Lesson: Radioactive Decay & Dating
Prentice Hall Conceptual Physics
Chapter 39, Atomic and Nuclear Physics
Section 39.2 Radioactive Decay
Section 39.4 Radioactive Isotopes
Section 39.5 Radioactive Half-Life
Support provided by:
Context of Lesson
The purpose of this lesson is to provide students with a basic understanding of radioactive
decay and its application—radiometric dating, in this instance—in the earth sciences. The
activity can be used to teach observation skills, data collection, interpretation of graphs,
organization of data, analyzing and mathematical skills, and making evidence based
conclusions. This lesson will build on the students’ study of atoms in sections 39.2, 39.4,
and 39.5 of Prentice Hall Conceptual Physics. The lesson will be taught over the course
of one class period, and the knowledge gained in this lesson will lay the foundation for
understanding scientists’ use of physics chemistry to study rocks, fossils, and the dating
(or “aging”) of them.
Main Goals/Objectives
Students will be able to:
 Explain radioactivity, including the concepts of isotopes, radioactive
decay, and half-lives.
 Collect, analyze, and interpret data, read graphs, and report results.
General Alignment to Standards
Mathematics State Goal 8. Use algebraic and analytical methods to identify
and describe patterns and relationships in data, solve problems and predict results.
D. Use algebraic concepts and procedures to represent and solve problems.
ILS 8.D.4 Formulate and solve linear and quadratic equations and
linear inequalities algebraically and investigate nonlinear inequalities
using graphs, tables, calculators and computers.
Science State Goal 11. Understand the processes of scientific inquiry and
technological design to investigate questions, conduct experiments and solve
problems.
A. Know and apply the concepts, principles and processes of scientific
inquiry.
1
ILS 11.A.4c Collect, organize and analyze data accurately and
precisely.
Science State Goal 12. Understand the fundamental concepts, principles and
interconnections of the life, physical and earth/space sciences.
E. Know and apply concepts that describe the features and processes of the
Earth and its resources.
ILS 12.E.4b Describe how rock sequences and fossil remains are used
to interpret the age and changes in the Earth.
Teacher Lab Preparation
In addition to having a clock (with a second hand) for the entire class and one calculator
per group, 48 small cards (each about 2x2 inches) are required. They may be cut from
cardboard or construction paper, preferably with a different color on opposite sides, and
each card or button should be marked with "U-235" on one colored side and "Pb-207" on
the opposite side.
Materials
For each group of 5 or 6 students:
 Watch or clock that keeps time (seconds required).
 Materials from the Harris Educational Loan Program:
o 300 Million Years Ago in Illinois Experience Box, or
o Fossil Plants of Illinois Exhibit Case
 One calculator for each group.
 48 small cards (each about 2x2 inches) for each group. The cards may be
cut from cardboard or construction paper, preferably with a different color
on opposite sides, each marked with "U-235" all on one colored side and
"Pb-207" on the opposite side.
 Copies of the Understanding Radioactive Decay and Ages of Rocks &
the Fossils in Them activity sheets; 1 copy of each activity sheet per
student (NOTE: Blank activity sheets are provided at the end of the
lesson).
 Transparency of Uranium-235 decay series (attached) to project to the
class.
 Optional if students are not graphing Uranium-235 atoms over time:
transparencies of graphs (attached).
 Optional but recommended: Internet access to view Dr. Meenakshi
Wadhwa’s video on radioactivity and radiometic dating at
http://www.fieldmuseum.org/evolvingplanet/precambrian_15.asp.
Lesson Introduction
This lesson should follow a discussion of subatomic particles and atoms, as presented in
sections 39.2, 39.4, and 39.5 of Prentice Hall Conceptual Physics textbook.
2
Introduce students to the concepts of radiation and radioactivity: radioactive atoms emit
radiation because their nuclei are unstable—a process called radioactive decay. As
indicated in Section 39.4 of the textbook, unstable radioactive atoms (called
radioisotopes) undergo radioactive decay until they form stable non-radioactive atoms,
often of a different element.
For example, uranium-235 is an unstable radioisotope that has 92 protons and 143
neutrons in the nucleus of each atom. As a result of radioactive decay, it emits several
particles, ending up with 82 protons and 125 neutrons. This is a stable condition, and
there are no more changes in the atomic nucleus. A nucleus with that number of protons
is called lead (Pb). The protons (82) and neutrons (125) total 207. This particular form of
lead is called lead-207. Uranium-235 is the parent radioisotope of lead-207, which is the
daughter radioisotope.
