radon: lesson one what is...
TRANSCRIPT
Radon Lesson 1
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Clear plastic or glass container with a lid (e.g., a petri dish)
Half Life Experiment
100 pennies A small cup or Ziploc bag Graph paper Graphing calculator
RADON: LESSON ONE
What is Radioactivity?
LESSON SUMMARY
This lesson introduces students to the origin of radioactive isotopes and how they react within the environment. Lab 1 “Vapor Trails,” allows students to observe energy rays emitted by a radioactive source, helping students gain a more complete understanding of how radiation is released from various sources. In Lab 2, “Pennicium, Pennithium, & Pennium” students will use pennies to simulate the decay process of three different “isotopes” and determine the equation for half-‐life. These activities are followed by application exercises where students solve problems related to the radioactive decay process of various isotopes.
CORE UNDERSTANDING/OBJECTIVES
By the end of this lesson, students will have a basic understanding of radioactivity, radioactive isotopes, the process of radioactive decay, half-‐life and the procedure for balancing radioactive reactions. Specific learning objectives and standards addressed can be found on pages 44 and 45.
MATERIALS/INCORPORATION OF TECHNOLOGY
The Cloud Chamber Experiment Gloves or forceps Flashlight Block of dry ice A radioactive rock/material* Pure ethyl or 90% Isopropyl alcohol Aluminum foil or flat tray Blotter/construction paper
*Potential radioactive sources include uranium ore, Fiesta dinnerware produced prior to 1972, or 0.01 microcuries of Lead-‐210 (available online from vendors such as Spectrum Techniques). A radioactive source can also be requested from CEHS. When it is not possible to complete the cloud chamber experiment, a video of a similar experiment can be shown (e.g., http://bit.ly/13dMJmB)
Personal Annual Radiation Dose Calculator: http://bit.ly/PMU9w4
SUGGESTED READINGS
Beneficial uses of radiation: http://1.usa.gov/11A9qUH Marie Curie and the science of radioactivity: http://bit.ly/c3me02 Radiation risk from Mars travel: http://nyti.ms/12Mh40M
Grade Level: 9 – 12
Subject(s) Addressed: Science, Math Class Time: 2-‐4 Periods
Inquiry Category: Guided
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INDIAN EDUCATION FOR ALL
Radiation and radioactive materials have been and continue to be a part of many Native American cultures. Some examples include sun dances, food preservation (e.g., drying salmon), and navigation using the sun. Granite, which can contain naturally occurring radioactive isotopes, was also used for tools (e.g., harvesting mauls) and in sweat lodges (i.e., heating granite rocks).
ENGAGE
Before introducing the lesson, distribute 3 x 5 index cards or a half sheet of paper to each student and have students number 1 through 4 on one side of the card, allowing for some space to write under each number. Instruct students to write their names on the top right corner. Ask students to record in their own words, 1) How would you define radioactivity?, 2) List 3 natural sources of radioactivity, and 3) List 3 manmade sources of radioactivity, 4) How does radioactivity play a role in our lives? When students are finished recording their answers, collect all of the cards and explain to the students that you will come back to their original responses at a later time. Note: This allows time in between assessing students’ knowledge about radioactivity and the “Vapor Trails” and “Pennicium, Pennithium, & Pennium” experiments, allowing for a true guided-‐inquiry experience.
VOCABULARY
Copies of blank student vocabulary banks (see page 4) can be distributed for completion as either a classroom or homework assignment.
EXPLORE
Distribute Lab 1: “Vapor Trails” (p. 6-‐8) for students to complete in small groups. This activity is a great way to help the students visualize radiation. Notes to the teacher: 1) Depending on available materials, the teacher may choose to complete one experiment and have students make observations in small groups, 2) The teacher may choose to assemble the experiments prior to the class arriving to allow time for the chamber to cool, 3) The teacher may want to have an alternate activity/discussion (e.g., see suggested readings) while students wait for their chambers to cool, 4) To facilitate rapid cooling of the experiment, use dry ice as soon as possible.
