Radiation Playhouse!

Pre-Lab: Articles and Simulations and Videos, Oh My!

A Bit of History

Henri Becquerel spent the first half of his life studying phosphorescence, the phenomenon by which a material absorbs and then (after a delay) re-emits light of a certain wavelength. The delayed emission occurs because the energy levels involved are associated with a forbidden quantum mechanical transitions (this is how objects glow-in-the-dark). When Willhelm Rӧntgen discovered X-rays in 1895, Becquerel thought they might somehow be related to his beloved phosphorescence. Becquerel’s experiments the next year centered on exposing uranium salts on photographic plates to sunlight. This caused the salts to emit X-rays and leave an image on the photographic plate - or so Becquerel thought. One morning he had his experiment all set up and ready to go when the weather refused to cooperate, and instead decided to rain all day (weathermen in 19th century Paris were about as accurate as meteorologists today). Grumpy that his experiment was ruined for the day, Becquerel put the uranium salts in a drawer. When he came back the next morning, he found that an image had still been created on the photographic plate, despite the distinct lack of sunlight in the drawer (Figure 1). Becquerel had discovered natural radioactivity. His discovery is a perfect example that great scientific achievements don’t always come about from meticulously designed experiments intended to answer burning scientific questions; they can also come about purely by a serendipitous accident (similarly, the discoveries of Teflon, penicillin, and vulcanized rubber were all happy accidents). The common denominator is that a scientist took the time to figure out what was going on and why it was happening. As Louis Pasteur (who himself got lucky on several important occasions) declared, “In the field of observation, chance favors only the prepared mind.” Becquerel’s prepared mind was awarded the Nobel Prize in Physics in 1903 for the discovery of natural radioactivity.

Figure 1: Image of Becquerel’s photographic plate, showing the effects of exposure to radioactive uranium salts. Becquerel wrapped the photographic plate in several sheets of thick black paper to prevent it from reacting with light in the room. He then placed a copper Maltese cross (distinctly visible in the lower black blob) on top of the paper and covered the whole thing in uranium salts. The radiation exposed (i.e., darkens) the photographic plate wherever it was spread, except where the metal cross shielded the plate. The light area around the two big black blobs wasn’t covered in uranium salts, and therefore wasn’t exposed to radiation. Fast forward 110 years, and radioactive substances are everywhere. Despite what the news may have you believe, these substances rarely pose a danger and are actually advantageous in many cases. We naturally encounter radioactive elements in the food we eat, the buildings in which we attend class, and the air around us. Radionuclides illuminate watches, alert us to the presence of smoke, allow us to date objects older than the earth, help us to diagnose all manner of illnesses, and power unmanned satellites to the farthest reaches of the Solar System. Radioactivity will not, however, turn you into a superhero or a supervillain (which may or may not be a positive, depending on your affinity for spandex).

For additional information on radioactivity, see Appendix A, as well as Moore Q12 – Q15 and Young & Freedman Chapter 43.

The Story

The energy released by the decay of a radioactive substance can power a circuit, just like a battery does. These devices, called radioisotope thermoelectric generators (RTGs), have been used since the 1960s to power spacecraft because they provide a lot of energy for fuel while adding relatively little mass to the spacecraft. Midway through your first week as a summer intern at NASA, your mentor informs you that NASA is moving forward with a project to create robots that can hop around the surface of Mars, like a wacky hybrid of Tigger and Wall-E. This would allow NASA to more efficiently explore the rocky terrain of Mars [Note: this is an actual idea floating around at NASA and the European Space Agency – the robot, that is, not the Disney cross-over event. If you’d like to learn more, go to www.space.com/9547- radioactivity-power-hopping-robots-mars.html]. These robots would require a sustained power source (you can’t very well plug them into a charging station on Mars) that is also light (jumping upwards of 1 km at a time only gets harder the more mass you have on board). RTGs are very likely the best way to do this. Unfortunately, a previous intern (who wasn’t as meticulous as you are) labeled the radioactive isotopes that NASA is considering but forgot to record his labeling scheme. You have three radioactive sources labeled A, B, and C. Further, you know that one source is Polonium-210, one source is Strontium-90, and one source is Barium-133. But which is which is which? They also lost some crucial data on an additional source NASA is considering. Before the project can move forward, the scientists at NASA need you to figure it out, and give them some preliminary information on the feasibility of each one as a power source.

