PHYSICS 220/230
Lab 13: Nuclear Radiation Measurements

We will investigate and verify the random behavior of radioactive decay and determine the half-life of a radioactive isotope.

THEORY

The nuclear decay process seems at the same time to be random yet predictable. How can a random event be predictable? This analogy may be helpful. Think about making popcorn. As you heat the kernels of corn, it would be very difficult to say exactly which kernel is going to explode next, yet it is fairly easy (simply by listening) to say how many kernels pop each second. In the same way, it is impossible to say which unstable nucleus will be the next one to decay; however, it is fairly easy to use a Geiger-Müller (GM) detector to count the number of nuclei which do decay each second throughout a radioactive sample (this is called the "decay rate" of the sample).

If you "listened" to the nuclear decay of a radioactive sample with a good GM detector and plotted counts per second over a period of time, what would the results look like? Well, that depends on how long a period of time you are talking about. For radioactive samples, the important time is the half-life, which is the time for half of the current number of unstable nuclei to decay. Over a time interval very short compared to the half-life, a very small fraction of the current number of nuclei would decay each second during that interval. Thus, the number of unstable nuclei can be considered almost constant over the interval, and the decay equation then tells us that the decay rate should also be almost constant over the interval. For example, say the half-life is a million years. Then, over the next few hours, the number of decays each second should be virtually constant. But because each decay happens independently of all others (i.e., decay is a random process), the actual number of counts will fluctuate up and down about this constant value, according to a well-tested theory of statistics. The size of the fluctuation depends on the value of the "constant" decay rate - the higher the rate, the smaller the fluctuations. In fact, the standard deviation should approach the square root of the mean decay rate.

Of course, the decay rate of any radioactive sample must eventually become smaller and smaller when monitored over a sufficiently long time interval; i.e., one comparable to or larger than the half-life. Using our previous example, we would expect the number of decays during the next second to be significantly higher than the number of decays during a second several hundred thousand years from now, and much higher than the number of decays during a second several thousand years from now.  The mode of decay for all nuclei are tabulated in the Chart of Nuclides.

APPARATUS

In this lab, you will use a computer-interfaced GM detector to monitor the decay rate of two different radioactive sources; each is an example of one of the situations discussed above.

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Every time a decay product (such as an alpha or beta particle) flies out of the source and enters the detector through its window, a voltage signal is sent from the GM tube to an interface, and then on to the computer program which keeps a running tally of all such counts.

PROCEDURE

Be sure you have read the Nuclear Safety Guides handout before you begin the exercises.

Plug in the power cord for the GM detector and connect its phone jack to Channel 1 of the Pasco Interface box.

Prepare the computer to record data. Double-click on "Py Software", then on the "Science Workshop" folder. Double-click on "Sciwkshp.exe" to launch the monitoring program. Choose "Open…" from the "File" menu and open the document "Radlab97.sws" that is in the "Phy220" folder. On the screen you should see three windows showing an Experiment Setup, a Table display, and a Graph display.

The TABLE window will display the number of counts (decays) during each sampling time (which lasts 5 seconds) as the monitoring goes on. When you click on the "REC" button in the Experiment Setup window at the top left of the screen, the program begins a new "Run" and will record and display the number of counts in each 5 second interval, one after the other, until either 10 minutes are up or you click on the "STOP" button. At the bottom of the Table window are the statistics for the counts of sampling times for the current run.

Carefully remove the plastic protective cap from the window of the LabNet Geiger-Müller detector. Clamp the GM detector vertically so its bottom edge is the cap's height (i.e., about 1 cm) above the tabletop.