EXPLAIN
Once students complete the “Vapor Trails” lab, distribute Comprehension 1: “What is Radioactivity” (p. 11-‐14) for students to review individually during the remainder of the class or as a homework assignment.
At the beginning of the next class, lead a class discussion to review the Vapor Trails lab and Comprehension 1.
Optional Demonstration: Place an undeveloped roll of film next to a radioactive source in a drawer for approximately 24 hours. Develop the film and discuss with students how and why the film was partially exposed.
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ELABORATE:
Distribute Lab 2: “Pennicium, Pennithium, & Pennium” (p. 18-‐19) for students to complete in pairs or small groups. For teacher instructions see page 16. When students have completed the lab, pass out “Calculating Half-‐Life” for students to complete individually or in pairs. Note: there are two versions of the Calculating Half-‐Life activity, A (p. 22-‐23) and B (p. 27-‐28). Calculating Half-‐Life (A) uses a graph and the half-‐life equation, and should be appropriate for most students. Calculating Half-‐Life (B) involves the use of logarithmic properties and may be appropriate for students who have completed Algebra II or above. The teacher may choose to have students complete one of the Calculating Half-‐Life exercises or both when appropriate and time allows. Following the half-‐life exercise, the teacher can distribute “Comprehension 2: Half-‐Life” (p. 29-‐33) for students to read in its entirety either individually or as a group. When all students have completed the assigned tasks, review the lesson material as a class and check for understanding using some of the following discussion points:
• How does ionizing radiation differ from penetrating radiation? (To guide students in answering this question, the teacher can refer students to their vocabulary lists.)
• What is radioactive decay? • Explain what the half-‐life of an isotope is in your own words. • How do alpha, beta, and gamma decay differ? • Why does the dentist put a lead apron over you during dental x-‐rays? • Do you think there are potential health risks associated with radiation
exposure? EVALUATE Distribute blank 3 x 5 index cards to each student and have students number 1 through 3 on one side of the card. Instruct students to write their names on the top right corner. Ask students to record in their own words, 1) How would you define radioactivity?, 2) List 3 natural sources of radioactivity, and 3) List 3 manmade sources of radioactivity. When students are finished recording their answers, hand out the student’s original cards that they completed prior to the Lesson 1 activities. Review questions 1 through 3 as a class and ask students to discuss how their answers changed from the first time they answered the three questions. At the end of the class, ask students to turn in both of their cards. Vocabulary sheets, lab sheets, Comprehension Guiding Questions, and the Evaluation Questions (p. 36-‐39) all provide opportunities for formal assessment.
Notes:
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What is Radioactivity? – Vocabulary
Atomic nuclei:
Ionizing radiation:
Penetrating radiation:
Progeny:
Isotope:
Radioactive decay:
Radioactivity:
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What is Radioactivity? – Vocabulary
Atomic nuclei: The central region of an atom consisting of protons and neutrons
Ionizing radiation: Radiation with enough energy to alter chemical bonds (i.e., removing or knocking out electrons from atoms), thus resulting in positively charged ions
Penetrating radiation: Radiation with enough energy to penetrate the skin and reach internal organs and tissues.
Progeny: An offspring or descendant
Isotope: A form of a chemical element that has the same atomic number (number of protons), but a different atomic mass (protons + neutrons)
Radioactive decay: The spontaneous disintegration of a radionuclide accompanied by the emission of ionizing radiation in the form of alpha or beta particles or gamma rays. Note: Nuclide is a general term describing a unique atom with an atomic number and mass number
Radioactivity: The act of spontaneously emitting particles and/or radiation from unstable atomic nuclei or as the result of a nuclear reaction
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Lab 1: Vapor Trails
Guiding Question: How can you see high-‐energy particles?