An Article: Getting to Know the Types of Radiation

All parts of the electromagnetic spectrum as well as many other types of energetic particles can be referred to as radiation. An important distinction to make is whether the radiation is ionizing or non- ionizing. Ionizing radiation has sufficient energy to remove an electron from an atom or molecule. A Geiger counter works by detecting the current that’s created when radiation passes through and ionizes an otherwise insulating gas. If ionizing radiation passes through your body, it can create dangerous free- radicals, which can damage DNA and lead to cancer. Ionizing radiation includes the high-frequency part of the electromagnetic spectrum (i.e., gamma, X-ray, and some UV radiation), along with alpha and beta particles and cosmic rays. The relatively low-frequency end of the spectrum (i.e., microwave, infrared, visible, and some UV radiation) doesn’t have enough energy to ionize particles and isn’t known to damage DNA or cause cancer.

All the radiation we’ll be dealing with in this lab is ionizing radiation. While this may seem a bit frightening, don’t forget that you encounter naturally occurring ionizing radiation in your everyday life and probably don’t think twice about it. Ionizing radiation can even be beneficial – the same processes that can harm healthy cells can be targeted at tumors to disrupt their growth. And although you may not realize it, ionizing radiation benevolently watches over you every day and may even save your life.

Do This: Read about smoke detectors at home.howstuffworks.com/home- improvement/household-safety/fire/smoke.htm. You may skip page 2 of the article if you want.

PL1. What type of ionizing radiation is used in smoke detectors and what is the typical activity (in whatever units of activity you prefer)?

PL2. Briefly describe how an ionization chamber works, either in words and/or with a picture.

PL3. What happens when smoke is present? In other words, why does the alarm sound?

Do This: Let’s delve into the types of radiation in a bit more depth by watching this video: www.youtube.com/watch?v=27qSAqafQ6o.

PL4. Now complete the following chart in your lab notebook. You should use the information you’ve learned thus far in class and in this lab. Be sure to look at the notes for each column before responding:

Type of Actual Relative Distance Chargeb Massc Reasoningf Radiation Particlea Speed d Travelede Alpha Beta Gamma a. For historical reasons, we refer to each type of radiation by a Greek letter (when scientists first discovered radioactivity, they didn’t know what the radiation really was, so they started sequentially naming them after Greek letters). You, however, know what these particles really are – list them here (e.g., photons, neutrons, neutrinos, etc). b. What is the charge of each type of radiation (sign and total charge, in whatever units you deem convenient)? c. What is the relative mass of each radiation type? You don’t need to give an exact value (although you can if you’d like). It’s sufficient to say that one radiation type is much, much lighter than the others – or something similarly qualitative. d. How fast, in general, will each type of particle be moving? Once again, you can give qualitative comparisons. e. Based on what you’ve summarized about each particle, how far is the particle likely to travel before it interacts with and loses energy to matter? Qualitative comparisons are fine. f. In a word or two, explain how you decided on your response in the previous column.

The Statistical Nature of Radioactivity

Do This: To get a feel for what the half-life of a radioisotope really represents, go to the Pre-Lab links on the course website to visit http://phet.colorado.edu/en/simulation/beta-decay and click the “Run Now!” icon (if you’re having trouble getting it to run, you may need to first select “Download”).

Do This: Choose the “Single Atom” tab and select your favorite radioactive atom from the list on the right side. This program will allow you to observe the simulated decay of an atom. Each time you want to see how long it takes an atom to decay, click the “Reset Nucleus” button.

PL5. Before you run the simulation, predict what you expect the average lifetime of your chosen radioactive atom to be if you only measure 5 atoms (remember, you know the half-life of your radioisotope). Do you expect it to be different if you measure 30 atoms? Why or why not?

PL6. Run the PhET simulation for a total of 5 atoms. How many atoms decayed before the half- life and how many decayed after? What is the average lifetime of an atom based on your 5 representative atoms? You don’t need to be exact – just estimate how long each atom lives. You should show your work, though.