Explain that radioactive decay rates are measured in half-lives. A half-life is the time
required for one-half of a radioisotope’s nuclei to decay into its products. For example,
the half-life of strontium-90 is 29 years. If you had 10.0g of strontium-90 today, 29 years
from now you would have 5.0g left. The half-life of uranium-235 is 704 million (that’s
704,000,000!) years. In other words, during 704 million years, half the U-235 atoms that
existed at the beginning of that time will decay to lead-207. Some half lives are several
billion years long, and others are as short as a ten-thousandth of a second.
Explain to your students that the “decay” presented in this activity is greatly simplified
from the actual decay of uranium-235. Uranium-235 does not become lead-207 in a
single step, but rather changes into a radioactive daughter isotope, thorium-231. The
thorium then decays into another radioisotope, which then decays into another
radioisotope, etc. The entire process is called a decay series and is shown in the attached
diagram (figure 2). You may use this diagram to show the atoms involved as the uranium
decays into lead.
For more advanced discussion, you may use figure 2 as you explain the emission of alpha
particles and beta particles from the nucleus. Nuclei of radioactive atoms are unstable
and they are unstable because there are either too many protons or too many neutrons in
the nucleus. An atom can change the ratio of protons to neutrons by ejecting an alpha
particle (2 protons and 2 neutrons) from the nucleus. This is called alpha decay. Also, an
atom may change the ratio of protons to neutrons when a neutron changes into a proton
with the simultaneous ejection of an electron from the nucleus. This is called beta decay.
In the uranium-235 decay series, there are alpha and beta emissions.
Because of the constant decay rates associated with radioactive atoms, they can be used
to determine the ages of rocks or fossils that contain the atoms. Many rocks contain small
amounts of unstable radioisotopes. When the amounts of parent and daughter
radioisotopes can be accurately measured, and when the half-life rate is known, the
ratio can be used to determine the age of the rock or fossil.
3
Some students may wonder how scientists know that there is no daughter nucleus in the
original mineral when it is first formed. You may point out that scientists don’t just
examine one mineral and they don’t measure the amount of just two isotopes. To
accurately determine the age of the rock, they must look at stable isotopes of daughter
isotopes that were formed with the original radioactive material. Then they must look at
the isotope ratios in other minerals. Finally, all of the data are compiled and analyzed to
determine the age of the minerals.
Uranium-235 is only one isotope that is used to date rocks and minerals. Table 1 lists
common parent isotopes (and their half-lives) used for radiometric dating. You might
want to copy this and hand it out or project it on a screen for your class.
These concepts can be reviewed by watching the video that features Dr. Meenakshi
Wadhwa at http://www.fieldmuseum.org/evolvingplanet/precambrian_15.asp You may
want to show this video in parts, stopping after a short section to explain what is going on
and to let the information sink in. After you show the video in sections, you might want
to repeat it so that students see the segment uninterrupted.
Note to Teacher
This is not a traditional cookbook lab and lacks a written procedure that the students can
follow. This may be extremely frustrating for most students. You need to support and
monitor their inquiry without directing it. Resist the temptation to tell them the answers;
rather, answer their questions with a guiding question.
Some students have been taught that the increments along graph axes must be constant
and unbroken. These students will have questions when they first see the logarithmic
scale on the fraction of uranium-235 remaining versus age of the rock graph. You may
have to help students understand the construction of this graph.
Lesson Modifications
Instead of 4-6 students per group, this activity could be done using 2 or 3 students per lab
group. Of course, this would require additional sets of 48 cards. If you can find enough
index cards, stock paper, or thick white construction paper, you can cut (or, students can
cut if you have enough scissors) the cards and then have students carefully make the
symbols on each side of the card. At the end of the activity, collect the cards to reuse
them for another class or for the following year.
A color indicator should be used so that students know when a card is representing a
stable atom, 207Pb, and when it is representing a radioactive atom, 235U. You should tell
students that stable atoms do not change, and that their 207Pb cards should not be turned
back—those cards should be left alone. Choose a color that you think best represents an
unstable particle, perhaps red, and a color that you think best represents stability, perhaps
blue. Use these colors to write the 235U and 207Pb symbols, respectively. Emphasize that
one color is to be turned over and one color must not be touched.
