We will investigate and verify the random behavior of radioactive decay and determine the halflife of a radioactive isotope.
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 GeigerMüller (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 halflife, which is the time for half of the current number of unstable nuclei to decay. Over a time interval very short compared to the halflife, 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 halflife 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 welltested 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 halflife. 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.
In this lab, you will use a computerinterfaced 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.
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. Doubleclick on "Py Software", then on the "Science Workshop" folder. Doubleclick 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 GeigerMüller detector. Clamp the GM detector vertically so its bottom edge is the cap's height (i.e., about 1 cm) above the tabletop.
QUESTION
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 your data, compare the standard deviation to the square root of the mean.
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.
Background Count Rate (cts per 5 seconds) 

Beta Source Count Rate (cts per 5 seconds) 
ycoordinate at time t = 0 

initial decay rate for sample 

1/2 initial decay rate + background rate 

Halflife determination 

1/4 initial decay rate + background rate 

Halflife determination 
QUESTIONS
1. How long will it take for Ba137m to decay to 1/32^{nd} of the original counts/second?
2. How do your measurements of the halflife of Barium137m compare to the accepted value of 2.6 minutes?
3. Is there any way to reduce the time it takes for Barium137m 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?