Science

Science

EDS 1021 Week 6 Interactive Assignment

Radiometric Dating

Objective: Using a simulated practical application, explore the concepts of radioactive decay and the half-life of

radioactive elements, and then apply the concept of radiometric dating to estimate the age of various objects.

Background: Review the topics Half-Life, Radiometric Dating, and Decay Chains in Chapter 12 of The Sciences.

Instructions:

1. PRINT a hard copy of this entire document, so that the experiment instructions may be easily referred to,

and the data tables and questions (on the last three pages) can be completed as a rough draft.

2. Download the Radiometric Dating Game Answer Sheet from the course website. Transfer your data

values and question answers from the completed rough draft to the answer sheet. Be sure to put your

NAME on the answer sheet where indicated. Save your completed answer sheet on your computer.

3. SUBMIT ONLY the completed answer sheet, by uploading your file to the digital drop box for the

assignment.

Introduction to the Simulation

1. After reviewing the background information for this assignment, go to the website for the interactive

simulation “Radioactive Dating Game” at http://phet.colorado.edu/en/simulation/radioactive-dating-game.

Click on DOWNLOAD to run the simulation locally on your computer.

2. Software Requirements: You must have the latest version of Java software (free) loaded on your computer

to run the simulation. If you do not or are not sure if you have the latest version, go to

http://www.java.com/en/download/index.jsp .

3. Explore and experiment on the 4 different “tabs” (areas) of the simulation. While playing around, think about

how the concepts of radioactive decay are being illustrated in the simulation.

Half Life Tab – observe a sample of radioactive atoms decaying – Carbon-14, Uranium-238, or ? (a custom-

made radioactive atom). Clicking on the “add 10” button adds 10 atoms at a time to the “decay area”. There

are a total of 100 atoms in the bucket, so clicking the “add 10” button 10 times will empty the bucket into the

decay area. Observe the pie chart and time graph as atoms decay. You can PAUSE, STEP (buttons at the

bottom of the screen) the simulation in time as atoms are decaying, and RESET the simulation.

Decay Rates Tab – Similar to the half-life tab, but different! Atom choices are carbon-14 and uranium-238.

The bucket has a total of 1000 atoms. Drag the slide bar on the bucket to the right to increase the number

of atoms added to the decay area. Observe the pie chart and time graph as atoms decay. Note that the

graph for the Decay Rates tab provides different information than the graph for the Half Life tab. You can

PAUSE, STEP (buttons at the bottom of the screen) the simulation in time as atoms are decaying, and

RESET the simulation.

Measurement Tab – Use a probe to virtually measure radioactive decay within an object – a tree or a

volcanic rock. The probe can be set to detect either the decay of carbon-14 atoms, or the decay of uranium-

238 atoms. Follow prompts on the screen to run a simulation of a tree growing and dying, or of a volcano

erupting and creating a rock, and then measuring the decay of atoms within each object.

Dating Game Tab – Use a probe to virtually measure the percentage of radioactive atoms remaining within

various objects and, knowing the half-life of radioactive elements being detected, estimate the ages of

objects. The probe can be set to either detect carbon-14, uranium-238, or other “mystery” elements, as

appropriate for determining the age of the object. Drag the probe over an object, select which element to

measure, and then slide the arrow on the graph to match the percentage of atoms measured by the probe.

The time (t) shown for the matching percentage can then be entered as the estimate in years of the object’s

age.

After playing around with the simulation, conduct the following four (4) short experiments. As you conduct

the experiments and collect data, fill in the data tables and answer the questions on the last three pages of

this document.

Experiment 1: Half Life

1. Click on the Half Life tab at the top of the simulation screen.

2. Procedure:

Part I – Carbon-14

a. Click the blue “Pause” button at the bottom of the screen (i.e., set it so that it shows the “play” arrow). Click the “Add 10” button below the “Bucket o’ Atoms” repeatedly, until there are no more atoms left in the bucket. There are now 100 carbon-14 atoms in the decay area.

b. The half-life of carbon-14 is about 5700 years. Based on the definition of half-life, if you left these 100 carbon-14 atoms to sit around for 5700 years, what is your prediction of how many carbon-14 atoms will decay into the stable element nitrogen-14 during that time? Write your prediction in the “prediction” column for the row labeled “carbon-14”, in data table 1.