4
Many students pick up the concept of half-life quickly, and shortening the time interval
of the card turning would keep these students engaged. Also, shortening the time
intervals would leave more time for graphing, answering questions, and discussion. To
greatly shorten the activity, use 48-second time intervals instead of 2-minute time
intervals. During the first 48-second interval, have students flip the cards every 2
seconds. During the next 48-second interval, flip the cards every 4 seconds. In the third
48-second interval, flip the cards every 8 seconds, and in the fourth and final interval, flip
the cards every 16 seconds.
An alternative to having lab groups time the card turning would be to have one official
timer (which could be you). The timer would announce when to flip cards and when the
time interval is complete. This type of organization further reduces the activity time and
allows the teacher more control in the case of mistakes. The teacher can check student
progress at the end of each interval, walking among the lab groups and checking the
status of the cards while students are completing their data tables.
Activity – Part 1 (Understanding Radioactive Decay)
Uranium-235 (also written as U-235) is found in many rocks. Unless the rock is heated to
a very high temperature, both the U-235 and its daughter lead-207 (also written as Pb207) remain in the rock. A scientist can compare the proportion of U-235 atoms to the
Pb-207 atoms produced from it and determine the age of the rock.
The following activity will demonstrate the technique of radioactive dating!
Divide the class into groups consisting of 4 to 6 students. Each group receives 48 small
pieces of paper (about 2x2 inches), with U-235 written on one side and Pb-207 written on
the other side. Also distribute the Understanding Radioactive Decay activity sheets
(one sheet per student).
Each group should place each marked piece of paper so that "U-235" is showing. This
represents uranium-235, which emits a series of particles from the nucleus as it decays to
Pb-207. When each team is ready with the 48 pieces all showing "U-235", a timed twominute interval should start. During the first two minute interval, each team turns over
one piece of paper every 5 seconds. After the first two minutes, 24 of the U-235 pieces,
or half, will have been turned over to now show Pb-207. This represents one "half-life" of
U-235; the half-life is the time for half the nuclei to change from the parent U-235 to the
daughter Pb-207.
A second two-minute interval begins. During the second interval, the team should turn
over half of the U-235 that was left after the first interval. To do so, students will have to
turn over one piece of paper every 10 seconds. Emphasize that the rate of change from U235 to Pb-207 changes from the first interval, but the overall result is the same: after the
two minutes, half of the U-235 pieces will have been turned over to show Pb-207. This
represents the second half-life.
5
There are now 12 pieces of paper with “U-235” showing. Continue through a third twominute interval, turning over one piece of the remaining U-235 every 20 seconds. After
two minutes, groups will end with 6 U-235.
Finally, continue with a fourth two-minute interval, turning over one piece of the
remaining U-235 every 40 seconds. After two minutes, groups will end with 3 U-235.
After all the timed intervals have occurred, the task now for each team is to determine
how many timed half-lives the set of pieces they are looking at has experienced. Ask
students to record this information in the appropriate column on the activity sheet.
NOTE: The number of half-lives equals the number of timed intervals.
The half life of U-235 is 704 million years. Based on the proportion of U-235 to Pb-207
present after the 4 timed intervals (i.e., half-lives), ask each team to determine how many
million years are represented by the proportion of U-235 and Pb-207 present. Ask
students to record this information in the appropriate column on the activity sheet.
NOTE: The age equals the number of half-lives multiplied by 704 million years.
6
Understanding Radioactive Decay
Name ______________________________
Period _____
Partners ________________________________________________________________
Procedure:
1) Place each marked piece of paper so that "U-235" is showing. Uranium-235 emits a
series of particles from the nucleus as it decays to Pb-207.
Time 1: Start a timed two-minute interval and turn over one piece of paper every 5
seconds. Only turn cards that show “U-235” and leave the cards that show “Pb-207”
untouched on the table. After the interval, record the number of “U-235” and “Pb-207”
cards showing and note the number of half-lives that just occurred in the “Time 1” line of
the data table. (You may change the time interval to 48 seconds. If so, cross out “twominutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 2 seconds. Then, cross out “5 seconds” and write “2 seconds”
instead.)
After the first two minutes, 24 of the U-235 pieces, or half, will have been turned over to now show Pb207. This represents one "half-life" of U-235; the half-life is the time for half the nuclei to change from the
parent U-235 to the daughter Pb-207.
