A Study of Radioactivity and Determination of Half-Life

Transcription

1 A Study of Radioactivity and Determination of Half-Life Purpose: To examine different types of radioactivity and their properties, and measure the half-life of a radioisotope Introduction A radioactive substance is one which emits particles or radiation from its nuclei in order to stabilize itself. Such radioactive emissions can be alpha particles (helium nuclei, 4 2 αα), beta particles (electrons, 1 0 ββ), positrons (particles with the mass of an electron but a positive charge, 1ββ 0 ), gamma rays (γ) and x-rays. Each radioactive emission of a particle or radiation is accompanied by a loss of energy by the nucleus. This energy, called the emission energy, is related to the type of emission. Some types of emission have characteristically low emission energies, while other types of emission are accompanied by characteristically high emission energies. All radioactive emission processes have a half-life, defined as the time required for half of a given number of nuclei to decay radioactively. Half-lives have been recorded for elements which range from a fraction of a second to millions of years. Since radioactive decays all follow first order kinetics, we can apply the first order equation ln ( NN tt NN 0 ) = kkkk (eq. 1) where Nt and N0 are number of nuclei at time t and initially, respectively, k is the decay constant, and t is the elapsed time. Since number of nuclei are directly proportional to counts per minute (cpm), we can substitute cpm in place of numbers of nuclei. Thus, ln ( cccccc tt cccccc 0 ) = kkkk (eq. 2) ln(cpmt) ln(cpm0) = -kt (eq. 3) ln(cpmt) = -kt + ln(cpm0) (eq. 4) Notice that this last equation is in the form y = mx + b, where ln(cpmt) corresponds to y values, and t corresponds to x values. Thus if a graph is made plotting time on the x-axis and the natural logarithm of counts per minute on the y-axis, a straight line will result, with a slope equal to k. (Note that the y-intercept in this case is a bit of a yawn...) Since tt 1/2 = kk

2 one can easily calculate the half-life from the decay constant k. In this experiment we will study the effects of distance from the source of radiation for some alpha, beta and gamma emitters. We will also study their emission energies and determine what protective shielding can protect us from their radiation. Lastly, we will measure the half-life of an isotope of barium. Geiger Counter Shields Grooves Each group will have its own Geiger counter that contains a Geiger tube below which are six grooves. There is also a storage compartment on the front of the Geiger counter that holds shield materials used in part of the experiment today. Figure 1 Procedure Directions for using the ST-160 Geiger Counter (Parts I and II) You need to set up the Geiger counter (see Figure 1) for this experiment to 460 V and a count time of 60 seconds. 1. Turn on the Geiger counter. The red power button is on the back of the instrument. 2. Press the H.V. button. Press the UP and DOWN buttons as needed to set the voltage at 460. Press the H.V. button again (red light over H.V. button should go off). 3. Press the TIME button. Press the UP and DOWN buttons as needed to set the time for 60 seconds. Press the TIME button again (red light over TIME button should go off). Operation is controlled with the COUNT button. When the COUNT button is pressed, previous data is cleared and a new count is started. The red light over the COUNT button is on. You should see the counts as they occur. Make sure the red light over the TIME button is off. If it is on, press the TIME button; the count should show. When the count is finished, the red light over the COUNT button goes off and the final reading is displayed.

3 Part I Relation between Radiation Counted and Distance of Sample from Counter. In this part of the experiment you will examine the relationship between the number of counts obtained from a radioactive source and the distance of the source from the detector. 1. Set up your sample as follows: Take the beta source ( SSSS ) from the small plastic box. Place it in a clear plastic sample holder (with the paper label facing up) and put this in the top set of grooves on the plastic frame. 2. Press COUNT. The Geiger counter will begin counting for exactly one minute. The red light over the COUNT button stays on while counting. If the red light over the TIME button is on, press TIME and the light should go off and the count should appear on the display. After 1 minute, the red COUNT light goes off and the display will read the count. Record this value in Data Table Repeat this process putting beta source in the second set of grooves. 4. Repeat this process for the third, fourth, fifth and sixth sets of grooves. Record all your data in Data Table Take the gamma source ( 27CCCC) from the small plastic box, place it (paper side up) on the sample holder and insert it into the top set of grooves under the Geiger tube. Measure the number of counts in one minute for the gamma source at all six grooves. At the end of this section you should have the same kind of data as in the previous section. Record these results in Data Table The procedure to obtain data using the alpha source will be slightly modified. The alpha source gives negligible counts below groove 1. Therefore, usable data can only be obtained using the first (top) groove and higher. Flipping the sample holder upside down works to create a raised platform which will raise the alpha source closer to the detector. Take the alpha source from the small plastic box, place it (paper side down) on the raised part of the sample holder. Carefully slide the sample holder onto the first (top) groove of the Geiger counter. Measure the counts for one minute. Remove the alpha source and sample holder from the Geiger counter, flip the sample holder, place the alpha source (paper side down) inside the well of the sample holder, and then take a 1-minute reading using the first groove again. Take the third measurement with the alpha source in the 2nd groove.