c. Click the blue “Play” arrow at the bottom of the screen. As the simulation runs, carefully observe what is happening to the carbon-14 atoms in the decay area, and the graphs at the top of the screen (both the pie chart and the time graph). Once all atoms have decayed into the stable isotope nitrogen-14, click the blue “Pause” button at the bottom of the screen (i.e., set it so that it shows the “play” arrow), and “Reset All Nuclei” button in the decay area.

d. Repeat step c. until you have a good idea of what is going on in this simulation. e. Repeat step c. again, but this time, watch the graph at the top of the window carefully, and click

“pause” when TIME reaches 5700 years (when the carbon-14 atom moving across the graph reaches

the red dashed line labeled HALF LIFE on the TIME graph). f. If you do NOT pause the simulation on or very close to the red dashed line, click the “Reset All Nuclei”

button and repeat step e. g. Once you have paused the simulation in the correct spot, look at the pie graph and determine the

number of nuclei that have decayed into nitrogen-14 at Time = HALF LIFE. Write this number in data table 1, in the row labeled “carbon-14”, under “trial 1”.

h. Click the “Reset All Nuclei” button in the decay area. i. Repeat steps e through h for two more trials. For each trial, write down in data table 1, the number of

nuclei that have decayed into nitrogen-14 at Time = HALF LIFE, in the row labeled “carbon-14”, under “trial 2” and “trial 3” respectively.

Part II – Uranium-238

a. Click “reset all” on the right side of the screen in the Decay Isotope box, and click “yes” in the box that pops up. Click on the radio button for uranium-238 in the Decay Isotope box. Click the blue “Pause”

button at the bottom of the screen (i.e., set it so that it shows the “play” arrow). Click the “Add 10” button below the “Bucket o’ Atoms” repeatedly, until there are no more atoms left in the bucket. There are now 100 uranium-238 atoms in the decay area.

b. The half-life of uranium-238 is 4.5 billion years!* Based on the definition of half-life, if you left these 100 uranium-238 atoms to sit around for 4.5 billion years, what is your prediction of how many uranium atoms will decay into lead-206 during that time? Write your prediction in the “prediction” column for the second row, labeled “uranium-238”, in data table 1.

c. Click the “Play” button at the bottom of the window. Watch the graph at the top of the window carefully, and click “pause” when the time reaches 4.5 billion years (when the uranium-238 atom

moving across the graph reaches the red dashed line labeled HALF LIFE on the time graph). d. If you don’t pause the simulation on or very close to the red line, click the “Reset All Nuclei” button and

repeat step c. e. Once you have paused the simulation in the correct spot, look at the pie graph and determine the

number of nuclei that have decayed into lead-206 at Time = HALF LIFE. Write this number in data table 1, in the row labeled “uranium-238”, under “trial 1”.

f. Click the “Reset All Nuclei” button in the decay area. g. Repeat steps c through e for two more trials. For each trial, write down in data table 1, the number of

nuclei that have decayed into lead-206 at Time = HALF LIFE, in the row labeled “uranium-238”, under “trial 2” and “trial 3” respectively.

3. Calculate the average number of atoms that decayed for all three trials of carbon-14 decay. Do the same for

all three trials uranium-238 decay. Write the average values for each element under “averages”, the last

column in data table 1.

4. Answer the five (5) questions for Experiment 1 on the Questions page. * Unlike Carbon-14, which undergoes only one radioactive decay to reach the stable nitrogen-14, uranium-238 undergoes MANY decays into many intermediate unstable elements before

finally getting to the stable element lead-206 (see the decay chain for uranium-238 in chapter 12 for details).

Experiment 2: Decay Rates

1. Set Up: Click on the Decay Rates tab at the top of the simulation screen.

2. Procedure

Part I – Carbon-14

a. In the Choose Isotope area on the right side of the screen, click the button next to carbon-14. Recall

that carbon-14 has a half-life of about 5700 years. b. Drag the slide bar on the bucket of atoms all the way to the right. This will put 1,000 radioactive atoms

into the decay area. When you let go of the slide bar, the simulation will start right away. If you missed seeing the simulation run from the start, start it over again by clicking “Reset All Nuclei”, and keep your eyes on the screen. Watch the graph at the bottom of the screen as you allow the simulation to run until all atoms have decayed.

c. Carefully interpret the graph to obtain the data requested to fill in data table 2 for “carbon-14”.

Part II – Uranium-238

a. In the Choose Isotope area on the right side of the screen, click the button next to uranium-238.