2) Time 2: Begin a second two-minute interval. During the second interval, turn over one
piece of “U-235” paper every 10 seconds. Only turn cards that show “U-235” and leave
the cards that show “Pb-207” untouched on the table. After the interval, record the
number of “U-235” and “Pb-207” cards showing and note the number of half-lives that
just occurred in the “Time 2” line of the data table. (Again, you may change the time
interval to 48 seconds, if you have done so for the last interval. If so, cross out “twominutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 4 seconds. Then, cross out “10 seconds” and write “4 seconds”
instead.)
Emphasize that the rate of change from U-235 to Pb-207 changes from the first interval, but the overall
result is the same: after the second two-minute interval, half of the 24 U-235 pieces will have been turned
over to now show a total of 12 U-235 cards and 36 Pb-207 cards. This represents the second half-life.
3) Time 3: Continue through a third two-minute interval, turning over one piece of the
remaining U-235 every 20 seconds. Only turn cards that show “U-235” and leave the
cards that show “Pb-207” untouched on the table. After the interval, record the number
of “U-235” and “Pb-207” cards showing and note the number of half-lives that just
occurred in the “Time 3” line of the data table. (Again, you may change the time interval
to 48 seconds, if you have done so for the previous two intervals. If so, cross out “two-
7
minutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 8 seconds. Then, cross out “20 seconds” and write “8 seconds”
instead.)
After two minutes, groups will end with 6 U-235 cards and 42 Pb-207 cards. This represents half-life
number three.
4) Continue with a fourth two-minute interval, turning over one piece of the remaining U235 every 40 seconds. Only turn cards that show “U-235” and leave the cards that show
“Pb-207” untouched on the table. After the interval, record the number of “U-235” and
“Pb-207” cards showing and note the number of half-lives that just occurred in the “Time
4” line of the data table. (For this last interval, you may change the time to 48 seconds, if
you have done so for the previous three intervals. If so, cross out “two-minutes” and
write “48-seconds” in its place. If you do this, you will be turning over a piece of paper
every 16 seconds. Then, cross out “40 seconds” and write “16 seconds” instead.)
After two minutes, groups will end with 3 U-235 and 45 Pb-207; this represents the fourth half-life.
5) Now, based on the number of half-lives, determine the age of the sample.
For each timed interval, the age equals the number of half-lives multiplied by 704 million years.
6) (Optional) Make two graphs of your data. On one graph place the number of uranium235 cards on the y-axis and the time elapsed when the cards were counted on the x-axis.
For the second graph, use a calculator to determine the base-ten logarithm (“log
function”) of the number of uranium-235 cards left. Then graph log (card number) on the
y-axis and the time elapsed when the cards were counted on the x-axis.
8
Table - Decay of U-235 to Pb-207
Time
elapsed
(seconds)
Time 0
Number of Number of
“U-235”
“Pb-207”
Cards
Cards
Age
(=No. of Half-Lives
x 704 million years)
0
0
0
24
1
704 million years
0
48
Time 1
Number of
Half-Lives
120
(or 48)
24
Time 2
240
(or 96)
12
36
2
1408 million years
(=1.408 billion years)
Time 3
360
(144)
6
42
3
2112 million years
(=2.112 billion years)
Time 4
480
(or 192)
3
45
4
2816 million years
(=2.816 billion years)
9
Activity – Part 2 (Ages of Rocks & the Fossils in Them)
Begin the second part of the activity by displaying the 300 Million Years Ago in Chicago
Experience Box or the Fossil Plants of Illinois Exhibit Case from The Field Museum’s
Harris Educational Loan Program. Explain that the fossils are found in rocks. Once taken
to a laboratory and removed, they provide clues to help scientists understand the history
of life on Earth, but key to this understanding is knowing the age of fossils. The fossils in
the boxes/cases are from Illinois—just 60 miles southwest of Chicago—and they are 300
million years old! But how do scientists determine the ages of fossils?
The following activity will demonstrate the dating of fossil-bearing rocks!
Distribute the Ages of Rocks & the Fossils in Them activity sheet to students. The block
diagram represents a section of the earth. Now…
1) Explain that, in the rocks depicted in the diagram, the ratio of U-235 to Pb207 atoms in the pegmatite is 1:1. Using the same reasoning about proportions
as in Part 1 above, ask students to determine how old the pegmatite and the
granite are. Remember, the half-life of U-235 is 704 million years. Ask
students to write the age of the pegmatite beside the names of the rocks in the
list below the diagram.
