. Two rock units contain the same radioactive substance. Rock A is buried deep
underground; rock B is at the Earth's surface. Which statement best describes the
half-life of the radioactive substance?
A)
B)
C)
D)
The radioactive substance in rock A has a longer half-life.
The radioactive substance in rock B has a longer half-life.
The radioactive substance has the same half-life in rock A and in rock B.
The radioactive substance's half-life has increased with time in rocks A and
B.
Radioactive Decay
Base your answers to questions 63 through 67 on the graph below which shows
the decay rates of four radioactive substances, A, B, C, and D.
63. Decay rates of radioactive substances such as these can be used to determine the
age of rocks and fossils because radioactive decay occurs
A)
B)
C)
D)
at a steady, predictable rate
in all types of sedimentary rock
only when a living organism dies
in all organic and mineral substances
64. The half-life of these radioactive substances depends on the
A) pressure acting on the material B) amount of the material
C) temperature of the material
D) composition of the material
65. When 90 percent of the original mass of isotope D remains, what total percent of
the original mass of isotope B remains?
A) 10%
B) 22%
C) 63%
D) 90%
66. The radioactive substance uranium-238 is represented by
A) A
B) B
C) C
D) D
Radioactive Decay
67. Which radioactive substance has a half-life of 13 billion years?
A) A
B) B
C) C
D) D
68. Compared to the length of time for the first half-life of a sample of a radioactive
isotope, the length of time for the second half-life is
A) less
B) greater
C) the same
69. The age of a Moon rock can be found by analyzing a sample to compare the
relative amounts of
A) U 238 and Pb 206
C) C 14 and Pb 206
B) U 238 and C 14
D) U 238 and Sr 87
70. The half-life of uranium-238 is
A) 4,500 years
C) 4,500,000,000 years
B) 4,500,000 years
D) 45,000,000,000 years
71. Radioactive carbon (C l4 ) would be especially useful in determining the age of
A)
B)
C)
D)
geologically young organic remains
geologically young inorganic remains
Precambrian igneous rocks
extremely small amounts of material
72. Which element is used by Earth scientists for radioactive dating of rocks?
A) cobalt-60
C) potassium-40
B) plutonium-244
D) silicon-28
Radioactive Decay
73. The decay rates of radioactive substances remain constant when the substances
are subjected to different temperature and pressure conditions. The best inference
that can be drawn from this statement is that decay rates are
A)
B)
C)
D)
independent of external factors
independent of the isotope's composition
affected by the mass of the isotope
affected by pressure, but not by temperature
74. The diagram below shows the relative proportions of carbon-14 (C-14) to
nitrogen-14 (N-14) in a rock.
What is the most likely age of the rock?
A) 2.85 × 10 3 B) 5.7 × 10 3
C) 1.3 × 10 9
D) 4.5 × 10 9
75. Which radioactive element has a half-life of 4.5 × 10 9 years?
A) carbon-14
C) uranium-238
B) rubidium-87
D) potassium-40
76. What are the respective decay products of uranium, potassium, and rubidium?
A)
B)
C)
D)
lead (Pb), argon (Ar), and strontium (Sr)
carbon (C), oxygen (O), and nitrogen (N)
hydrogen (H), lithium (Li), and helium (He)
silicon (Si), oxygen (O), and aluminum (Al)
Radioactive Decay
77. One similarity between uranium-238 and carbon-14 is that both
A)
B)
C)
D)
decay at a predictable rate
have the same half-life
are normally found in large quantities in living matter
are found in granite
78. The diagram below represents a clock used to time the half-life of a particular
radioactive substance. The clock was started at 12:00. The shaded portion on the
clock represents the number of hours one-half of this radioactive substance took
to disintegrate.
Which diagram best represents the clock at the end of the next half-life of this
radioactive substance?
A)
B)
C)
D)
79. Which radioactive element would be most useful for determining the age of
clothing that is thought to have been worn 2,000 years ago?
A) carbon-14
C) uranium-238
B) potassium-40
D) rubidium-87
Radioactive Decay
Base your answers to questions 80 through 84 on the graph below which shows
the rate of radioactive decay of element A and the rate at which decay product B is
formed.
80. Two rocks containing radioactive element A were taken from a mine. One had a
mass of 2 grams; the other had a mass of 4 grams. Compared to the half-life of
element A in the 4-gram sample, the half-life of element A in the 2-gram sample
will be
A) shorter
B) longer
C) the same
81. If the radioactive element in a rock sample is potassium-40, which resulting decay
product would be present?
A) Sr 87
B) Ar 40
C) N 14
D) C 12
82. If the half-life of radioactive element A is 10,000 years, for which time interval
would this element be most useful in determining the age of rock?