Do This: Now go to the “Multiple Atoms” tab at the top of the PhET window. Choose the same radioisotope you used in Step PL6. Add a total of 30 atoms from the “Bucket o’ Atoms” and watch them decay.

PL7. Once more, how many atoms decayed before the half-life and how many decayed after? What is the average lifetime of an atom based on the sample of 30 atoms? For this question, you don’t need to show your work – just do your best to estimate the average lifetime of an atom.

PL8. What does all of this tell you about the half-life of an atom? Is it the same as the lifetime for a single, randomly chosen atom? Why or why not? If they’re not the same thing, how are they related?

RTGs and NASA

Now that you know all about the types of radioactive particles and how they decay, it’s time to learn a bit more about the storyline of this lab by watching a video from NASA and then answering a few questions related to the video. One big question you might have is how RTGs actually turn all that heat into real, useful electrical power? Do This: To find out, watch a video at www.youtube.com/watch?v=EjWe77bYrXQ (Note that NASA uses the acronym RPS, which stands for Radioisotope Power System, and is just another way of referring to the same technology as a RTG).

PL9. When and where are RTGs most useful? Why can’t NASA just use solar power since the sun provides such a massive amount of energy?

PL10. How exactly does a decaying isotope provide power to an electrical system in a spacecraft? What is this setup called?

PL11. What is the next generation of NASA radioisotope powered system? Why is it better than the current version?

Physics 198 Students Only: Keep this last bit of information in mind when you get to Chapter 3 in Unit T!

Part I: Half-life

Make Some New Friends: You may need to work in a group of 3-4 for this entire lab. There are a lot of opportunities to take data, so be sure to take turns. Everyone should get a chance to make measurements and use the equipment.

1. Finding the Half-life

One pressing issue at NASA involves equipping the hopping robot with a supplementary source of power to give it an extra boost to scale particularly big mountains (basically, nitrous for robots to make them Faster and Furiouser). A radionuclide with a large initial activity and a short half-life might be exactly what’s needed. Unfortunately, your pesky predecessor lost the data on this particular radionuclide, so you need to investigate it.

Equipment

• Planchet containing radioactive 137mBa – decays via γ decay • Vernier Radiation Monitor (i.e., a Geiger counter) • Computer with LabPro interface • Stand to hold radiation monitor • Data from 133mBa decay (from “In-Lab Links” on the lab webpage)

Read This: For the first Part of the lab, your TA will measure the half-life of radioactive 137mBa (see Appendix B for more details). This sample is safe for use in lab, but because of the number of people in lab and the precise timing necessary, you will need to watch your TA as he/she uses the radiation detector to record measurements with Logger Pro. You will then be able to determine the half-life for 137mBa from similarly acquired data that is available under the “In-Lab Links”.

Do This: Watch carefully as your TA prepares a planchet (shallow disc) containing a sample of 137mBa. Your TA will need to immediately place the planchet under the radiation detector and begin taking data. It’s essential that your TA does this quickly because the 137mBa has a short half-life and it’s already decaying! Logger Pro will record counts vs. time (s) with a sampling rate of 30 s/sample for a total of 10 minutes and display the results on the Smart Board. [This means the collector will count radiation for 30 seconds and display the number of counts collected during that time period. This will be repeated until 10 minutes have elapsed.] Each time the detector measures a decay, it will emit a “click!” that’s characteristic of Geiger counters and 1950s horror movies. You don’t need to watch the Smart Board for the entire 10 minutes, but be sure to check back occasionally to see how the measurement is progressing!

Do This: Download the previously recorded 137mBa data from the “In-Lab Links” tab on the Radioactivity page of the lab website. This data was collected in exactly the same way your TA is currently collecting data. For clarity, the data on the website will be referred to as YOUR data from now on. The data on the Smart Board will be referred to as your TA’s data.

1.1. Use the “Curve Fit” option in Logger Pro to fit a function to your 137mBa data. Be sure to Plot print out and include your graph. Record the title of this plot as your response to this Step.

