Generally, there are four main concepts that students struggle with when thinking about radioactive decay:

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1 Name: Radioactivity Lab Date: Reading Comprehension: Read the portion of the article on radioactive decay below and answer the following questions based on the reading. Use complete sentences. How Does Radioactive Decay Work? created by Jennifer M. Wenner, Geology Department, University of Wisconsin-Oshkosh Essential Concepts Generally, there are four main concepts that students struggle with when thinking about radioactive decay: 1. the spontaneity (or randomness) of radioactive decay, 2. the reason isotopes are important, 3. the concept of half-life, and 4. knowing which system is appropriate Radioactivity: A steady but unpredictable (spontaneous) process Radioactivity and radioactive decay are spontaneous processes. Students often struggle with this concept; therefore, it should be stressed that it is impossible to know exactly when each of the radioactive elements in a rock will decay. Statistical probability is the only thing we can know exactly. Often students get bogged down in the fact that they don't "understand" how and why radioactive elements decay and miss the whole point of this exercise. If they can begin to comprehend that it is random and spontaneous, they end up feeling less nervous about the whole thing. Radioactive decay involves the spontaneous transformation of one element into another. The only way that this can happen is by changing the number of protons in the nucleus (an element is defined by its number of protons). There are a number of ways that this can happen and when it does, the atom is forever changed. There is no going back -- the process is irreversible. This is very much like popping popcorn. When we pour our popcorn kernels into a popcorn popper, there is no way to know which will pop first. And once that first kernel pops, it will never be a kernel again...it is forever changed! (And coincidentally, much yummier!) Isotopes: same element, different atomic mass The atoms that are involved in radioactive decay are called isotopes. In reality, every atom is an isotope of one element or another. However, we generally refer to isotopes of a particular element (e.g., Rubidium-87 ( 87 Rb) or Lead-206 ( 206 Pb)). The number associated with an isotope is its atomic mass (i.e., protons plus neutrons). The element itself is defined by the atomic number (i.e., the number of protons). Only certain isotopes are radioactive and not all radioactive isotopes are appropriate for geological applications -- we have to choose wisely. Those that decay are called radioactive (or parent) isotopes; those that are generated by decay are called radiogenic (or daughter) isotopes. The unit that we use to measure time is called half-life and it has to do with the time it takes for half of the radioactive isotopes to decay (see below). Half-life: a useful way of telling geologic time Half-life is a very important and relatively difficult concept for students. Mathematically, the half-life can be represented by an exponential function, a concept with which entry-level students may not have much experience and therefore may have little intuition about it.

2 I find that entry-level students in my courses get stuck on the term "half-life". Even if they have been given the definition, they interpret the term to mean one-half the life of the system. Instead, it is really the lifetime of half of the isotopes present in the system at any given time. Half-life is a term that describes time. The definition is: The time required for one-half of the radioactive (parent) isotopes in a sample to decay to radiogenic (daughter) isotopes. --modified from Webster's Third International Dictionary, Unabridged In other words, it is the lifetime of half the radioactive isotopes in a system. The units of half-life are always time (seconds, minutes, years, etc.). If we know the half-life of an isotope (and we can measure it with special equipment), we can use the number of radiogenic isotopes that have been generated in a rock since its formation to determine the age of formation. Radiometric dating is the method of obtaining a rock's age by measuring the relative abundance of radioactive and radiogenic isotopes. Using demonstrations of half-life such as a coin toss for large classes or M&M demonstration for smaller classes can help students to better understand what is happening. Plotting the results of these demonstrations results in a curve of an exponential decay function. Showing this plot and asking them questions about the shape and changes in number of isotopes through time may help students to develop some intuition about half-life. Although most introductory students may not be prepared for the equation for exponential decay, discussion of half-life and radioactive decay prepares entry-level students for the introduction of more mathematical discussion of exponential growth and decay in upper level classes. So many systems, how do we choose? Most students don't really know how isotopes are used to determine age. In particular, they have a hard time understanding that different systems are appropriate for different types of radiometric dating and why. There are several important points that can be emphasized to help avoid confusion when talking about the various systems: Geologists have a plethora of choices for calculating the age of a rock using big and complicated systems. Check out this table of isotope systems and half-lives; all of these are used to date rocks or sediment! Isotope Systems Useful for Geological Applications and their Half-Lives (Radioactive) Isotope Daughter (Radiogenic) Isotope Half Life (t 1/2 ) Scientific Notation Carbon C Nitrogen N 5,730 years 5.73 x 10 3 years Beryillium Be Boron B 1.5 million years 1.5 x 10 6 years Uranium U Lead Pb 704 million years 7.04 x 10 8 years Uranium U Lead Pb 4.4 billion years 4.4 x 10 9 years Potasium P Argon Ar billion years x years Rubidium Rb Strontium Sr 48.8 billion years 4.88 x years With all these systems, how do we choose? Geologists use a number of criteria to decide which of the systems to use: 1. Is the half-life of the system appropriate for the rock that you are trying to date? Most geologists have an idea of the age of a rock (if age is less than 6 half-lives, it'll work) 2. Does the rock have minerals that can be used for the isotope system you want to use? You need to have minerals in your rock that contain the element(s) you want to use. 3. What event do you want to date? Some systems are very good for dating igneous events, others are very good for dating metamorphic events. (Remember, it is impossible to date sedimentary minerals because they eroded from some igneous or metamorphic rock.) Together, the answers to those questions help geologists decide which system they should use.