Teacher Directions Note: The teacher may choose to set up this demonstration and allow students to observe the experiment individually or in small groups, or the teacher may choose to show the YouTube video of the Vapor Trails experiment (https://www.youtube.com/watch?v=a9tl7O7AWhE -‐ also known as the Cloud Chamber experiment) to the students and have the students observe the vapor trails experiment in the classroom. An added benefit of the video is that the video can be stopped and the length of the different ions can be measured, and their speed can be calculated. One to three different source materials can be used, showing a radioactive source(s) (e.g., Fiesta dinnerware and Lead-‐210) and a non-‐radioactive source (e.g., a piece of concrete). The teacher may also choose to use one large chamber with multiple sources. This approach would ensure that the amount of vapor would be the same for each source material. Note: The isotopes suggested for use in this demonstration emit very low-‐level radiation and are not harmful.
1. Cut a circular piece of black blotter or construction paper large enough to cover the bottom of two to three clear containers (e.g., a glass or plastic petri dishes with lids).
2. Insert the paper inside each container, covering the bottom of the container. 3. Cut a ½-‐1 inch section of black blotter or construction paper long enough to cover the bottom ½ inch – 1
inch of the sides of each container. 4. Insert the blotter/construction paper inside the bottom of the containers, fitting it snuggly against the sides. 5. Pour ethyl alcohol into each container until approximately 1/8 inch of alcohol covers the bottom of the
containers. Note: The paper will absorb some of the alcohol. 6. Using forceps, place the source material in the center of one container. 7. In the center of the other container(s), place a non-‐radioactive material (e.g., a dinnerware fragment, rock,
iron, etc.) 8. Next, place blocks of dry ice (large enough to cover the bottom of your containers) in a flat tray or on a piece
of aluminum foil. 9. Carefully set your containers on top of the dry ice and let them cool for approximately 5-‐10 minutes. Note:
Longer cooling times will have better results. 10. Turn off the lights and shine a flashlight through the top or the sides of the containers. 11. Observe what is happening by looking through the lid or the sides of the containers. 12. (Optional) Have students share their data/tables on the whiteboard in question #5 so the students/groups
can compare their data to the class data.
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Lab 1: Vapor Trails
Guiding Question: How can you see high-‐energy particles?
In this lab, two to three chambers will be set up. Each chamber will contain a different source material. Follow the directions below to complete this lab.
Student Observations (possible student answers):
1. Once the lights are turned off, view the inside of each chamber for a minimum of three minutes. Describe your observations.
2. Are any of your observations measurable or quantifiable? If so, please describe.
3. Two to three different tracks or trails should be emitted from one or more of the source materials. Develop a table below to record your data (e.g., estimate the length, describe the shape or speed of your observations, etc.).
4. Hypothesize as to the relationship between your observations and the source material(s).
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5. One or more of the source materials provided contained radioactive isotopes. (Note: These isotopes emit very
low-‐level radiation and are not harmful.) Radioactive isotopes are unstable, and therefore they are constantly decaying and emitting radiation. There are three main types of radiation emitted during radioactive decay – Alpha and Beta particles and Gamma rays. Alpha particles are slower moving particles that extend in a straight line approximately one centimeter or less in length. Beta particles move at a faster speed than alpha particles, and extend in thinner straight lines approximately three to ten centimeters in length. Gamma rays (if present) may be seen as fast, spiraling puffs of vapor.
Using your data and answers from question 3, determine if the tracks you observed were Alpha or Beta particles, and/or Gamma rays. Support your findings with data.
6. If possible, view the chambers for two to three more minutes to confirm your observations above. Record any new or revised observations below.
7. Based on your observations how would you modify your data table?
8. If you had a sample of Polonium-‐214 (a radioactive isotope known to emit alpha particles) what would you expect to see? Explain your reasoning.
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Lab 1: Vapor Trails-‐ Teacher Key
Guiding Question: How can you see high-‐energy particles?
In this lab, two to three chambers will be set up. Each chamber will contain a different source material. Follow the directions below to complete this lab.