1.2. What is the decay constant of 137mBa? What is the half-life?

1.3. Determine the error in your half-life measurement compared to the actual value.

1.4. Once 10 minutes have elapsed, take a careful look at your TA’s data. What are the similarities between this data and your data? What are the differences? Be specific!

1.5. You should have observed some differences between your data and your TA’s data. If you fit a curve to your TA’s data and determined the half-life, would you find a similar answer to what you already calculated? Why or why not?

1.6. Qualitatively, what happens to the activity of your sample as time passes? How about the decay constant? The half-life?

1.7. After some amount of time, your TA can safely throw the planchet of (now stable) 137Ba in the trash can. How long should your TA wait until the activity of the 137mBa sample is roughly the same as the background radiation? [You will need information from Part II to answer this question.]

1.8. If you have one 137mBa nucleus and you wait exactly one half-life, what is the likelihood that the nucleus has decayed to stable 137Ba? Explain your reasoning.

Part II: Sorting Out Sources

Equipment

• Sources A, B, and C which are (in no particular order): 210 o Po (t½ = 138 days) – decays via α decay 90 - o Sr (t½ = 28.8 years) – decays via β decay 133 o Ba (t½ = 10.5 years) – decays via γ decay • Sealed radioactive source of unknown decay type (Labeled D, E, F, or G) • Vernier Radiation Monitor (i.e., a Geiger counter) • Computer with LabPro interface • Shielding material (Plexiglas, lead, and paper) • Stand to hold radiation monitor • Gloves

NWarning: All of the radioactive sources used in this lab are certified as Exempt Quantities by the United States Nuclear Regulatory Commission, meaning that the sources are of very low activity and do not pose a danger for use in schools. These sources are sealed inside a plastic disc and under no circumstances should you attempt to open them or puncture the plastic. Alert your TA immediately if your radioactive source becomes broken or cracked. You should always hold your radioactive sources by the sides of the disk to minimize contact. Food and drink is strictly prohibited in the room during this lab. You should always wear gloves when handling the lead shielding material and should wash your hands after lab, especially before eating or drinking. See Appendix C for a complete guide to general handling procedures for radioactive sources, provided by the Health Physics Society.

2. Background Radiation: There’s No Escaping It - It’s Everywhere!

You now turn your attention to the collection of unidentified isotopes. From your introductory physics class, you may know that ionizing radiation is always present wherever you go on Earth. The number one source of radiation is naturally occurring radon in the air, distantly followed by cosmic rays passing through the atmosphere around you, ingestion of occasional bits of radiation (usually in the form of 14C and 40K), and naturally occurring radionuclides in the Earth’s crust. None of these sources are anything to worry about, and even if you enjoy worrying, these sources are completely unavoidable! In order to get accurate readings of the radioactive sources in this lab, you must first determine the natural background radiation in the lab.

Read This: For this entire experiment, you will need to be cognizant of the location of nearby radiation sources. Don’t forget about sources belonging to your neighbors. Your measurements can be significantly affected by nearby radiation, so try to keep all sources (other than the one you’re measuring) as far away from the detector as possible while you make a measurement.

Do This: Connect the radiation meter to Dig/Sonic 1 on the LabPro computer interface. For this measurement, it’s especially important to be sure that the radiation monitor is as far away from all radiation sources as possible. Visit the Radioactivity page on the lab website and click on the “In-Lab Links” to download the Logger Pro template. Unzip the newly downloaded file “RadioactivityLoggerProTemplate.zip”. Open the folder and open “CountsvTime.cmbl”. This will plot counts vs. time (s). Click on the clock icon on the menu bar to set the sampling to 1 sample/s and the duration to 10 s. (This means the collector will count radiation for 1 second and display the number of counts collected during that second. This will be repeated until 10 seconds have elapsed.)

2.1. Collect data using the radiation monitor for 10 s, then use the Statistics feature in Logger Pro (located under the “Analyze” menu) to find the mean number of counts/s in your measurement. Record this value in your notebook. Repeat this measurement so that you have two values of the background radiation measured over a 10 s duration.

2.2. Repeat Step 2.1 for a 60 s duration (you should end up with two measurements for a 60 s duration). Record the mean number of counts/s in your notebook. Don’t forget to adjust the measurement duration to 60 s. 2.3. You should also be sure to write down the background radiation level given in the “In-Lab Links” (yes, this Step involves simply writing a number).

