Half-life of Barium-137^m

Nuclear decay is a random process, yet it proceeds in a predictable fashion. To resolve this paradox, consider an everyday analogy. An unstable nucleus in a sample of radioactive material is like a popcorn kernel in a batch of popcorn that is being heated. When a kernel pops, it changes form. Similarly, an unstable nucleus changes form when it decays.

It is practically impossible to predict which particular kernel will pop at any given instant, and in this way the popping of corn is a random process, much like radioactive decay. However, the corn-popping process is predictable in the sense that you can say how much time it will take to prepare a batch of popcorn. Similarly, a sample of radioactive material decays within a known time period. This period is called a half-life.

The half-life of a radioactive species is defined as the time it takes for the activity of the sample to drop by 50%. In this activity, you will investigate the decay of ¹³⁷Ba^m, a metastable isotope of barium that undergoes gamma decay with a half-life of several minutes.

Problem

What is the half-life of ¹³⁷Ba^m?

Objectives

1. Verify the random behavior of radioactive decay.
2. Determine the half-life of ¹³⁷Ba^m.

Materials

gamma ray detector

counter or timer

sample of ¹³⁷Ba^m

Safety Precautions

1. Always wear safety goggles, gloves, and a lab apron.
2. Skin or clothing that comes into contact with the barium should be washed thoroughly with soap and water.
3. The depleted sample may be washed down the sink drain.

Pre-Lab

1. A nuclide that undergoes a gamma decay event emits a gamma ray. A gamma ray detector counts the rate at which gamma rays are emitted. The decay rate of a radioisotope is often expressed in counts per min (cpm). Consider ⁸⁷Sr^m, a metastable isomer of strontium that undergoes gamma decay with a half-life of 2.8 hours. A particular sample of ⁸⁷Sr^mhas an initial decay rate of 1280 cpm. After 2.8 hours, the rate drops 50% to 640 cpm. Complete the table on the next page.

   Decay Rate of 87Srm
   Time (h)	0	2.8	5.6	8.4	11.2	14.0	16.8
   Decay rate (cpm)	1280	640	320	160	80	40	20

   
   
   
2. Plot a graph of decay rate versus time and draw a smooth line through the data points. This curve is an example of an exponential decay curve. Label the graph Figure A.
3. Read over the entire laboratory activity. Hypothesize how the activity of the¹³⁷Ba^m sample will behave. Record your hypothesis in the next column.

Procedure

1. Connect the detector-counter apparatus by following the directions given by your teacher. Switch the apparatus on.
2. There is always some level of ambient radioactivity in an environment. This radiation is known as background radiation. Measure and record the background activity by recording the counts registered by the gamma ray detector in 30-s intervals for 5 min. Record the data in Data Table 1.
3. CAUTION: Wear gloves, a lab apron, and safety goggles. Ask your teacher to bring a sample of ¹³⁷Ba^m to your workstation.
4. Place the sample near the detector. The precise location of the sample is not critical, provided that the detector is registering a good signal. However, the sample should not be moved once it has been placed in a satisfactory location. Record the number of counts registered by the detector in 30-s intervals in Data Table 2 until the count rate becomes indistinguishable from the background radiation count rate recorded in step 2.

Hypothesis

Cleanup and Disposal

1. Wash the depleted sample down the drain.
2. Clean up your work area.

Data and Observations

1. Convert the background radiation readings in Data Table 1 to a count rate in cpm by multiplying them by 2.
   
   

   Data Table 1
   Time (s)	0	30	60	90	120	150	180	210	240	300
   Counts
   Count rate (cpm)

   
   
   
2. Calculate the average background count rate in cpm.
   
   

   ---

   
   
3. Convert the readings in Data Table 2 to a count rate in cpm by multiplying them by 2. Subtract the background radiation rate obtained in step 2 from each count rate to obtain the corrected count rate.

   Data Table 2
   Time (min)	Counts	Count rate (cpm)	Corrected count rate (cpm)	Time (min)	Counts	Count rate (cpm)	Corrected count rate (cpm)

Analyze and Conclude

1. Making and Using Graphs Plot a graph of corrected count rate versus time using data from Data Table 2. Choose suitable scales for each axis. Draw a smooth curve through the plotted points. Label the graph Figure B.
2. Measuring and Using Numbers Calculate the half-life of ¹³⁷Ba^m. Choose a count rate (r) within the range of corrected count rate values in Data Table 2. Use this count rate and the graph in Figure B to determine the time related to this rate, t(r). Repeat this process for half the chosen count rate (r/2). Record all values in Data Table 3. Estimate the half-life of ¹³⁷Ba^m by subtracting t(r) from t(r/2). Repeat this procedure for several values of r.
   
   

   Data Table 3
   r	t(r)	r/2	t(r/2)	t(r/2) – t(r)

   
   
   
3. Measuring and Using Numbers Calculate the average value of the half-life from your estimated values in Data Table 3.
   The half-life of ¹³⁷Ba^m is 2.6 min. Expect answers within 10 percent of this value.
   

   ---

   
   

   ---

   
   
4. Error Analysis
   
   
   1. Over what range did the background count rate fluctuate?
      The background rate fluctuations should be one the order of the square root of the value of the background rate.
      

      ---

      
      
   2. Based on the range of values in Data Table 3, estimate the uncertainty in your determination of the half-life of ¹³⁷Ba^m.
      The half-life should be determined to be within 10 percent. A quick way to estimate the error in the average value obtained
      

      ---

      for the half-life is to calculate the percentage fluctuation in the half-life values in Data Table 3.

      ---

      
      

Real-World Chemistry

1. Radioactive liquids are sometimes used medically to trace blood flow. Do you think the radioactive isotopes used for this purpose should have a long or a short half-life? Why?
   Radionuclides with short half-lives are used for medical purposes. Short lived nuclideds become inactive quickly and are less likely to damage
   

   ---

   healthy cells.

   ---

   
   
2. Some waste fuel rods from the nuclear power industry contain radioactive nuclei with very long half-lives. Explain why this is a problem.
   Long-lived radionuclides can remain active for thousands of years. This makes their storage a significant problem. If the waste leaks into the
   

   ---

   enviroment, it could cause significant damage to the ecosystem.

   ---