In this laboratory you will determine radioactive the half-life of Barium-137m, a metastable state of Barium.  You will measure the activity of the Ba-137m as a function of time by detecting the gamma rays with a Geiger-Mueller (GM) tube.  From the data you will determine the decay constant and the half-life of the sample.

Background information:

The decay constant  of a radioactive sample cannot be measured instantaneously.  The number of radioactive decays must be measured over a series of short time intervals.  The decay rate R = R₀ exp(-λt) of the sample decreases exponentially with time.  The number of particles detected with a GM tube is a fraction of the total number of decays since the radiation is emitted from the source in all directions and the detector only intercepts a small portion of these directions.  The detector also has less than 100% efficiency for counting particles that enter it.   Detectors cannot accurately count particles that enter nearly simultaneously.  This dead-time problem can be avoided by keeping the count rates low enough, so that chance of two particles entering within a time interval smaller than the time resolution of the detector/counter system is negligible.  The detected number of particles per unit time interval is then proportional to the activity of the sample and has the same decay constant.

Background radiation is a common source of error when measuring radioactive decay.  This error can lead to inaccuracies in the determination of the half-life.  The background radiation comes from many naturally occurring sources and from cosmic rays entering our upper atmosphere from space.  Background radiation is a constant addition to the activity from the sample.  It does not exponentially decay and cannot be fitted with an exponential function.  To account for the background we must fit our results with an exponential function plus a constant offset.

The source of the Ba-137m is an isotope generator consisting of an exempt quantity of Cs-137.  An exempt quantity is a quantity small enough so that no license is required to purchase the material.  It is deemed to be a minimal health hazard.  The Cesium atoms are in molecules of a Cesium salt, CsCl, that have been adsorbed by small beads of a resin material.  The Ba-137m nuclei are a daughter product that results from the λ-decay of Cs-137.

¹³⁷₅₅Cs   -->  ^137m₅₆Ba + e^- + ν_e.

As the Cs-137 nuclei decay to the Ba-137m nuclei, the Ba-137m atoms remain adsorbed on the surface of the resin.  But because Barium has a different chemistry than Cesium, it is more loosely bound to the resin and can be de-adsorbed with a weakly acidic salt solution containing HCI and NaCI.  Small amounts of the short lived Ba-137m isotope can be extracted from the resin by this eluting solution.  The Cesium nuclei have a half-life of 30 years and Cesium is  always decaying, building up an equilibrium amount of Ba-137m.  Ba-137m has a short half-life and quickly decays down to its stable ground state by the emission of a 0.662 MeV gamma ray.

The Ba-137m is said to be selectively "milked" from the generator that is sometimes called a "cow."  The Ba-137m daughter product is washed out of the generator, and the Cesium parent product is left behind to regenerate additional Ba-137m atoms.  Equilibrium is again reached in less than an hour.  Since Ba-137m has a short half-life, it only takes 30 minutes after a sample is acquired for the residual activity in the solution to essentially disappear.

However, should a spill occur, wipe up any liquid and wash any exposed skin thoroughly with soap and water.
 

Equipment needed:

• Nucleus Scaler/Timer
• Geiger Tube with Stand and Source Holder
• Pasco Science Workshop 750 Data Acquisition System
• BNC to Phone Plug Cable
• Cesium/Barium-137m Isogenerator
• Planchet

Procedure:

• Make sure the Science Workshop Interface (SW) is on.
• Connect the Geiger-Mueller tube to the Nuclear Scaler/Timer and the Scaler/Timer to the Science Workshop interface.  Insert the phone plug to digital channel 1 of the interface.
• Make sure the high voltage for the scaler is set to 900 V, and the counting mode switch is set to Preset Time, Manual.
• Turn on the scaler.  Place it into stop mode by pressing the Stop and then the Reset switch.  Then press count.  It should start counting.
• Open Data Studio and choose to create an experiment.
• Click on the circle for channel 1 and add a Geiger counter.  Choose sample rate 30 seconds.
• Click "Sampling Options".  Choose Delay Start, None.  Choose Automatic Stop, Time, and set the time to 901 s.  This will allow 30 measurements of the number of counts recorded in a 30 s interval.  Click "OK".  
• Minimize the "Experiment Setup" window.
• From the "Displays" double click the graph icon.  This will display the data collected from the Geiger counter in a graph.
• Once you are sure you data acquisition system is set up correctly, obtain a sample of Ba-137-m from the lab instructor.  You must be able to start taking data immediately, since the sample decays very quickly.  Put the sample into the second slot from the top of the sample holder stand.  Make sure the scaler is registering counts.
• Click Start and start collecting data for 15 minutes.
• After the data acquisition stops, click Fit on the graph.  Chose natural exponent fit. 
  The program will try to fit your data with a fitting function of the form A*exp(-Ct)+B.
  The computer adjusts the values of A, B, and C until the the sum of the squares of the differences between the actual data points and the corresponding points of the fitting function is minimized.
• Obtain another sample from the lab instructor and collect data for a second time to verify that you get consistent results.

Data Analysis:

• For both of your data sets record the values of A, B, and C you obtained from fitting your data.
• The value of B tells you the average number of background counts recorded in a 30 second time interval.
• The value of C is the decay constant.  Use the decay constant to calculate the radioactive half-life of Ba-137m for both of your data sets.