The pegmatite is 704 million years old (i.e., it formed 704,000,000 years ago).
2) By plotting the half-life on a type of scale known as a logarithmic scale, it is
possible for students to find the ages of rocks based on the ratios of U-235 to
Pb-207 atoms. Such a graph is especially helpful for ratios of parent isotope to
daughter isotope that represent less than one half life. This scale (“Figure 4.
Half life of U-235”) can be found on the last page of this lesson.
Present the following example to the students:
If geochemical analyses determine that the volcanic ash that is in the siltstone
has a ratio of U-235:Pb-207 of 47:3, find its age. To find its age using the
logarithmic scale…
STEP 1: 47 + 3 = 50;
STEP 2: 47 / 50 = 0.94 = 94%
STEP 3: Use the logarithmic scale to find the age.
The ash in the siltstone is 70 million years old.
3) The U-235:Pb-207 ratio in the granite is 1:3, and the U-235:Pb-207 ratio in
the basalt is 7:3. Using the steps outlined directly above, find the ages of the
10
granite and the basalt. Ask students to write the age of the siltstone, granite,
and basalt beside the names of the rocks in the list below the diagram.
The basalt is 350 million years old.
STEP 1: 7 + 3 = 10;
STEP 2: 7 / 10 = 0.70 = 70%
STEP 3: Use the logarithmic scale to find the age.
The granite is 1400 million years old.
STEP 1: 1 + 3 = 4;
STEP 2: 1 / 4 = 0.25 = 25%
STEP 3: Use the logarithmic scale to find the age.
11
Ages of Rocks & the Fossils in Them
Name ______________________________
Period _____
Partners ________________________________________________________________
Procedure:
1) In the rocks depicted in the diagram below, the ratio of U-235 to Pb-207 atoms in the
pegmatite is 1:1. Determine how old the pegmatite and the granite are. Remember, the
half-life of U-235 is 704 million years. Write the age of the pegmatite in the blank beside
the name of the rock in the list below the diagram.
The pegmatite is 704 million years old (i.e., it formed 704,000,000 years ago).
2) By plotting the half-life on a type of scale known as a logarithmic scale, it is possible
to find the ages of rocks based on the ratios of U-235 to Pb-207 atoms. For example…
If geochemical analyses determine that the volcanic ash that is in the siltstone has a ratio
of U-235:Pb-207 of 47:3, you can use the scale to find the age…
STEP 1: 47 + 3 = 50;
STEP 2: 47 / 50 = 0.94 = 94%
STEP 3: Use the logarithmic scale to find the age.
ANSWER: The ash in the siltstone is 70 million years old.
3) The U-235:Pb-207 ratio in the granite is 1:3, and the U-235:Pb-207 ratio in the basalt
is 7:3. Using the same steps in #2 above, find the ages of the granite and the basalt and
write their ages in the blanks below.
The basalt is 350 million years old:
STEP 1: 7 + 3 = 10;
STEP 2: 7 / 10 = 0.70 = 70%
STEP 3: Use the logarithmic scale to find the age.
The granite is 1400 million years old:
STEP 1: 1 + 3 = 4;
STEP 2: 1 / 4 = 0.25 = 25%
STEP 3: Use the logarithmic scale to find the age.
12
FOSSIL OCCURRENCES:
Bacteria remains are found in the slate.
Fossils of trilobites (ancient relatives of insects) are found in the limestone.
Dinosaur bones are found in the siltstone.
ROCK UNIT
Most Recent Rock Formed: Siltstone
RADIOMETRIC AGE
70 Million Years Ago
Basalt
350 Million Years Ago
Limestone
Pegmatite
704 Million Years Ago
Sandstone
Slate
Oldest Rock: Granite
1400 Million Years Ago
13
Questions
1) Based on the available radiometric ages, can you determine the possible age of the
rock unit that has the bacteria? What is it? Why can't you say exactly what the age of the
rock is?
The slate that contains the bacteria is between 704 million years and 1400 million years
old, because the pegmatite is 704 million years old and the granite is 1400 million years
old. The slate itself has not been radiometrically dated, so can only be bracketed between
the ages of the granite and the pegmatite.
2) Can you determine the possible age of the rock unit that has trilobites? What is it?
Why can't you say exactly what the age of the rock is?