Recall that the half-life of uranium-238 is about 4.5 billion years. b. Repeat step b. of part I for uranium-238. c. Carefully interpret the graph to obtain the data requested to fill in data table 2 for “uranium-238”.

3. Answer the two (2) questions for Experiment 2 on the Questions page.

Experiment 3: Measurement

1. Set Up: Click on the Measurement tab at the top of the simulation screen.

2. Procedure

a. In Choose an Object, click on the button for Tree. In the Probe Type box, click on the buttons for

“carbon-14”, and “Objects”. b. Click “Plant Tree” at the bottom of the screen. Observe that the tree grows and lives for about 1200

years, then die and begin to decay. As the simulation runs, observe the probe reading (upper left box) and graph (upper right box) at the top of the screen. The graph is plotting the probe’s measurement of the percentage of carbon-14 remaining in the tree over time.

c. On the right side of the screen, in the “Choose an Object” box, click the reset button. Set the probe to measure uranium-238 instead of carbon-14 (in the Probe Type box, click on the button for “uranium-

238”). Click “Plant Tree” and again observe the probe reading and graph. This time, the graph will plot the probe’s measurement of uranium-238 in the tree.

d. On the right side of the screen, in the “Choose an Object” box, click the reset button and click the button for Rock. Keep the probe type set on “uranium-238”.

e. Click “Erupt Volcano” and observe the volcano creating and ejecting HOT igneous rocks. As the simulation runs, observe the probe reading (upper left box) and graph (upper right box) at the top of the screen. The graph is plotting the probe’s measurement of uranium-238 in the rock over time.

f. On the right side of the screen, in the “Choose an Object” box, click the reset button. Set the probe to measure carbon-14 instead of uranium-238 (in the Probe Type box, click on the button for “carbon-14”).

Click “erupt volcano” and again observe the probe reading and graph. This time, the graph will plot the probe’s measurement of carbon-14 in the rock.

3. Answer the six (6) questions for Experiment 3 on the Questions page. Repeat the Measurement

experiments as necessary to answer the questions.

Experiment 4: Dating Game

1. Set Up: Click on the Dating Game tab at the top of the simulation screen. Verify that the “objects” button is

clicked below the Probe Type box.

2. Procedure

a. Select an item either at or below the Earth’s surface to determine the age of. Set the Probe Type to

either carbon-14 or uranium-238, as appropriate for the item you are measuring, based on your findings in experiment 3.

b. Drag the probe directly over the item you chose. With the probe over the item, the box in the upper left, above “Probe Type”, shows the percentage of element that remains in the item.

c. Drag the green arrow on the graph to the right or left, until the percentage in the box on the graph matches the percentage of element in the object. Once you have the arrow positioned correctly, enter, in the “estimate” box, the time (t) shown, as the estimate for the age of the rock or fossil. Click “Check Estimate” to see if the estimate is correct.

d. Example: 1) Drag the probe over the dead tree to the right of the house. Since this is a once-living thing, set the

Probe Type to Carbon-14. 2) Look at the probe reading: it shows that there is 97.4% of carbon-14 remaining in the dead tree. 3) Drag the green arrows on the graph at the top of the screen to the right or left until the top line tells

you that the carbon-14 percentage is 97.4%, matching the reading from the probe. 4) When the graph reads 97.4%, it shows that time (t) equals 220 years. 5) Type “220” into the box that says “Estimate age of dead tree:” and click “Check Estimate”. 6) You should see a green smiley face, indicating that you have correctly figured out the age of the

dead tree, 220 years. This means that the tree died 220 years ago.

e. Repeat step c. for all the other items on the Dating Game screen. Fill in data table 3.

Hints:

*When entering the estimate for the age of an object, you MUST enter it in YEARS. So, if t = 134.8 MY

on the graph, which means 134.8 million years, you would enter the number 134,800,000 as the

estimate in years for the age of a rock. The estimates entered do not have to be EXACT to be

registered as correct, but must be CLOSE. For example, if 134,000,000 were entered for the above

example, the simulation would return a green smiley face for a correct estimate.

**For the last four items on the list, neither carbon-14 nor uranium-238 will work to determine the item’s

age. Select “Custom”, and pick a half-life from the drop-down menu that allows the probe to detect

something (i.e., a reading other than 0.0%). All of the “custom” elements are, like carbon-14, elements

that would be found in living or once living things.

3. Answer the (1) question for Experiment 4 on the Questions page.

Name:

Data

Each box to be filled in with a value is worth 1 point.

