Radioactivity and Half Life Prelab
1. Define the following terms and write the variable associated with it:
a. Activity or decay rate:
b. Half-life
2. Write out the equation that shows the exponential decay in terms of a) activity and b)
radioactive nuclei, N:
a:
b:
3. What is happening at the same time you are doing the coin toss experiment?
4. When will you measure the background radiation of the Barium-137 experiment?
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Radioactivity and Half Life
NOTE: The data collection portion of this experiment is worth half the possible points in
this lab. Please follow all instructions!!
The activity (A) of a radioactive samples is the number of decays per unit time. The activity is
also called the decay rate. The activity of a sample is proportional to the amount of radioactive
material in the sample (A  N, where N is the number of radioactive nuclei). Since N decreases
exponentially, then so must A:
A  A0 e  t
In this equation  is the decay constant, commonly measured in s–1 or min–1. Note this value is
not the same as A, the decay rate. A0 is the activity at t = 0. The SI unit of activity (A) is the
becquerel (Bq), defined as one decay per second.
You will use a source called an isogenerator to produce a sample of radioactive barium. The
isogenerator contains cesium-137, which decays to barium-137. The newly made barium nucleus
is initially in a long-lived excited state, which eventually decays by emitting a gamma photon.
The barium nucleus is then stable, and does not emit further radiation. Using a chemical
separation process, the isogenerator allows you to remove a sample of barium from the cesiumbarium mixture. Some of the barium you remove will still be in the excited state and will
subsequently decay. It is the activity and half-life of the excited barium you will measure.
While the decay constant  is a measure of how rapidly a sample of radioactive nuclei will
decay, the half-life of a radioactive species is also used to indicate the rate at which a sample will
decay. A half-life is the time it takes for half of a sample to decay. That is equivalent to the time
it takes for the activity to drop by one-half. Note that the half-life (often written as T1/2) is not the
same as the decay constant , but they can be determined from one another.
OBJECTIVES


Use a radiation counter to measure the decay constant and half-life of barium-137.
Construct a manual exponential decay curve using a “coin” toss to use as a model for
radioactive decay
 Determine if the observed time-variation of radiation from a sample of barium-137 is
consistent with simple radioactive decay.
MATERIALS FOR BARIUM-137 EXPERIMENT
computer
Gray printer cable (if necessary)
LabPro computer interface and power supply OR
Mini Lab Quest interface
Support stand
Barium-137 sample,
Vernier Radiation Monitor
USB connector cable for interface
1. Connect the interface to the USB port of the computer. If using the LabPro interface, turn it
on first by plugging in the power supply (unit will beep).
2. Set up the radiation monitor on the support stand if it has not already been done. Plug it into
the Dig/Sonic 1 port of the interface.
3. Turn the radiation monitor ON (switch is on the monitor itself).
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4. Turn on the computer and start the LoggerPro progam (calipers icon on desktop). Go to File,
Experiments, Nuclear Radiation with Vernier, and choose the 03 Lifetime file. This should
bring up a graph of Radiation Counts vs. Time (min).
5. VERIFY the following: Rad monitor ON, probe icon visible in upper left corner, monitor in
dig/sonic #1,
button green. You are ready to obtain your Ba-137 sample.
6. Follow instructor’s instructions about obtaining your sample and where to place it under the
radiation monitor. NOTE: The radioactive decay starts immediately after the sample is
prepared. You should start data collection within 20 seconds of receiving your sample. Go!
7. Click
to begin collecting data. Logger Pro will begin counting the number of gamma
photons that strike the detector during each 30 second count interval. Data collection will
continue for 30 minutes. Do not move the detector or the barium cup during data collection.
8. After data collection is complete, the
button will reappear. Set the radiation monitor
aside, dispose of the barium solution as directed and use the graph to answer the questions.
MATERIALS FOR COIN TOSS EXPERIMENT (TO DO DURING DATA
COLLECTION PERIOD FOR BA-137)
computer (not the same one measuring the Ba-137 decay)
bag of 100 pink and black chips (count to verify quantity)
1. Place all of the pink/black chips in a container, shake them and pour them out onto the desk.
2. Locate all the chips that landed with the solid pink side up. These represent daughter isotope,
so remove them from the pile. Record the number of pink/black chips (parent isotope) remaining
in the data table next to Toss 1, Trial 1.