Student Observations (possible student answers):
1. Once the lights are turned off, view the inside of each chamber for a minimum of three minutes. Describe your observations.
Students should notice that there are two distinct types of vapor trails produced. One of the types of trails is shorter and the particles (alpha particles) appear to move a little slower than the particles (beta particles) that produce trails that are significantly longer.
2. Are any of your observations measurable or quantifiable? If so, please describe.
Students could determine approximate lengths of the vapor trails produced, they could record relative speed, and they could count the relative number of each type of vapor trail produced over a specified time period.
3. Two to three different tracks or trails should be emitted from one or more of the source materials. Develop a table below to record your data (e.g., estimate the length, describe the shape or speed of your observations, etc.).
Table 1: Comparisons of Vapor Trails Produced in the Cloud Chamber
Type of Vapor Trail Approximate Vapor Trail Length, cm
Relative Speed of Particle
Relative Number of Particles
Shortest ≈ 1 cm Slower 18/minute
Longest ≈5 cm Faster 22/minute
Do not introduce the names of the different particles at this point so students have to develop their own labels for the “Type of Vapor Trail” column. To determine the relative number of particles, suggest to students that they count the number of trails produced over a specified time period such as a minute. Students should do several trials here as this is not easy. These counts are much easier to do using the video suggested in the instructions.
4. Hypothesize as to the relationship between your observations and the source material(s). Based on the data collected in question 3 above, the source material appears to produce two different types of particles in approximately equal numbers. One of the particles produces shorter vapor trails and moves more slowly than the second particle.
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5. One or more of the source materials provided contained radioactive isotopes. (Note: These isotopes emit very low-‐level radiation and are not harmful.) Radioactive isotopes are unstable, and therefore they are constantly decaying and emitting radiation. There are three main types of radiation emitted during radioactive decay – Alpha and Beta particles and Gamma rays. Alpha particles are slower moving particles that extend in a straight line approximately one centimeter or less in length. Beta particles move at a faster speed than alpha particles, and extend in thinner straight lines approximately three to ten centimeters in length. Gamma rays (if present) may be seen as fast, spiraling puffs of vapor.
Using your data and answers from question 3, determine if the tracks you observed were Alpha or Beta particles, and/or Gamma rays. Support your findings with data.
The tracks labeled shorter in Table 1, question 3, are alpha particles as they are shorter in length and the particles producing the tracks move more slowly. The tracks labeled longer are beta particles as the vapor trails are longer and the particles producing the trails move faster.
6. If possible, view the chambers for two to three more minutes to confirm your observations above. Record any new or revised observations below.
Students may notice the trajectories of the vapor trails vary; some are relatively straight while others appear to be arcs. The alpha particles appear to produce more arcing trails than the beta particles.
7. Based on your observations how would you modify your data table?
This response would depend on the student’s original table developed in question 3. After observing the cloud chamber over a period of time, they should recognize that they can collect data in at least three areas – length of vapor trail, relative speed of the particles, and relative number of particles.
8. If you had a sample of Polonium-‐214 (a radioactive isotope known to emit alpha particles) what would you expect to see? Explain your reasoning.
According to the data collected in Table 1, question 3, and the information from question 5, students should observe relatively short vapor trails of approximately 1 cm in length. Students would not be able to supply information on the speed of the particles or relative number of particles produced because there would not be other types of trails produced for comparison.
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COMPREHENSION 1
What is Radiation? INTRODUCTION
During the formation of the Earth nearly 4.6 billion years ago, radioactive minerals became a small but significant part of the Earth’s crust. Today, these minerals can be found naturally in the environment in rocks, soil, and water. Radioactive minerals exist in most countries and within all 50 states.
In order to gain an understanding of radioactivity, one must have a basic understanding of radiation science.
WHAT IS RADIATION?