The limestone with the trilobites overlies the pegmatite; it underlies the basalt. Therefore,
limestone must be younger than 704 million years (the age of the pegmatite) and older
than 350 million years (the age of the basalt). The limestone itself is not radiometrically
dated, so can only be bracketed between the ages of the granite and the pegmatite.
3) What is the age of the rock that contains the dinosaur fossils? Why can you be more
precise about the age of this rock than you could about the ages of the rock that has the
trilobites and the rock that contains fossilized bacteria?
The dinosaur fossils are definitely younger than 350 million years because the siltstone
formed on top of the basalt. But we can be more precise and say that the dinosaur remains
are approximately 70 million years old because they are found in shale and siltstone that
contain volcanic ash, which was radiometrically dated at 70 million years. Any dinosaur
found below the volcanic ash may be a little older than 70 million years, and any found
above may be a little younger than 70 million years. The age of the dinosaur fossils can
be determined more closely than those of the bacteria and trilobites because the rock unit
that contains the dinosaur is radiometrically dated, whereas that of the other fossils could
not.
4) From your first graph (U-235 atoms (cards) on the y-axis and time on the x-axis), is
there a relationship between the rate of decay and the number of U-235 atoms left? How
will the radioactivity change over time?
As the number of cards decreases, the rate of decay decreases proportionally. For
example, when the number of cards decreases by one-half, the rate of decay decreases by
one-half. (This is an example of a first-order reaction and students may review this again
later in the unit on reaction rates.) The radioactivity will decrease just as the rate of
14
decay decreases. That is, fewer particles and less energy will be emitted over time as the
sample decays.
5) What is the shape of the graph with log (U-235 atoms (cards)) on the y-axis versus
time on the x-axis?
This is a linear graph. It is an identifying characteristic of a first order reaction.
15
16
Table 1
Primary Parent and Daughter Isotopes
Used to Determine the Ages of Rocks and Minerals
Parent Isotope
(Radioactive)
40
K
87
Rb
147
Sm
176
Lu
187
Re
232
Th
235
U
238
U
Daughter Isotope
(Stable)
40
Ar
87
Sr
143
Nd
176
Hf
187
Os
208
Pb
207
Pb
206
Pb
Half-life
(Millions of Years)
1 250
48 800
106 000
35 900
43 000
14 000
704
4 470
From Dalrymple, G. Brent, The Age of the Earth, Stanford University Press, 1991
17
18
19
Understanding Radioactive Decay
Name ______________________________
Period _____
Partners ________________________________________________________________
Procedure:
1) Place each marked piece of paper so that "U-235" is showing. Uranium-235 emits a
series of particles from the nucleus as it decays to Pb-207.
Time 1: Start a timed two-minute interval and turn over one piece of paper every 5
seconds. Only turn cards that show “U-235” and leave the cards that show “Pb-207”
untouched on the table. After the interval, record the number of “U-235” and “Pb-207”
cards showing and note the number of half-lives that just occurred in the “Time 1” line of
the data table. (You may change the time interval to 48 seconds. If so, cross out “twominutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 2 seconds. Then, cross out “5 seconds” and write “2 seconds”
instead.)
2) Time 2: Begin a second two-minute interval. During the second interval, turn over one
piece of “U-235” paper every 10 seconds. Only turn cards that show “U-235” and leave
the cards that show “Pb-207” untouched on the table. After the interval, record the
number of “U-235” and “Pb-207” cards showing and note the number of half-lives that
just occurred in the “Time 2” line of the data table. (Again, you may change the time
interval to 48 seconds, if you have done so for the last interval. If so, cross out “twominutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 4 seconds. Then, cross out “10 seconds” and write “4 seconds”
instead.)
3) Time 3: Continue through a third two-minute interval, turning over one piece of the
remaining U-235 every 20 seconds. Only turn cards that show “U-235” and leave the
cards that show “Pb-207” untouched on the table. After the interval, record the number
of “U-235” and “Pb-207” cards showing and note the number of half-lives that just
occurred in the “Time 3” line of the data table. (Again, you may change the time interval
to 48 seconds, if you have done so for the previous two intervals. If so, cross out “twominutes” and write “48-seconds” in its place. If you do this, you will be turning over a
piece of paper every 8 seconds. Then, cross out “20 seconds” and write “8 seconds”
instead.)
