PHYSICS 220/230 Lab 12: Nuclear Radiation Measurements

 Introduction:  In this experiment we will investigate and verify the random behavior of radioactive decay and determine the half-life of a radioactive isotope.

Background 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 million years from now.  The mode of decay for all nuclei are tabulated in the Chart of Nuclides. For each of the nuclear reactions which you will be investigating, look up the parent nuclei in the Chart of Nuclides and write a few sentences about each reaction.

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.

Initial Setup: You must read the Nuclear Safety Guides (in the back of your lab manual) before you begin the exercises.

Plug in the power cord for the GM detector and connect its phone jack to Channel 1 of the Science Workshop Interface box.  Prepare the computer to record data.

• Open Data Studio.  Click on Create Experiment.

• Click on the “add sensor or instrument” tab.  Select “digital sensors” from the pull down menu. Click “Geiger Counter” and then click OK.

• Drag a Graph into digital channel 1.

• Drag a Histogram into digital channel 1.
• Drag a Table into digital channel 1.

• Under the “sample rate” tab, select seconds from the pull down menu.  Then make the time box 5 seconds.

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 about 5 cm above the tabletop.

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

Procedures:

1. Carefully place the long-half-life beta source, foil side down, on a paper towel directly underneath the GM detector.
2. You will want to do a 600 second run.  Use the Autostop feature found in the Experiment Setup/Options menu.  Click on "Start" 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 less than 1000, 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 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, Table and Histogram windows. Click "Start" 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 arrow next to the Sigma icon button to show the "Stats" popup menu. From the pop-up menu, choose Mean and Standard Deviation.  Record these numbers.
6. Double click on the histogram window.  Under the “Bins” tab, set the “bin size” to 2.  Study the overall shape of the histogram.  What does it tell you about the nature of radioactive decay?  Click on the Histogram window and then choose "Print" from the "File" menu to print a copy of the histogram for your notebook.
7. Click on the Graph window and then choose "Print" from the "File" menu to print a copy of the graph for your notebook.

Analysis:  Theory says that radioactive decay obeys a statistics for which the standard deviation of the counts is equal to the square root of the mean for a large number of counts. For your data, compare the standard deviation to the square root of the mean.

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.

Procedures:

1. Lower the detector to about 1 cm above the table.  Remove all radioactive sources from the vicinity of the GM tube. Click "Start". 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.
2. It will not be necessary to collect data for a full ten minutes. After three minutes, the "Stop" button can be used to abort the collection of data.  Copy the Table and paste it into Excel.  Then print a copy for your notebook. Record a value for the background as the mean of counts per 5-second interval.
3. 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  ), which we will measure

Procedures:

1. Select "No Data" from the pop-up "Data" menu in the Graph, Table and Histogram windows.
2. When you are ready to start recording, ask the instructor to supply a short-half-life radioactive sample. You will be provided with a couple of drops of liquid containing ¹³⁷Ba_m  by milking a radioactive "cow" into a metal planchette placed on the paper towel. Carefully slide the sample under the window of the GM tube, with the GM tube located close to the sample.
3. Click on "Start" to begin data recording and record for 600 s.
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 much greater than 1000, try adjusting the height of the detector. Before you restart recording, choose "No Data" from the pop-up "Data" menu in the graph window. Then immediately click "Start" 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 between the tables and leave it there. Save the data on the desktop.
6. Unplug the GM tube.

Analysis:

1. Click on the Fit icon at the top of the Graph window. From the pop-up menu that appears when you click and hold the arrow, choose "Natural Exponent Fit."  If the curve doesn't appear to fit the data, try a polynomial fit instead.  Change the polynomial degree to 4 by double clicking in the polynomial fit box and changing “terms” to 4.  While a polynomial is not the correct function for your results, the fit should produce a smooth curve through your data points.
2. Reset the x-axis to range from zero to 600 s if necessary. Click on the Graph window and then choose "Print" from the "File" menu.
3. Use the Smart Tool (click on the icon with “xy and a cross” on 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.
4. 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.

Discussion:

1. How long will it take for Ba-137m to decay to 1/32^nd of the original counts/second?

2. How do your measurements of the half-life of Barium-137m compare to the accepted value of 2.6 minutes?

3. Can you think of any way to reduce the time it takes for Barium-137m to decay to 1% of its original activity?

4. Does the time it takes to decay to 1% of its original activity depend on how much radioactive material there is to start with?