2.4. Are the number of counts in each time block the same? Are the two measurements of background radiation over a 10 s interval identical? What about the two measurements made over a 60 s time interval?

2.5. Let’s start thinking about what types of errors can affect your measurements of radioactive decay. If you measured for one randomly chosen second in time, would you be assured of measuring background radiation? Support your answer with data you acquired in the previous Steps.

2.6. If you answered “No” to any of the previous questions, how is it possible that two measurements made under the same lab conditions could yield different results? What does this tell you about likely sources of uncertainty in this experiment? If you had the most accurate Geiger counter in the universe and it never missed a decay, would you still have an intrinsic uncertainty associated with your measurement of the background radiation over a given interval of 1s?

2.7. Is the source of uncertainty you just discussed fundamentally different from the uncertainty you normally encounter in labs (say, for example, the error in measuring the length of an object with a ruler)? Why or why not?

2.8. Based on your above arguments, which one of the time intervals (10 s, 60 s, or 10 min) best represents the background radiation? Use this to determine the background radiation in counts per minute and the background radiation in counts per 30 s.

3. Getting to Know Your Sources

Before you can learn anything useful about the specific radioactive sources, you need to familiarize yourself with them.

Read This: If we plan to use the radioactive source for power, we want to utilize as much of the energy as possible. The only way to find the orientation that gives the maximum output is to test a variety of options. In this Section, you will experiment with putting the source above, below, and next to the radiation detector. For consistency, try to keep the source at roughly the same distance from the body of the detector for each measurement (~1 – 2 cm separation). In Steps 3.1 - 3.3 you will explore the following ideas: does it matter if the label is facing towards or away from the detector? What about if the source is on its edge as opposed to flat? What part of the radiation detector is most sensitive? It may help organize your data to draw a diagram of the detector and indicate the detector reading for each source orientation.

3.1. Securely fasten the radiation detector to the stand and then use Source A to experiment with various orientations of the source relative to the radiation detector. Set the measurement duration to 15 s and the sampling rate to 15 s/sample. This will simply add up all the counts over a 15 second interval for you and display the total – it is equivalent to reporting a measurement every second for 15 s and then adding them up. For each orientation you try, record the number of counts per 15 seconds. [Note: You should have concluded from Section 2 that 15 s isn’t long enough to get a good background reading. However, with a radioactive source present, the count rate should be much higher. This improves the accuracy of your measurement. While 15 s still isn’t a long enough measurement time to get extremely accurate data, you’re just looking at the big picture right now.]

3.2. Repeat Step 3.1 with Source B.

3.3. Repeat Step 3.1 once more, this time with Source C. If it has become clear that a certain orientation is far inferior to the other possibilities, you don’t need to continue testing it, but be sure to state your assumption.

3.4. What can you conclude about the most effective way to orient each source? If your conclusions depend on the source in question, be sure to list the preferred orientation for each source separately.

3.5. You should see that there are at least some differences between the sources. What might be the underlying cause?

4. Solving a Mystery

One of the first issues you need to tackle is sorting out what type of sources you have. You know from your predecessor’s notes that Sources A, B, and C are 210Po, 90Sr, and 133Ba, but you don’t know which isotope goes with which label. In addition, there is nothing in the notes about the other source in your possession. After thinking about how you can solve this mystery, you have an idea. You recall learning in class that different densities and thicknesses of material are necessary to stop alpha, beta, and gamma radiation. Assuming NASA doesn’t want to irradiate all of their sensitive scientific equipment on board, it will be necessary to determine how much shielding is required to protect the equipment. This is an important factor when choosing a power source – remember, in space travel, mass is money!

Do This: You’re ready to learn the identity of each source. Securely fasten the radiation detector to the stand so that the radiation detector is 1 cm above the surface of the table. Set the measurement duration to 15 s and the sampling rate to 15 s/sample. Place Source A in whatever orientation you found maximized the number of counts per second.

4.1. Record the total number of counts/s over a 15 s interval. Be sure to subtract the amount of background radiation when reporting your final value.

