AP Chemistry Lab s1

β decay of 137Cs and the half-life of metastable 137Ba by γ photon emission

Introduction:

Radionuclides emit various particles and γ photons during their disintegration as a first order reaction. Alpha (α ) and beta ( β-) emitters decay at various rates as characterized by their decay constant, λ . The relationship between radioactive decay and the data collected in this lab is shown in the equation:

- t N = No e λ

Where No is the original activity, λ is the decay constant, and t is the elapsed time.

Using natural logarithms, we have:

ln N – ln No = -λ t

Also, it is known that, for first order reactions:

t½ = 0.693/ λ and λ = 0.693/ t½

Hence, if we can measure the original and final activities of the radionuclide, we can calculate the half-life and decay constant.

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 of the sample decreases exponentially with time. The number of particles detected with a GM tube or nuclear scaler 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. Background radiation is also 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 adjusted detected number of particles per unit time interval is then proportional to the activity of the sample and has the same decay constant. Half-life can then be calculated using a graphical representation of data. The half-life of a radioisotope is defined as the amount of time necessary for one-half of the quantity of nuclide to decay, i.e., be converted into another species. The conversions involve either alpha or beta particle release, and the reaction can be followed by measuring the number of particles given off. In this lab, 137Cs is the parent nuclide that emits a β particle and decays to metastable 137Ba* and normal 137Ba. The half-life of this transition is approximately 30 years. However, the 137Ba* represents a metastable state that eventually emits a γ photon and becomes 137Ba. It is the half-life of this transition that is the focus of this lab. An isogenerator will produce an exempt quantity of the radioisotope, cesium-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 b-decay of Cs-137.

As the Cs-137 nuclei decay to the Ba-137* nuclei, the Ba-137* 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-137* 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-137*. Ba-137* has a short half-life and quickly decays down to its stable ground state by the emission of a 0.662 MeV gamma ray photon. The Ba-137* is said to be selectively "milked" from the generator that is sometimes called a "cow." The Ba-137* daughter product is washed out of the generator, and the Cesium parent product is left behind to regenerate additional Ba-137* atoms. Equilibrium is again reached in less than an hour. Since Ba-137* has a short half-life, it takes very little time after a sample is acquired for the residual activity in the solution to essentially disappear.

Pre-Lab Questions:

1. Write the nuclear equation for the transformation of Cs-137 to Ba-137*.

2. Write the nuclear equation for the transformation of Ba-137* to Ba-137.

3. Use the Chemistry Handbook to determine the half-life of barium-137* (theoretical value). This value will be used for your conclusion.

4. Using adjusted counts measured per unit time, explain how to graphically determine the half- life.

Materials:

Geiger-Mueller (GM) counter, 137Cs source (Isogenerator), Logger Pro Procedure:

1. Make sure the Spectech ST-350 Geiger counter is assembled based on your instructor’s directions, and turned on. 2. Set high voltage control to the appropriate voltage taped onto your Geiger counter. 3. Dial the control to time, and set the time interval to 30 seconds. 4. To take a reading, dial the control to counts, and hit the count button. After the time interval has expired, hit the reset button. 5. Determine the background radiation (in cpm) over a five-minute interval, and then convert to counts per 30-second interval. Calculate an average background count per 30- second interval. 6. Extract 137Ba* from the 137Cs source following the methods as outlined below: a. Place the planchet on the sample tray to be used. b. Draw the eluting solution into the syringe from the bottle. c. Remove the stoppers from the generator column. d. Insert the syringe firmly into the hole on the top of the generator and while holding the generator vertically, force approximately seven drops of solution through the generator onto the planchet. e. Immediately place the sample into the counter and begin counting. 7. Make sure the Geiger counter is still set to a 30-second time interval. Dial the control to counts, and hit the count button. 8. When the count stops, record the number of counts in your data table. Hit the reset button again! Begin timing another 30-second interval immediately by hitting the count button. 9. Continue to record the count every 30 seconds for approximately 15 minutes. 10. Subtract the background count from each value to get the adjusted counts.

Graphs/Data:

1. Create a data table that shows background radiation counts per unit time, average background radiation count per 30-second interval, unadjusted counts per unit time, and adjusted counts per unit time.

2. Appropriately graph the adjusted counts vs. unit time. Think about what type of graphical representation you should get with first order decay kinetics.

3.Create a secondary graph that allows you to graphically determine the decay constant, k, for the observed nuclear decay of 137Ba*. Calculations/Conclusions:

1. What is the decay or rate constant, k, for the observed nuclear decay of 137Ba*, determined from your secondary graph? Use appropriate units!

2. Calculate a half-life value from this graphically determined decay or rate constant, k from conclusion question #1. Use appropriate units!

3. Using the equation from your secondary graph, determine the half-life for the observed 137 nuclear decay of Ba using appropriate values for N and N0.

4. Calculate your average half-life. Compare this second half-life value to your graphically determined half-life value from number 1 by doing two percentage deviation calculations using the average half life.

5. Why are the two values for half-life different? Discuss why the determination of half-life using the slope is different than utilizing the equation and appropriate N and N0 values.

6.Calculate your percentage error for the half-life of Ba-137*, determined from your graphically determined half-life in #2. Use the standard table value for the correct or actual value. Show your work. Use your average value to calculate the error.

7. Write the entire nuclear decay of 137Cs to 137Ba by beta and gamma photon emission.

8.Why did you start measuring counts at t = .5 minutes instead of t = 0 minutes?

9. Define decay constant. What does a small decay constant imply?

10. Why should all citizens understand the concept of half-life of radioisotopes? Provide a real-world example.

11. Explain how this experiment could be practically applied to the technique of radiometric dating.

12. Assuming the secondary decay emits a gamma photon with an energy equal to 0.662 MeV, calculate the wavelength in pm of the radiation emitted.