Radiation is a general term, defined as a process in which energy is transmitted or propagated through matter or space. Radiation exists on Earth and comes to Earth from outer space from the sun and in the form of cosmic rays. Light, sound, microwaves, radio waves, and diagnostic x-‐rays are all examples of radiation. Most radiation is not detected by our senses – we cannot feel it, hear it, see it, taste it, or smell it. However, if radiation is present it can be detected and measured.
The Discovery of Radioactive Minerals. Radioactivity was discovered in 1896 by Henri Becquerel and grew as a result of later investigations, including those of Pierre and Marie Curie. In 1902, Ernest Rutherford and Frederick Soddy determined that radioactivity results from the spontaneous decomposition of an atom (i.e., radioactive decay), resulting in the formation of a new element. These changes are often accompanied by the emission of particles and/or rays.
Ionizing Radiation. Although not all radiation is harmful, ionizing radiation (or radiation that alters chemical bonds and produces ions) often comes to mind when the topic is discussed. To understand ionization, it is important to review the basic composition of an atom. An atom consists of a central nucleus that contains comparatively larger particles known as protons and neutrons. These particles are orbited by smaller particles known as electrons. Their relative masses are displayed in the sidebar. One way to think of an atom is to
Relative Masses
Proton – 1.6727 x 10-‐24 g
Neutron – 1.6750 x 10-‐24 g
Electron – 9.110 x 10-‐28 g
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visualize a miniature solar system where the sun represents the nucleus and the orbiting planets represent electrons. In a normal situation or in the case of a neutral atom, the number of electrons orbiting a nucleus equals the number of protons in the nucleus.
When an atom or molecule gains or loses electrons, it becomes an ion. Ions can be either positively or negatively charged. A positively charged ion (i.e., cation) results from the removal of one or more electrons, while a negatively charged ion (i.e., anion) results from gaining extra electrons.
Radiation that has enough energy to remove or knock out electrons from atoms, and thus create positively charged ions is known as ionizing radiation. Many types of ionizing radiation exist, but the most well known include alpha, beta and gamma radiation. These basic types of ionizing radiation are also emitted during the process of radioactive decay, which is described below.
Radioactive Decay. Many atomic nucleuses are radioactive or in other words, unstable. As a result, these nuclei often give up energy to shift to a more stable state. Known as radioactivity, this spontaneous disintegration of unstable atomic nuclei, results in the emission of radiation.
Sources of Radiation Exposure. We are exposed to radiation every day. For example, radon is a radioactive gas produced from uranium decay. Radon gas can be dispersed into the air as well as ground and surface water. Radioactive potassium (which comes from uranium, radium, and thorium in the Earth’s crust) can be found in our food and water. Radiation can also come to us via cosmic rays and the sun. These are all examples of natural or background radiation. In the United States, it is estimated that a person is exposed to an average of 300 millirems of background radiation each year. However, 300 millirems only equates to half of an adult’s average yearly exposure. The other 300 millirems of exposure come from manmade sources of radiation, primarily from medical tests such as x-‐rays and CT scans. Some additional manmade radiation sources that people can be exposed to include: tobacco or cigarettes, television, smoke detectors, antique/vintage Fiesta dinnerware, lantern mantles, and building materials.
Radioactive decay processes can be natural or manmade. Different units exist for radiation. These units are dependent on what is being measured:
Biological damage from radiation is measured in millirems.
Absorbed energy from radiation is measured in rads.
The decay rate of a radioactive substance is measured in curies.
Radiation intensity of x-‐rays or gamma rays is measured in roentgens. The biological equivalent dose to human tissue is measured in sieverts.