4.2. Choose one type of shielding material and place it between the detector and Source A. Use Logger Pro to measure the total number of counts/s over a 15 s interval and don’t forget to subtract the background radiation from your final value. Repeat this procedure with other types of shielding material until the radiation is either completely blocked or until you run out of shielding material. For each type of shielding material, record what material you’re using and what the count rate is.

Read This: If you realize that the source and the detector are too close together to squeeze shielding material in between them, you should move the detector the minimum distance necessary to fit the rest of your shielding material. If you move the detector, you will need to take a new baseline measurement of the radiation with no shielding in order to see if adding shielding material changes the radiation counts. You don’t need to repeat measurements with the shielding material you’ve already done (if a material didn’t block the radiation when the source and the detector were close, it won’t block it now that they’re farther apart). You should always start with the detector and source at 1 cm and take whatever measurements you can at this distance. Why do you need to start with a small distance? Well, remember that air is actually full of lots of tiny molecules zipping around, ready to collide with anything that gets in their path. Thinking about the type(s) of radiation this would most significantly impact may help you rationalize which source is which.

4.3. Repeat the above Steps with Source B. You don’t need to use the exact same procedure that you used in Step 4.2 if you think proceeding differently would be more useful. Just be sure to record what materials you’re using and what the count rate is.

4.4. Repeat Steps 4.1 and 4.2 one more time using Source C.

4.5. Identify each source as one of the isotopes listed in the Equipment Section. Explain your rationale for each source. Be sure to comment on why you expect various types of shielding to block (or not block) each of the three types of radiation. [Hint: If you aren’t sure where to start, consider what your work on PL4 tells you about each types of radiation.]

Do This: Check with your TA to be sure that you have correctly identified each type of source STOP before proceeding to Step 4.6.

4.6. With your newfound theoretical and experimental knowledge of how different types of radiation interact with matter, identify which type of radiation (alpha, beta, gamma, or some combination) your mystery source (labeled D, E, F, or G) is emitting. Be sure to explain how you reached your conclusion.

4.7. Did you ever get any results that aren’t plausible (e.g., adding shielding increased the amount of radiation, or you ended up with a negative value when you subtracted the background radiation, etc.)? If so, describe your nonsensical result and briefly explain why your answer doesn’t really defy the laws of physics.

4.8. The isotope 210Po has an interesting history. It has been used in actual RTGs, including the 1970 Soviet Lunokhod 1 rover, which explored the surface of the Moon (the heat generated by 0.5 g of 210Po will result in a temperature of 500°C ≈ 930 °F). Carefully explain the big advantage 210Po would have over the other isotopes explored in this lab. 4.9. Polonium-210 was also used to murder former Soviet spy, Alexander Litvinenko, in 2006 (and possibly Yasser Arafat in 2004). Subsequent investigations determined that Alexander had ingested the 210Po in a pot of tea. He was dead within the month. Polonium-210 decays into lead, which, in itself, is quite poisonous (this is one of the multitude of reasons that eating old paint chips is a bad idea). However, it’s the radiation that did poor Alexander in, not the lead poisoning. Why is drinking polonium-laced tea much worse than tea flavored with any of the other isotopes in this lab (assume the total activity for each radionuclide is the same)? [Safety Note: Alexander Litvinenko ingested orders of magnitude more 210Po than we are using in this lab – the quantity you have in front of you is not deadly. Regardless of the quantity, though, you still shouldn’t eat polonium. ]

4.10. Based on the description of Becquerel’s setup, what type of radiation do you think his uranium salts emitted? Explain your rationale.

Head-Scratchers

Don’t forget to complete the following problems. They should be at the end of your lab report. If you want to work on them during lab, start a new page in your lab notebook.

• 1.7 • 1.8 • 3.5 • 4.8 • 4.9 • 4.10

Appendix A: Radioactive Decay

Radioactive decay always occurs because a nucleus finds a way to lower its energy state. This happens by a variety of processes: turning a neutron into a proton (β- decay); turning a proton into a neutron (β+ and electron capture decay); shedding a He nuclei (α decay); spontaneously breaking apart into smaller pieces (fission); combining with another nucleus (fusion); or just rearranging what’s already there into a new configuration (γ decay). Besides releasing way more energy than any chemical reaction could, all these processes have one thing in common: they follow statistical behavior. If a nucleus is unstable, it will decay, but when that happens can only be statistically predicted. This is a crucial distinction.