20
4) Continue with a fourth two-minute interval, turning over one piece of the remaining U235 every 40 seconds. Only turn cards that show “U-235” and leave the cards that show
“Pb-207” untouched on the table. After the interval, record the number of “U-235” and
“Pb-207” cards showing and note the number of half-lives that just occurred in the “Time
4” line of the data table. (For this last interval, you may change the time to 48 seconds, if
you have done so for the previous three intervals. If so, cross out “two-minutes” and
write “48-seconds” in its place. If you do this, you will be turning over a piece of paper
every 16 seconds. Then, cross out “40 seconds” and write “16 seconds” instead.)
5) Now, based on the number of half-lives, determine the age of the sample.
6) (Optional) Make two graphs of your data. On one graph place the number of uranium235 cards on the y-axis and the time elapsed when the cards were counted on the x-axis.
For the second graph, use a calculator to determine the base-ten logarithm (“log
function”) of the number of uranium-235 cards left. Then graph log (card number) on the
y-axis and the time elapsed when the cards were counted on the x-axis.
21
Table - Decay of U-235 to Pb-207
Time
elapsed
(seconds)
Number of Number of
“U-235”
“Pb-207”
Cards
Cards
Time 0
48
Time 1
24
0
Time 2
Time 3
Time 4
22
Number of
Half-Lives
Age
(=No. of Half-Lives
x 704 million years)
0
0
Ages of Rocks & the Fossils in Them
Name ______________________________
Period _____
Partners ________________________________________________________________
Procedure:
1) In the rocks depicted in the diagram below, the ratio of U-235 to Pb-207 atoms in the
pegmatite is 1:1. Determine how old the pegmatite and the granite are. Remember, the
half-life of U-235 is 704 million years. Write the age of the pegmatite in the blank beside
the name of the rock in the list below the diagram.
2) By plotting the half-life on a type of scale known as a logarithmic scale, it is possible
to find the ages of rocks based on the ratios of U-235 to Pb-207 atoms. For example…
If geochemical analyses determine that the volcanic ash that is in the siltstone has a ratio
of U-235:Pb-207 of 47:3, you can use the scale to find the age…
STEP 1: 47 + 3 = 50;
STEP 2: 47 / 50 = 0.94 = 94%
STEP 3: Use the logarithmic scale to find the age.
ANSWER: The ash in the siltstone is 70 million years old.
3) The U-235:Pb-207 ratio in the granite is 1:3, and the U-235:Pb-207 ratio in the basalt
is 7:3. Using the same steps in #2 above, find the ages of the granite and the basalt and
write their ages in the blanks below.
23
FOSSIL OCCURRENCES:
Bacteria remains are found in the slate.
Fossils of trilobites (ancient relatives of insects) are found in the limestone.
Dinosaur bones are found in the siltstone.
ROCK UNIT
Most Recent Rock Formed: Siltstone
RADIOMETRIC AGE
__________
Basalt
__________
Limestone
Pegmatite
__________
Sandstone
Slate
Oldest Rock: Granite
__________
24
Questions
1) Based on the available radiometric ages, can you determine the possible age of the
rock unit that has the bacteria? What is it? Why can't you say exactly what the age of the
rock is?
2) Can you determine the possible age of the rock unit that has trilobites? What is it?
Why can't you say exactly what the age of the rock is?
3) What is the age of the rock that contains the dinosaur fossils? Why can you be more
precise about the age of this rock than you could about the ages of the rock that has the
trilobites and the rock that contains fossilized bacteria?
4) From your first graph (U-235 atoms (cards) on the y-axis and time on the x-axis), is
there a relationship between the rate of decay and the number of U-235 atoms left? How
will the radioactivity change over time?
5) What is the shape of the graph with log (U-235 atoms (cards)) on the y-axis versus
time on the x-axis?
25
Figure 1
26
Figure 2
27
Table 1
Primary Parent and Daughter Isotopes
Used to Determine the Ages of Rocks and Minerals
Parent Isotope
(Radioactive)
40
K
87
Rb
147
Sm
176
Lu
187
Re
232
Th
235
U
238
U
Daughter Isotope
(Stable)
40
Ar
87
Sr
143
Nd
176
Hf
187
Os
208
Pb
207
Pb
206
Pb
Half-life
(Millions of Years)
1 250
48 800
106 000
35 900
43 000
14 000
704
4 470
From Dalrymple, G. Brent, The Age of the Earth, Stanford University Press, 1991
28
29
30