3. Repeat this process 7 times, or until no pink/black chips remain.
4. Repeat this for a total of 3 trials. Record data in the tables.
5. Add your data to the class average, as instructed.
TRIAL 1
Toss #
pink/black remaining
0
100
1
2
3
4
5
6
7
3
TRIAL 2
Toss #
pink/black remaining
0
100
1
2
3
4
5
6
7
TRIAL 3
Toss #
pink/black remaining
0
100
1
2
3
4
5
6
7
AVERAGE OF 3 TRIALS AND CLASS DATA
Toss #
Your average
Class average
0
100
100
1
2
3
4
5
6
7
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6. Graph your average and the class average results in Logger Pro, Don’t use the computer
measuring the Ba-137! There should be two columns already there, X and Y.
7. Go to the option menu and choose graph options. Uncheck the option to connect the data
points and check “point protectors”.
8. Fill in the number of tosses in the X column and your lab group’s average in the Y column.
9. Go to the Data menu and make a new manual column. Name it Class. Fill in the class data.
10. Click on the name of the y-axis on the graph and choose to display all data.
11. Put an appropriate title on your graph, go to the print menu, and put the last initials of each
group member in the footer for full credit.
12. PRINT ONE COPY OF PAGE 1 for each member of the group.
13. After you have printed, click on y-axis again and choose the Class data ONLY.
14. Perform a curve-fit on this data curve to see how compares to an exponential decay curve.
Use the curve-fit function (just to the right of the “R=” icon) and choose exponential. The bestfit equation will be of the form Y = A exp ( – C*X ) + B. You can ignore B; it should be very
small.
15. Choose try fit, and then click ok.
16. Change the title of your graph to Coin Toss Class Data and PRINT this graph. Make sure
the analysis box is visible.
ANALYSIS FOR COIN TOSS EXPERIMENT
1. The equation for radioactive decay can be written as: N = N0 e-λt. How does this equation
compare with Y = A exp ( – C*X ), the one you used for the best-fit curve of the coin toss?
2. Assume the 100 coins represent 100 atoms of a radioactive sample, with a T1/2 of 1 toss. In
this case, what should be the theoretical value of C? Recall λ = [ln2/ T1/2 ].
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3. Calculate the percent difference between the class data value for C and the theoretical value:
% difference ={|(exp. value – theoretical value)| divided by theoretical value} x 100%.
DATA TABLE FOR BA-137 EXPERIMENT
Average background counts
Value of parameter
Definition of parameter
fit parameters for Y = A exp ( – C*X ) + B
A
B
C
 (min–1)
T1/2 (min) (calculated from A,B,C 
T1/2 (min) (determined from graph)
ANALYSIS FOR BA-137 EXPERIMENT
1. Inspect your graph. Without use of statistics or curve-fit, determine the half-life directly from
the activity vs time graph (when the activity has decreased by half, that means the number of
radioactive nuclei have decreased by half as well.) Record the value in the last row of the
data table above.
2. When you perform a curve-fit for your data, you will have to include a term to account for
background radiation. You can measure this background count rate from your graph by
determining the average count rate during the last 5 minutes of the data collection (when
counts due to barium are no longer a factor). To do this:
a. Select the data on the graph between 25 and 30 minutes by dragging across the region
with your mouse.
b. Click on the statistics button on the toolbar.
c. Read the average counts during the intervals from the floating box, and record the value in
your data table (“B”).
4. Determine an appropriate curve fit for your data (curve fit button ), and apply it for the
first fifteen minutes only of your data. Use the value of B from the previous step.
5. PRINT your graph, with both best-fit equation and data, and statistics for the last 5 minutes
(that’s 2 analysis boxes). Print page 1 only, with your group’s initials in the footer.
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6. Record and define the fit parameters A, B, and C in your data table. If one of these
parameters is the decay constant (, make sure to note that in the data table.
7. From the fit parameters, determine the half-life T1/2:
8. Determine the percent difference between the two half-lives you established. Consider the
value determined in #7 to be the “theoretical value” (goes in denominator).
9. Calculate the fraction of the initial activity of your barium sample that would remain after 25
minutes. Was it a good assumption that the counts in the last five minutes would be due
entirely to non-barium sources? Why or why not?
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