3 What about Carbon-14? Most students have heard of Carbon-14; yet, it doesn't appear in the table of isotopes used to date rocks and minerals. Why not? Carbon-14 is not appropriate for rocks because it must involve organic carbon. Rocks are made of minerals that are by definition inorganic. The discussion of 14 C below is a great way to illustrate important points of how to choose a system. Carbon-14 is special for two reasons. 1. With 14 C, we can only calculate the age of something that was once living (contains organic carbon). Since (most) rocks were never alive, we can't use this to date a rock. 2. The half life of 14 C is geologically short years -- and is therefore not useful for materials older than about 35,000 years. That's well over 4 billion years of geologic history that we can't touch. So, what geologists and archaeologists date when they use 14C is the death of an organic life form. Most geologists want to know the age of crystallization or metamorphism of rocks that are millions or billions of years old C won't work for that. 1. Explain the process of radioactive decay. 2. Explain how the atomic mass of an isotope is determined, and how is this different from the atomic number of an element? 3. What is the difference between a parent isotope and its daughter isotope? 4. Why is it impossible to determine the age of sedimentary rocks?

4 The Case of the Missing M&M s You will determine the half-life of the M&M s by performing the following: 1. Count 100 M&M s to start with. Enter this information on the data table below. 2. Start the stop watch. 3. Put all of the M&M s in the cup, shake gently, and pour them out onto the plate. 4. Separate the M s up from the M s down - count the number of M s up that remain and record on the table. 5. Place the M s up back into the cup and EAT all the M s down!! 6. Repeat steps #3 - #5 until one or no M&M s remain. 7. Stop the stop watch and convert the total time into seconds. 8. After all data is obtained, graph the class average on the attached graph: # of Half- Lives Radioactive Element M&M s Remaining yours class average Daughter Product DANGER!!!! M s up = Radioactive!!! DO NOT EAT!! M s down = Nonradioactive - Safe to Eat!!! Construct the Radioactive Decay Curve Below:

5 Vocabulary - Define the following: Radioactive Isotope: Daughter Product: Half-Life: Discussion Questions: 1. What is the half-life of the M&M s (show your work as to how you found it) 2. What does the graph tell you about the rate of radioactive decay? 3. Using the half-life you calculated and your graph, how long will it take for the M&M s to go through 2 half-lives? 4 half lives? 4. What percentage of the parent radioactive element is left after 3 half lives? 5. What is the ratio of parent to daughter product for a radioactive element after 2 half-lives? 6. How many half-lives has a radioactive element gone through if only 3% of the original radioactive isotope remains? 7. Using your data, how old would the M&M s be in question #6? BONUS - At how many half-lives does radioactive decay become unreliable for absolute dating? Explain your answer.