One way to express the likelihood of decay for a certain radionuclide is with the decay constant (�), measured in units of s-1:

the probability of a decay � = time interval

As the definition suggests, this is a statement of probability obtained by looking at a large number of nuclei. It is not the same thing as saying that an individual nucleus will decay in some fixed amount of time. The best we can do is talk about the average lifetime of a particle, which is found by taking 1/� (note the units work out to give the time per decay).

In order to keep track of how many nuclei (�) exist at any given time, we define a quantity that measures the number of decays per time interval. This quantity is called the activity (�) and it is measured in the SI unit of becquerels (1 Bq ≡ 1 decay/s):

!" � = �� = − !"

This relationship indicates that the activity gets smaller as time passes and there are fewer nuclei sitting around, waiting to decay. It is often of interest to simply know how much of a sample is still around after some amount of time, compared to the amount that was initially present (�!). This can by found by integrating the activity from the time the clock started (when there was �! of the sample) to some later time (�) when there is some smaller amount (�) of the sample left. Doing this integral gives the expression:

� � = �!!" �!

A final quantity that is useful to know is the half-life (�½), which is defined as the amount of time it takes half of the sample to decay. It doesn’t depend on the amount of a sample that’s present or how long the sample has already been around – if you wait another half-life, then half of whatever is there will decay. Note that this only works because the half-life is a statistical quantity. At its heart, radioactivity is a quantum phenomenon, so it makes sense that radioactivity is also probabilistic. Therefore, the half- life does not mean that if you have a radioactive nucleus and wait one half-life, it will decay. That individual nuclei may decay before one half-life has passed, it may decay later, or it may decay after exactly one-half life. The best you can say is the statistical likelihood of the decay happening. However, if you have a bunch of nuclei and wait for one half-life, then half of those nuclei will decay – you just can’t say beforehand which of the nuclei will decay (sadly, radionuclides don’t come equipped with little watches that let us observe their countdown to decay).

Mathematically, the half-life is just the amount of time it takes to reduce the amount of your substance by half:

� � 1 = = �!!!½ �! 2

Solving for the half-life gives:

ln 2 � = ½ � Appendix B: The 137Cs – 137Ba Isotopic System

Most isotopes have a half-life that is far too long or far too short to accurately measure during physics lab. In both cases, extremely sensitive equipment and advanced scientific techniques beyond the scope of this lab are necessary to accurately measure the isotope’s half-life. However, if the half-life is on the order of seconds or minutes, it is possible to accurately determine the half-life given a simple Geiger counter. The radioactive isotope 137Cs is the parent of just such an isotope. It also has the added benefit that all quantities involved are considered Exempt Quantities by the United States Nuclear Regulatory Commission and are therefore safe to use in lab. The decay scheme is pictured below in Figure 2.

Figure 2: Decay scheme of radioactive 137Cs to stable 137Ba. There are two options for this decay. Most of the time (94.6%), 137Cs decays into metastable Ba (denoted as 137mBa). It’s called “metastable” because the Ba nucleus exists in an excited state for a significant amount of time before the nucleons figure out how to rearrange themselves into the lowest possible energy configuration (denoted as plain old 137Ba) and in doing so, emit the extra energy in the form of a gamma ray. The other 5.4% of the time, 137Cs completely skips the metastable state of Ba and just decays directly to stable 137Ba.

The half-life of 137mBa is perfect for measurement in the lab. However, since it’s so short, you can’t just have a bunch of metastable Ba sitting around on the shelf, waiting to be measured. You also don’t want to measure a random mixture of 137mBa and 137Cs. Since both are radioactive, it would be very difficult to tell what part of the signal is coming from the Ba and what is coming from the Cs.