Radioactive Isotopes. An isotope of an element is a form of a chemical element that has the same atomic number (proton number) but a different atomic mass (protons + neutrons). An element can have more than one isotope. For example, Thorium, a heavy metal that occurs naturally in the Earth’s crust, has 26 known isotopes. Although most elements have isotopes, not all isotopes are radioactive. For example, the most common isotopes of hydrogen and oxygen are stable or non-‐reactive. A commonly studied radioactive isotope is Uranium-‐238 (U-‐238). When U-‐238 decays over time, a cascade of different decay products (also known as daughters or progeny) are formed. Of these daughters or progeny, a number
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of them also go through radioactive decay leaving Lead-‐206 (Pb-‐206) remaining. This cascade of decay stops with Pb-‐206 because it is a stable isotope.
Notes:
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Comprehension 1 -‐ Guiding Questions
1. Explain the difference between radiation and radioactivity.
2. Who was primarily responsible for the discovery of radioactivity? When was this discovery made?
3. Explain how ionizing radiation affects an atom. What radioactive particles are primarily responsible for causing ionization to occur? How are those radioactive particles produced?
4. What is an isotope? Why do some isotopes produce high-‐energy, radioactive particles?
5. A number of radioactive progeny are produced by the decay of Uranium 238. Why does the decay ultimately end?
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Radioactivity Comprehension 1 -‐ Guiding Questions Teacher Key
1. Explain the difference between radiation and radioactivity.
Radiation is a general term, defined as a process in which energy is transmitted or propagated through matter or space. Radiation exists on Earth and comes to Earth from outer space from the sun and stars. Examples include visible light, microwaves, radio waves, and diagnostic x-‐rays. Radioactivity results from the spontaneous decomposition of an atom (i.e., radioactive decay), resulting in the formation of a new element or isotope. These changes are often accompanied by the emission of particles and/or rays.
2. Who was primarily responsible for the discovery of radioactivity? When was this discovery made?
Radioactivity was discovered in 1896 by Henri Becquerel and grew as a result of later investigations, including those of Pierre and Marie Curie. In 1902, Ernest Rutherford and Frederick Soddy determined that radioactivity results from the spontaneous decomposition of an atom (i.e., radioactive decay), resulting in the formation of a new element.
3. Explain how ionizing radiation affects an atom. What radioactive particles are primarily responsible for causing ionization to occur? How are those radioactive particles produced?
Radiation that has enough energy to remove or knock out electrons from atoms, and thus create positively charged ions is known as ionizing radiation. Alpha and beta particles are the radioactive particles that cause ionizing radiation to occur. Alpha and beta particles are produced during radioactive decay.
4. What is an isotope? Why do some isotopes produce high-‐energy, radioactive particles?
An isotope of an element is a form of a chemical element that has the same atomic number (proton number) but a different atomic mass (protons + neutrons). An element can have more than one isotope. Unstable isotopes, such as those in the decay series of U-‐238 undergo radioactive decay, which emit radioactive particles.
5. A number of radioactive progeny are produced by the decay of Uranium 238. Why does the decay ultimately end?
Uranium decays through a number of radioactive elements and isotopes. The decay series ultimately ends with the stable isotope Lead-‐206.
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Lab 2: Pennicium, Pennithium, & Pennium Guiding Question: How can the rate of radioactive decay be determined by using isotopes of Pennicium, Pennithium, and Pennium?
Teacher Instructions In this activity, students will be working with three (fictitious) distinct isotopes: Pennicium-‐100, Pennithium-‐80, and Pennium-‐30. The teacher can have students complete the data tables for all of the isotopes in small groups or break the class up into groups, assigning one isotope to each group. Note: If the math is too advanced for a specific class of students, the teacher can go through the different types of regression with the class to determine the type of regression used in question #9. The teacher can also demonstrate how to determine the equation for the line of best fit in question #10. The students can then follow this example and complete questions #11-‐15 in small groups. When each group has finished collecting data for their assigned isotope, they can then write their data and equations on the board for the other students to analyze when completing the rest of the activity.
A TI graphing calculator or the freeware program, Meta-‐Calculator 2.0, can be used to determine the regression equation for the student-‐generated graph.