4 Record these results in Data Table 1. Part II Emission Energy, Penetrability and Shielding. In this part of the experiment you will determine which type of radiation is most penetrating and what substances can be used to shield the Geiger tube (block the radiation from reaching the Geiger tube). A shield is just some material which may block, or shield, some of the radiation from reaching the Geiger tube. The shield may be lead, aluminum foil, tissue paper, plastic, etc. 1. First, determine the background radiation for one minute by determining the number of counts in one minute with no radioactive source under the Geiger tube. Make sure the other radioactive sources are well removed from the detector as they could give you an erroneously high background count. Record this value in Data Table Next place the beta emitter (paper side up) in the top set of grooves. Record the number of counts measured by the counter in one minute. 3. The shields for this part of the experiment are located in the shield storage compartment. The shields will be placed directly on top of the clear plastic holder (see Figure 2). Be certain that the shield completely covers the source. Record the number of counts measured by the instrument in one minute for the shielded source, and compare these to the unshielded counts per minute. Try at least three different shields for the beta source (one should be a metal). Subtract the background count from all readings, and record all data in Data Table Repeat steps 2-3 for the gamma source (paper side up). You do not have to determine the background again. Use the same shields that you used for the beta source. Record all data in Data Table Repeat steps 2-3 for the alpha source (paper side down). You do not have to determine the background again. Use the same shields that you used for the beta source. Record all data in Data Table Share your data with that of another group in order to obtain data on six different shields.

5 Figure 2. Placement of shield material with alpha source. The shield material rests on top of the clear plastic source holder in the top groove of the Geiger counter. Part III- Half Life Determination 1. Reboot the Geiger counter: Turn off the Geiger Counter by pressing the red button on the back of the instrument. Wait 5 seconds. Turn the Geiger Counter back on by pressing the red button. 2. Press H.V. to set the voltage. Light above H.V. will come on. Use the up down arrows to set the voltage to 460. Press H.V. once again to turn off- light should go off. 3. Press the Time button. The Time light will come on. Use the up down arrows to set the time to 60 seconds. Press the time button again. The light will stay on but the LED screen will read Coordinate the next few steps with your lab partner. You need to work quickly once you have your sample of Ba-137. You will be taking readings every 60 seconds. Obtain a sample of Ba-137 from your instructor. Without delay, slide the sample into the top set of the grooves. Press COUNT on the Geiger counter. o The COUNT light will be lit. o The LED will display the time in seconds. Wait and watch the TIMER on the LED for 60 seconds. o The COUNT light will go off after 60 seconds. o After 60 seconds, quickly do the following: Press TIME to turn off TIME. Write down the reading on the LED. o Light above TIME should be off. o Light above COUNT should be off. 5. Take the next reading. Do this quickly. Press COUNT and then press TIME.

6 Lights for both should be on. Wait and watch the counter for 60 seconds. o The COUNT light will go off after 60 seconds. o After 60 seconds, quickly do the following: Press TIME. Write down the reading on the LED. o Light above TIME should be off. o Light above COUNT should be off. Repeat step 5- taking readings for a total of 20 minutes. 6. Record all your data in Data Table Wait at least 10 additional minutes before disposing of the liquid containing the Ba At that point the radiation from the sample will have decreased to less than 1/1000 th of its original value, and can safely be disposed in the appropriate waste container. Rinse the plancet thoroughly with water, dry, wipe with a Kim wipe, and leave at your lab station. 8. Please turn off and unplug the Geiger counter when you are done. Calculations Part I - Relation between Radiation Counted and Distance of Sample from Counter. 1. Using the Excel spreadsheets for CH132 in the Science Learning Center (or other similar software), plot the number of counts for the gamma source on the vertical axis vs. the groove number (1 through 6) on the horizontal axis. 2. On the same graph, construct similar curves for your beta and alpha data. Use different colored data points for the three types of radiation. Part II - Emission Energy, Penetrability and Shielding 3. For each source, refer to Data Tables 2, 3, and 4 and list the shields that will reduce the number of counts to 10% or less of the original unshielded count for the source. Do this for all three sources. Part III Half Life Determination 4. Using the Excel spreadsheets for CH132 in the Science Learning Center (or other similar software), prepare a graph of counts per minute due to Ba-137m versus time, in minutes. 5. The Excel spreadsheet will also simultaneously plot ln(cpm) versus time in minutes, and will perform a linear regression analysis of this graph to obtain the slope, which will equal k. Include a printout of the graph and data table with your lab report.

7 6. Calculate the half-life of the metastable Ba Look up, either on the internet or on a chart of the nuclides, the value of the half-life of metastable Ba-137, and include this value with your lab report.

8 A Study of Radioactivity and Determination of Half-Life Data Table 1 Counts vs. Distance from Source Grooves alpha beta gamma 1 st set 2 nd set 3 rd set 4 th set 5 th set 6 th set Data Table 2 Effect of Various Shielding Materials on Beta Radiation shield β counts β background corrected β counts none

9 Data Table 3 Effect of Various Shielding Materials on Beta Radiation shield γ counts γ background corrected γ counts none Data Table 4 Effect of Various Shielding Materials on Beta Radiation shield α counts α background corrected α counts none

10 Data Table 5 Time (minutes) Counts per minute

11 A Study of Radioactivity and Determination of Half-Life Post-lab Questions 1. a) Why do the counts per minute fall off as the distance of the source to the Geiger tube increases? b) Which form of radiation falls off most rapidly with distance? Which one least rapidly? c) What does this tell you about the emission energy of these types of radiation? 2. a) Of the three types of radiation studied in this experiment, which type of radiation is easiest to shield against? b) Which is the hardest to shield against? 3. What is the half-life of an isotope if 436 seconds are required for the number of cpm to diminish from 14,227 to 367? Show your calculations.

12 A Study of Radioactivity and Determination of Half-Life Pre-laboratory Assignment 1. Write balanced nuclear equations for the radioactive decay of the isotopes which make up the alpha (both), beta, and gamma sources used in this experiment. (The gamma source undergoes simultaneous beta emission as well.) alpha: beta: gamma: 2. If a radioisotope has a half-life of 2.6 minutes, how long will it take, in minutes, for the radioactivity of the isotope to diminish to less than 1.0% of its original value? Show your calculations. 3. Why is it not necessary to take any special precautions in disposing of the waste from the half-life determination in this experiment? Last revised 12/12/16 VK&DN