An isotope generator solves this problem by “milking” a 137Cs source. Although 137Cs and 137Ba have the same number of nucleons, they are chemically very different (Cs is in the first column of the periodic table, Ba is in the second). A pH specific chemical solution is passed through a sample of 137Cs (some of which has already decayed to 137mBa and 137Ba) in a special container with an opening in the top and bottom. This solution is designed to chemically react only with Ba – it won’t bond with Cs. The liquid flows from the top of the container to the bottom, bonding with the Ba along the way. What comes out of the bottom is a liquid full of both 137mBa and 137Ba. Because 137Ba is stable, it doesn’t emit radiation – meaning it can’t interfere with any radioactivity measurements. Since 137mBa has such a short half-life, it will all decay to stable 137Ba in a relatively short period of time. After ~10 minutes, the activity of the sample is essentially zero, so you can just throw the whole sample away in the trash can and not worry about special disposal! The same milking process can be done with many other isotopic systems; you just need to pick the right liquid solution to use. The concept of milking the 137Cs is simple, but it must be done very precisely, or the entire (very expensive) sample of 137Cs could be ruined. Your TA will milk the sample for you to be sure everything goes as planned.

Appendix C: General Handling Procedures for Exempt Quantities of Radioactive Materials1

Exempt Quantity Radioactive Sources

Exempt quantities of radioactive sources fall into two categories: sealed sources and liquid sources. One source of radioactivity, an isogenerator, is a sealed source that produces a liquid source when a solution passes through it. For teaching purposes, sealed sources and isogenerators may be used. All these sources produce minimal radiation dose and, when handled properly, do not pose a risk of contamination.

General Handling Procedures

Although the radiation from exempt quantity sources is not hazardous, the basic principle of minimizing radiation dose should be followed:

• No eating, drinking, or applying cosmetics while handling the sources. • Do not hold sources unless necessary. • Only hold edges of disk. Avoid touching the unlabeled flat side of disk. • Place sources away from living organisms with labeling facing up when not in use. • Wash hands after handling sources. • Sources must be accounted for. Take an inventory before and after each class period. • Sources must be locked up at the end of each day.

These sources, although not hazardous, should be handled with respect. Students should not put any sources in their pockets or hold them in their hands when not necessary.

Normal Radiation Exposure

Radiation has the potential to affect the health of those exposed to it. Health effects only occur from very large doses of radiation. The radiation doses received from the use of exempt quantities of radioactive materials are extremely low compared to the doses that cause adverse health effects. It is safe for teachers and students to handle these sources. The dose from handling the sources is much less than the radiation we are exposed to from natural background radiation in one day.

Special Precautions for Isogenerators

Isogenerators typically contain cesium-137, which is radioactive and decays to barium-137, which is also radioactive. Barium-137 has a half-life of 2.5 minutes, emitting gamma radiation, and then becomes stable. When an eluting solution flows through the cesium, barium attaches to the eluting solution and the liquid leaving the solution then contains some radioactive barium. Because of the short half-life, the barium activity decreases to less than one percent of its original activity in a little more than 15 minutes.

When using an isogenerator:

• Be certain that the eluting solution enters the proper side of the isogenerator so that cesium- 137 is not eluted in addition to barium-137. • Do not let anyone ingest any of the liquid. • Wipe up spills with a paper towel and dispose of it in the trash. • If any liquid solution splashes onto clothes, use a damp cloth to wipe off as much as possible. The remaining radioactivity in the solution will decay rapidly, thus producing minimal radiation exposure. • Wipe sample holders with a paper towel after use and dispose of towels in the trash. • Wash hands after handling.

1All material in Appendix C is taken directly from The Health Physics Society’s “Guidance for the Use of Exempt Quantities of Radioactive Materials in the Secondary Schools” document, published by the Health Physics Society Science Support Committee, August 2010. The Health Physics Society is a nonprofit scientific professional organization whose mission is excellence in the science and practice of radiation safety. Formed in 1956, the Society has approximately 5,500 scientists, physicians, engineers, lawyers, and other professionals. Activities include encouraging research in radiation science, developing standards, and disseminating radiation safety information. The Society may be contacted at 1313 Dolley Madison Blvd., Suite 402, McLean, VA 22101; phone: 703-790-1745; fax: 703-790-2672; email: [email protected].