Physics Lab
Physics Sequence 2
Physics Sequence 2 Lab 11: Exponentials: Half-Life
Lab 12: Exponentials: Half Life
Equipment:
Pentium Computer, Excel Software, Cesium Barium Mini-generator, Geiger-Counter, Box of Cubes, Stopwatch, 50ml Glass Beaker.
Introduction:
The Isotope Generator contains 370 kBq of Cs-137 as the long-lived parent nuclide which has a half life of 30.25 years. Cs-137 decays, by the emission of beta radiation, into the isotope Ba-137m (t1/2 = 2.552 min.), which then emits a gamma ray to become the stable isotope Ba-137. This gamma decay has a half life of only “few” minutes. Ba-137 is milked out of the isotope generator during an eluting process. After the “milking”, the generator reaches radioactive equilibrium without 15-20 minutes and can be milked again. The solution decays so rapidly (after 30 minutes it is lower than 1/1000 its initial activity); therefore it can be safely emptied into the standard drainage system after approximately 30 minutes.
Radioactive Decay is described by the following equation: N=Noe-t
This is exponential decay, because the amount of decays is proportional to the number of remaining nuclei.
The time that it takes for half of the atoms to decay, is called the half life
Substituting N=1/2 No into the equation and solving for t produces the half life,
Thalf life = (ln 2)/. Lambda (is called the decay constant.
Procedure:
A Cesium Barium Minigenerator
1. Using the BNC connection at the back of the Geiger-Counter, connect the Geiger tube. (If using a “The Nucleus” counter, set the voltage to 430 Volts) Depress the POWER button to turn on the counter. Set the toggle switch at the top to Preset Time, and rotate the left hand dial to .5 minutes. (If you have a SPECTECH counter, follow the instructions on the last page of this lab to set up the counter operations.)
2. Remove any radioactive sources from the vicinity of the counter tube, press the COUNT Button. After 30 seconds (.5 minute) the counter will automatically stop, giving you the “background” count. This is the count of cosmic rays, natural radioactivity, etc. Repeat this operation by pressing RESET, and then COUNT until you have for four more 30 seconds intervals. Copy the data below. (Be sure to reset the counter when you are finished.) Compute the average “background” count.
________ ________ ________ ________ ________ Average _________
3. Reset the counter. Prepare the Ba-137 solution as described in the Elution Process below. (Note: Before doing so, acquaint yourself with the step 4 of the procedure.)
Elution Process :
Connect a plastic tube onto the syringe, and draw approximately 2 ml of the eluting solution into the syringe and remove the tube. Remove the protecting cap from the generator (blue-labeled screw socket) and connect the generator with the syringe tip by screwing it lightly into the screw socket. To start the eluting process, pull the protecting cap off the discharging socket (no screw thread) and hold the generator with its discharging hole facing downwards above the 50ml Glass Beaker. By carefully pressing the syringe piston the eluting solution is forced through the generator and discharged into the receiving vessel. The piston should not be pressed too strongly. The whole eluting procedure should take approximately 10-20 seconds. (After the elution process has been completed, the generator should be sealed with both sealing caps. The eluting process cannot be redone until after equilibrium has been established. This takes approximately 15-20 minutes.)
4. Immediately place the container with the Ba-137 solution under the Geiger tube. You will then simultaneously press the COUNT Button and start your stopwatch. The counter will stop automatically after 30 seconds. Record the count, and then reset the counter. Do not stop the stopwatch. When the stopwatch arrives at 1:00 minute, you will start the counter again. When the counter stops again, record the count and reset the counter. The stopwatch should read 1 min 30 seconds. Wait until the stopwatch reads 2 minutes, and then start the counter again. You are in effect counting for 30 seconds, then resting for 30 seconds. Continue this process until you have obtained 12 readings.
