Radioactivity and Half Life

Transcription

1 Radioactivity and Half Life NOTE: The data collection portion of this experiment is worth points. Please follow all instructions!! The activity (A) of a radioactive samples is the number of decays per unit time. The activity of a sample is proportional to the amount of radioactive material in the sample (A N, where N is the number of radioactive nuclei). Since N decreases exponentially, then so must A: t ( t) A e A 0 In this equation is the decay constant, commonly measured in s or min. A 0 is the activity at t = 0. The SI unit of activity is the becquerel (Bq), defined as one decay per second. You will use a source called an isogenerator to produce a sample of radioactive barium. The isogenerator contains cesium-, which decays to barium-. The newly made barium nucleus is initially in a long-lived excited state, which eventually decays by emitting a gamma photon. The barium nucleus is then stable, and does not emit further radiation. Using a chemical separation process, the isogenerator allows you to remove a sample of barium from the cesiumbarium mixture. Some of the barium you remove will still be in the excited state and will subsequently decay. It is the activity and half-life of the excited barium you will measure. While the decay constant is a measure of how rapidly a sample of radioactive nuclei will decay, the half-life of a radioactive species is also used to indicate the rate at which a sample will decay. A half-life is the time it takes for half of a sample to decay. That is equivalent to the time it takes for the activity to drop by one-half. Note that the half-life (often written as T / ) is not the same as the decay constant, but they can be determined from one another. OBJECTIVES Use a radiation counter to measure the decay constant and half-life of barium-. Construct a manual exponential decay curve using a coin toss to use as a model for radioactive decay Determine if the observed time-variation of radiation from a sample of barium- is consistent with simple radioactive decay. MATERIALS FOR BARIUM- EXPERIMENT computer Gray printer cable LabPro computer interface with USB connector cable and power supply Support stand Barium- sample, Vernier Radiation Monitor. Turn on the LabPro interface box by plugging in the power supply. Connect the LabPro to the side USB port of the computer.. Set up the radiation monitor on the support stand if it has not already been done. Plug it into the Dig/Sonic port of the LabPro.. Turn the radiation monitor ON (switch is on the monitor itself).. Turn on the computer and start the LoggerPro progam (calipers icon on desktop). Go to File, Experiments, Nuclear Radiation with Vernier, and choose the 0 Lifetime file. This should bring up a graph of Radiation Counts vs. Time (min).

2 Toss #. VERIFY the following: Rad monitor ON, probe icon visible in upper left corner, monitor in dig/sonic #, button green. Tell one of the instructors that you are ready to obtain your Ba- sample.. Follow instructor s instructions about obtaining your sample and where to place it under the radiation monitor. NOTE: The radioactive decay starts immediately after the sample is prepared. You should start data collection within 0 seconds of receiving your sample. Go!. Click to begin collecting data. Logger Pro will begin counting the number of gamma photons that strike the detector during each 0 second count interval. Data collection will continue for 0 minutes. Do not move the detector or the barium cup during data collection. 8. After data collection is complete, the button will reappear. Set the radiation monitor aside, dispose of the barium solution as directed and use the graph to answer the analysis questions. MATERIALS FOR COIN TOSS EXPERIMENT (TO DO DURING DATA COLLECTION PERIOD FOR BA-) computer (not the same one measuring the Ba- decay) bag of 00 pink and black chips (count to verify quantity). Place all of the pink/black chips in a container, shake them and pour them out onto the desk.. Locate all the chips that landed with the solid pink side up. These represent daughter isotope, so remove them from the pile. Record the number of pink/black chips (parent isotope) remaining in the data table next to Toss, Trial.. Repeat this process times, or until no pink/black chips remain.. Repeat this for a total of trials. Record data in the tables.. Add your data to the class average, as instructed. TRIAL pink/black remaining 0 00

3 TRIAL Toss # pink/black remaining 0 00 TRIAL Toss # pink/black remaining 0 00 AVERAGE OF TRIALS AND CLASS DATA Toss # Your average Class average

4 . Graph your average and the class average results in Logger Pro. Don t use the computer measuring the Ba-! There should be two columns already there, X and Y.. Go to the option menu and choose graph options. Uncheck the option to connect the data points and check point protectors. 8. Fill in the number of tosses in the X column and your lab group s average in the Y column. 9. Go to the Data menu and make a new manual column. Name it Class. Fill in the class data. 0. Click on the name of the y-axis on the graph and choose to display all data.. Put an appropriate title on your graph, go to the print menu, and put the last initials of each group member in the footer for full credit.. PRINT ONE COPY OF PAGE for each member of the group.. After you have printed, click on y-axis again and choose the Class data ONLY.. Perform a curve-fit on this data curve to see how compares to an exponential decay curve. Use the curve-fit function (just to the right of the R= icon) and choose exponential. The bestfit equation will be of the form Y = A exp ( C*X ) + B. You can ignore B; it should be very small.. Choose try fit, and then click ok.. Change the title of your graph to Coin Toss Class Data and PRINT this graph. Make sure the analysis box is visible. ANALYSIS FOR COIN TOSS EXPERIMENT. The equation for radioactive decay can be written as: N = N 0 e -λt. How does this equation compare with Y = A exp ( C*X ), the one you used for the best-fit curve of the coin toss?. Assume the 00 coins represent 00 atoms of a radioactive sample, with a T / of toss. In this case, what should be the theoretical value of C? Recall λ = [ln/ T / ].

5 . Calculate the percent difference between the class data value for C and the theoretical value: % difference ={ (exp. value theoretical value) divided by theoretical value} x 00%. DATA TABLE FOR BA- EXPERIMENT Average background counts Value of parameter Definition of parameter fit parameters for Y = A exp ( C*X ) + B A B C (min ) T / (min) (calculated from A,B,C T / (min) (determined from graph) ANALYSIS FOR BA- EXPERIMENT. Inspect your graph. Without use of statistics or curve-fit, determine the half-life directly from the activity vs time graph (when the activity has decreased by half, that means the number of radioactive nuclei have decreased by half as well.) Record the value in the last row of the data table above.. When you perform a curve-fit for your data, you will have to include a term to account for background radiation. You can measure this background count rate from your graph by determining the average count rate during the last minutes of the data collection (when counts due to barium are no longer a factor). To do this: a. Select the data on the graph between and 0 minutes by dragging across the region with your mouse. b. Click on the statistics button on the toolbar. c. Read the average counts during the intervals from the floating box, and record the value in your data table ( B ).. Determine an appropriate curve fit for your data (curve fit button ), and apply it for the first fifteen minutes only of your data. Use the value of B from the previous step.. PRINT your graph, with both best-fit equation and data, and statistics for the last minutes (that s analysis boxes). Print page only, with your group s initials in the footer.

6 . Record and define the fit parameters A, B, and C in your data table. If one of these parameters is the decay constant (, make sure to note that in the data table.. From the fit parameters, determine the half-life T / : 8. Determine the percent difference between the two half-lives you established. Consider the value determined in # to be the theoretical value (goes in denominator). 9. Calculate the fraction of the initial activity of your barium sample that would remain after minutes. Was it a good assumption that the counts in the last five minutes would be due entirely to non-barium sources? Why or why not?