Exercise 1: Radioactive Decay as a Random Event   ( Tl^204__> Pb²⁰⁴ + e^-  )

1. Carefully place the long-half-life beta source onto the edge of a paper towel. Slide the source to center it directly underneath the GM detector.
2. On the GRAPH window, click on the x-axis and set the maximum value to 600 seconds, then click OK. Click on "REC" to begin data recording. A data point should appear every 5 seconds in the TABLE display and also on the Graph.
3. When the run has gone on for about 30 seconds (6 sampling times), check to see about how many counts you are getting in each sampling time. If the number is somewhere between 30 and 70, there is no need to interrupt the run before the 10 minutes are up. But if the counts are outside this range, then you should click "STOP" and then adjust the height of the GM detector from the tabletop to either increase or decrease the count rate. Before you restart monitoring, choose "No Data" from the pop-up "DATA" menu in the GRAPH window. Click "REC" to begin a new run.
4. Once you have completed a run, carefully slide out the paper towel with the beta source and replace the source in the storage box. Close the box and put it aside.
5. On the Graph display, click on the Sigma icon button to show the "Stats" popup menu (sigma sign) in the right hand area of the plot. From the pop-up menu that appears when you click and hold the sigma icon at the top right of the GRAPH window, choose "Histogram, 50 Divisions".




6. Reset the x-axis scale to 600 seconds if necessary. Study the overall shape of the histogram. Click on the GRAPH window and then choose "Print the Active Display" from the "File" menu.
7. Record the mean and standard deviation (values at the lower part of the TABLE window) of the samples for this run. Write these on your printed graph.
8. Close the "Stats" pop-up menu.

Exercise 2: Background Radiation

We are always subject to radiation from natural sources in the universe. Cosmic rays as well as radioactive atoms in water, soils, and even our bodies all contribute to the background count. The background count rate must be determined and subtracted from all determinations of count rate to yield the corrected count rate.

1. Reset the height of your GM detector, if necessary, so that it is one cap's height above the table.
2. Remove all radioactive sources from the vicinity of the GM tube. From the Experiment Setup window, click "REC". Again, the random nature of the activity can be noted. The counts per unit time will give the average Background count rate and should be subtracted from any measured radioactive sample count rates in order to obtain the net rates due to the source alone.
3. It will not be necessary to collect data for the full ten minutes. After three minutes, the "STOP" button can be used to abort the collection of data, and the table data for this Run can be printed for your notebook. Record a value for the background as the mean of counts per 5 second interval.
4. Use the background rate to adjust your value of the mean decay rate in Exercise 1 to represent the actual decay rate of the beta source. Display the answer in your notebook in the following way:

Exercise 3: The Half-Life of a Radioactive Decay
            ( Cs^137__> Ba¹³⁷_m + e^-  ) and later ( Ba¹³⁷_m^__> Ba¹³⁷ + g  )

1. Select "No Data" from the pop-up "DATA" menu in the GRAPH window.
2. When you are ready to start recording, ask the instructor to supply a short-half-life radioactive sample. You will be provided with about 5 drops of liquid containing ^137m Ba by milking a radioactive "cow" into the metal planchette placed on the paper towel. Carefully slide the sample under the window of the GM tube.
3. Click on "REC" to begin data recording.
4. After the first couple of data points have been recorded, check to see about how many counts you are getting in each sampling time. If the number is less than 250, let the run proceed. But if the counts are higher than this, you should click "STOP" when the most recent data point gets down below 300. Before you restart recording, choose "No Data" from the pop-up "DATA" menu in the graph window. Then immediately click "REC" to begin a new run.
5. When the run is over, carefully slide the paper towel with the source over to the edge of the sink. Save the data in the C:\temp folder.
6. Click on the sigma icon at the bottom left of the GRAPH window to open up the statistics portion of the GRAPH window. From the pop-up menu that appears when you click and hold the sigma icon at the top right of the GRAPH window, choose "Curve Fit", and then "Polynomial Fit". Change the polynomial degree to n = 4. This should draw a smooth curve through your data points.
7. Reset the x-axis to range from zero to 600 s. Click on the GRAPH window and then choose "Print the Active Display" from the "File" menu.
8. Use the Smart Cursor tool (click on the second icon [with a xy and a cross] at the bottom left of the GRAPH window) to read the y coordinate of the fitted line at t = 0. Taking into account the mean background count rate you measured in Exercise 2, determine how long it takes for the decay rate of the source to fall to one-half its starting value. Carefully document your steps in determining the half-life of the source by using, in your notebook, a table similar to that shown below.
9. Repeat the previous steps for the time it takes for the decay rate to fall to one-quarter its starting value. Use this time to make a second determination of the half-life.