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Counts |
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T=0 |
T=1 |
T=2 |
T=3 |
T=4 |
T=5 |
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T=6 |
T=7 |
T=8 |
T=9 |
T=10 |
T=11 |
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B. Half Life Simulation
1. Watch the video to observe how this activity would have been done in a laboratory setting, then record the data from the end of the video in the table. This will be the data you analyze. Part II Video
2. Place 400 wooden blocks into the large box. Close the top and shake vigorously to randomize the blocks. After shaking, remove every wooden block whose X is facing up. These are considered to be the “decayed” atoms. Record the number of blocks removed after each shake.
3. Shake the box again, pull out the blocks with the X’s facing up, record the number removed, and repeat until you have filled in the data table. When you have completed the data table, replace all of the blocks that you have removed.
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Shake # |
1 |
2 |
3 |
4 |
5 |
6 |
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Blocks Removed |
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Analysis:
A. Cesium Barium Minigenerator
1. Watch the video to observe how this activity would have been done in a laboratory setting, then record the data from the end of the video in the table. This will be the data you analyze. Part I Video
2. Subtract the average background radiation from each of the counts, and then plot Counts vs. Time on a graph using Excel (Scatter-Graph with no connecting lines). Place the Time (expressed in Minutes) in Column A, the Counts minus Background in Column B.
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Counts – Background |
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T=0 |
T=1 |
T=2 |
T=3 |
T=4 |
T=5 |
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T=6 |
T=7 |
T=8 |
T=9 |
T=10 |
T=11 |
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3. Now right click on one of the data points and select ADD TRENDLINE. Then choose Exponential Trendline, and add the equation and the R-squared value to the graph. Copy your graph below. the decay constant, is the coefficient of the x in the exponent. The decay constant is always a positive number.
Equation_____________________ R2 ______ Decay Constant
4. Compute the half life of Barium 137 m by using the equation on the first page.
Half-life= (ln 2)/Compute your percentage error, by comparing against the actual half life of 2.55 minutes.
Half Life = ______________ % Error ___________
5. Take a point on the exponential curve and record its time and counts. Now pick a second point that is at a time that is one half life (according to your calculations away, and record its number of counts.
Time A__________ Counts A__________
Time B__________ Counts B___________
Now take “Counts B/CountsA”=____________
B. Half Life Simulation:
1. From your data, fill in one column of the data table below that indicates that total number of cubes left in the box after each shake. Record your values on the blackboard as well, and copy the results of the other groups. Compute the average number left after each shake. All columns are blacked out but avg because the video only give you the average value per shake.
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Shake # |
Grp 1 |
Grp 2 |
Grp 3 |
Grp 4 |
Grp 5 |
Grp 6 |
Grp 7 |
Grp 8 |
Average |
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0 |
400 |
400 |
400 |
400 |
400 |
400 |
400 |
400 |
400 |
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1 |
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6 |
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2. Using Excel, enter the number of shakes (0-8) in column A as the independent variable, and the cubes remaining from your measurement as the dependent variable in column B. Graph this as a Scatter graph with no lines, and then add an Exponential Trendline with equation and R2 value. Compute the decay constant and half life in the same way as for the Ba-137. Also indicate the R2 for the trendline.
Copy your graph below.
Decay constant_________ Half Life___________ R2 _________
4. Since one sixth of the cubes decay per roll (unit time), then 5/6 are remaining. The decay constant for this type of reaction is 0.182, which produces a half life of 3.8 rolls.
What is your % error – Show your work for calculation?
Post-Lab Quiz:
1. If the half-life of carbon-14 is 5730 years, what would the decay constant be in carbon-14’s exponential decay equation? Show your work.
2. If you start off with 100 grams of carbon-14, 100 years later how many grams of carbon-14 will remain? Show your work.
3. If you start off with 100 grams of carbon-14, how many years will it take for you to have 50 grams of carbon-14 left? Show your work, or explain your reasoning in words.
4. The half-life of cobalt-60 is 5 years. How many half-lives have passed after 15 years? Show your work or explain your reasoning in words.
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Tidewater Community College Virginia Beach, VA
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