A) Precambrian
C) Mississippian
B) Devonian
D) Pleistocene
Radioactive Decay
83. An igneous rock contains 2 grams of radioactive element A and 2 grams of decay
product B. How old is the rock sample?
A) 1 half-life
C) 3 half-lives
B) 2 half-lives
D) less than 1 half-life
84. According to the graph, what is the total percentage of radioactive element A
present after 3 half-lives?
A) 12.5%
B) 25.0%
C) 75.0 %
D) 87.5%
85. Which graph best represents the decay rate of potassium-40?
A)
B)
C)
D)
86. If a specimen of a given radioactive substance is reduced in size, its half-life will
A) decrease
C) remain the same
B) increase
87. A geologist uses carbon-14 to determine the age of a sample of material found in
a sedimentary deposit. If the sample shows that 50 percent of the original
carbon-14 is left, what is the approximate age of the sample?
A) 1,400 years
C) 5,600 years
B) 2,800 years
D) 11,200 years
Radioactive Decay
88. Radioactive elements can be used for dating rocks because the disintegration rate
of radioactive elements
A)
B)
C)
D)
is not affected by the environment
is linked to the Earth's motions
can be controlled by scientists
can increase with time
89. Which graph best represents the relationship between the remaining mass of a
radioactive element and time?
A)
B)
C)
D)
90. The graph below shows the relationship between mass and time for four
radioactive elements during radioactive decay.
Which line best represents the decay curve for potassium-40?
A) A
B) B
C) C
D) D
Radioactive Decay
91. What is the half-life of carbon-14?
A) 5.7 years
C) 5,700 years
B) 570 years
D) 5,700,000 years
92. Which radioactive substance shown on the graph below has the longest half-life?
A) A
B) B
C) C
D) D
93. Radiocarbon dating shows that a fossil contains half of its original radioactive
carbon-14. What is the approximate age of the fossil?
A) 5,600 years
C) 16,800 years
B) 11,200 years
D) 4,500,000 years
Radioactive Decay
94. The graph below shows the percent remaining (not decayed) of the original
amount of carbon-14 at different times (A, B, and C) during radioactive decay.
How many half-lives of time are represented by point B along the time axis?
A) 1 half-life
B) 2 half-lives C) 3 half-lives D) 4 half-lives
95. Why are radioactive materials useful for measuring geologic time?
A) The disintegration of radioactive materials occurs at a predictable rate.
B) The half-lives of most radioactive materials are less than five minutes.
C) The ratio of decay products to undecayed material remains constant in
sedimentary rocks.
D) Measurable samples of radioactive materials are easily collected from most
rock types.
Radioactive Decay
96. Base your answer on the diagram below which represents a cube of radioactive
material (figure A) cut into eight identical cubes (figure B).
Compared to the half-life of the material in figure A, the half-life of the material
in each small cube in figure B is
A) 1/8 as long
C) 8 times longer
B) 1/64 as long
D) the same
97. Which radioactive substance would probably be used in dating the recent remains
of a plant found in sedimentary deposits?
A) carbon-14
C) rubidium-87
B) potassium-40
D) uranium-238
98. Which radioactive substance has the longest half-life?
A) carbon-14
C) rubidium-87
B) potassium-40
D) uranium-238
99. One half of the radioactive potassium-40 (K 40 ) in an igneous rock has decayed to
argon-40 (Ar 40 ). About how many years ago was this rock formed?
A) 1.4 × 10 9
B) 2.8 × 10 9
C) 4.2 × 10 9
D) 9.8 × 10 9
Radioactive Decay
100. A rock sample containing the radioactive isotope potassium-40 is calculated to
be 4.2 × 10 9 years old. How much of the original potassium-40 would be left in
this rock sample?
A) 0
B) 1/8
C) 1/4
D) 1/2
101. The element K 40 radioactively decays to Ar 40 . The diagram below shows a
model of the relative amounts of K 40 and Ar 40 remaining after one half-life.
Which diagram best illustrates the relative amounts of K 40 and Ar 40 remaining
after two half-lives?
A)
B)
C)
D)
102. Which radioactive element would a scientist most likely have used to date the
age of a fossil that is 10,000 years old?
A) potassium-40
C) uranium-238
B) carbon-14
D) rubidium-87
103. A rock sample contained 8 grams of potassium-40 (K 40 ) when it was formed,
but now contains only 4 grams due to radioactive decay. What is the
approximate age of this rock?
A) 0.7 × 10 9 years
C) 2.8 × 10 9 years
B) 1.4 × 10 9 years
D) 5.6 × 10 9 years