Data Table 1

Radioactive

Element

Number of atoms in the

sample at Time = 0

Prediction of # atoms

that will decay when

time reaches one half-

life

Number of atoms that

have decayed when

Time = Half Life

Average number of

atoms that have

decayed when

Time = Half Life Trial

#1

Trial

#2

Trial

#3

Carbon-14 100

Uranium-238 100

Data Table 2

Radioactive

Element

Percentage of the original element remaining after:

Percentage of the decay product present after:

1 half-life 2 half-lives 3 half-lives 1 half-life 2 half-lives

3 half-lives

Carbon-14

Uranium-238

Data Table 3

Item Age Element Used

Animal Skull

House

Living Tree

Dead Tree

Bone

Wooden Cup

Large Human Skull

Fish Bones

Rock 1

Rock 3

Rock 5

Fish Fossil*

Dinosaur Skull*

Trilobite*

Small Human Skull*

Questions

For multiple choice questions, choose the letter of the best answer choice from the list below the question.

For short answer questions, type your answer in the space provided below the question.

Note that there are TWO PAGES OF QUESTIONS below. Each multiple question is worth 3 points and each

short answer question is worth 5 points.

Experiment 1

1. In 1 or 2 sentences, describe, in the space below, what you observed happening to the atoms in the decay area

when the simulation is in “play” mode.

2. In this simulation (and in nature), carbon-14 is radioactively decays to nitrogen-14. What type of radioactive decay is carbon-14 undergoing? a. alpha decay b. beta decay c. gamma decay

3. In data table 1, compare your calculations for the average number of atoms that decayed to your predictions for how many atoms would decay. How did your predictions compare to the averages? a. Close b. Exact c. Nowhere Close

4. Which of the following statements best describes the decay of a sample of radioactive atoms?

a. A statistical process, where the sample as a whole decays predictably, but individual atoms in the sample decay like popcorn kernels popping.

b. An exact process where the time of decay of each atom in the sample can be predicted. c. A completely random process that is in no way predictable.

5. Based on your observations, the data you collected, and the comparison of the calculated averages to

predictions in experiment 1, write in the space below, IN YOUR OWN WORDS, a definition of “half-life”. Phrase the definition in a way that you would explain the concept to one of your classmates.

Experiment 2

1. Suppose you found a rock. Using radiometric dating, you determined that the rock contained the same percentage of lead-206 and uranium-238. How old would you conclude the rock to be?

a. 2.25 billion years old b. 4.5 billion years old c. 9 billion years old

2. Using the data in data table 2, if the original sample contained 24 grams of carbon-14, how many grams of carbon-14 would be left, and how many grams of nitrogen-14 would be present, after 2 half-lives?

a. 12; 12 b. 6; 18 c. 2; 22

Experiment 3

1. When half of the carbon-14 atoms in the tree have decayed into nitrogen-14, it has been approximately 5700

years since the tree _____.

a. was planted b. died

2. The probe measures that the percentage of carbon-14 in the tree is 100% while the tree is alive, and then

measures the percentage of carbon-14 decreasing with time after the tree dies. This means that radiometric

dating using carbon-14 is applicable to:

a. living objects. B. once-living objects c. both living and once-living objects.

3. When half of the Uranium-238 in the rock has decayed, ______ years have passed since the volcano erupted.

a. 4.5 billion years b. 5700 years

4. In step c of experiment 3, the probe was used to measure uranium-238 in the tree. In step f of experiment 3, the

probe was used to measure carbon-14 in the rock. In both steps (c and f), the probe reading was _____.

a. 100%, then decreasing with time. b. zero (0) . c. decreasing with time.

5. Uranium-238 must be used to measure the age of the rock, and not carbon-14, because:

a. The isotope carbon-14 did not exist when the rock was created.

b. rocks do not contain carbon-14, and even if they did, the carbon-14 would have likely decayed away

prior to measuring the rock’s age.

c. it is easier to measure uranium in rocks than it is carbon.

6. Based on your observations for experiment 3, and the answers to your questions above, _______ should be

used to determine the ages of once-living things, and _______ should be used to determine the ages of rocks.

a. carbon-14; uranium-238 b. uranium-238; carbon-14 c. either can be used for both objects.

Experiment 4

1. Briefly explain why neither carbon-14 nor uranium-238 could be used to determine the ages of the last 4 items in

data table 3.

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