TI Graphing Calculator Option: 1. To enter the data, press STAT then choose option 1 Edit. 2. Enter the number of shakes in the L1 column (if there is existing data in the column, scroll up to the
top of the column until L1 is highlighted then press CLEAR). Enter the number of heads remaining for each shake in the L2 column.
3. To determine the line of best fit and corresponding equation based on the chosen regression type, use STAT then toggle over to the second option CALC. Under CALC, scroll down to ExpReg then press ENTER. A screen will appear with the heading ExpReg. Press ENTER again, the regression equation will appear in the form y=a∙b^x with the corresponding values of a, b, r2, and r included. Be sure to write down the equation that appears on your screen before moving onto the next step.
4. To graph the equation, use Y= (it is on the upper most row of buttons) and enter your equation from step 3 above then press ENTER. To view the graph of the equation use 2ND then STAT PLOT (it is the same as the Y= button) scroll down to 1:Plot 1 and press enter. Under Plot1, be sure the On command is highlighted; scroll down to choose the graph type; and insure Xlist is L1 and YList is L2. Press the ZOOM button (top row of buttons), scroll down to 9:ZoomStat and press ENTER. If a student’s line is not a good fit, he/she probably did not choose the exponential regression option so they should review the options from question 8, choose a different regression option, and repeat steps 3 and 4 above.
Examples Using Actual Experimental Data
L1 L2 0 100 1 54 2 20 3 12 4 6 5 4
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5. When the data is entered into the calculator according to steps 1-‐3, the following information should
be presented: ! = #×%&, # = 92.98, % = 0.5154, 01 = 0.9867, 0 = −0.9933. 6. When the equation is graphed according to step 4, the graph displayed above should result.
Meta-‐Calculator 2.0 Option:
1. Proceed to the web address http://www.meta-‐calculator.com/online/ and open the Statistics Calculator.
2. Open the Regression Analysis window and enter the number of shakes in the xi column and the number of heads remaining in the fi column. Select Exponential as the type of regression then press the Analyze>> button at the bottom of the page. The Regression Analysis window will show the regression equation in the form y=a∙b^x and it will also show the co-‐efficient of co-‐relation, r, as well as the co-‐efficient of determination, r2.
3. To graph the equation, press the Plot Graph>> at the bottom of the Regression Analysis window. A graph will appear with options for changing the minimum and maximum X and Y values. If a student’s line is not a good fit, he/she probably did not choose the exponential regression option so they should review the options from question 8, choose a different regression option, and repeat steps 2 and 3. The graph can be saved as an image file by right-‐clicking on it (the Save Graph function is not operational). Example Using Actual Experimental Data:
4. After the data is entered according to step 2 and the Analyze>> button is pushed, the following information will be provided:
Regression Analysis
1. Regression Equation ! = 92.9809×0.5154∧- 2. Co-‐efficient of co-‐relation -‐0.9933 3. Co-‐efficient of determination 0.9867
5. Pressing the Plot Graph>> button generates the following graph (the X and Y minimum and maximum values were adjusted accordingly to show the graph in this format):
xi fi 1. 0 100 2. 1 54 3. 2 20 4. 3 12 5. 4 6 6. 5 4
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Lab 2: Pennicium, Pennithium, & Pennium
Guiding Question: How can the rate of radioactive decay be determined by using isotopes of Pennicium, Pennithium, and Pennium?
In this activity, you will be working with three distinct isotopes, Pennicium-‐100, Pennithium-‐80, and Pennium-‐30. Follow the directions below to determine the rate of radioactive decay for each isotope.
Student Directions 1. Obtain 100 pennies (i.e., Pennicium-‐100) and place them in a cup or Ziploc bag. 2. Shake the contents of your container and empty the pennies onto a flat surface. 3. Remove all of the pennies with the tails side facing up. 4. Record the number of “heads” that remain in the table below. Note: One or more heads must remain each time
to record an observation. If no heads remain, simply return the remaining pennies to your container and repeat steps 2-‐4.
5. Weigh each group of “heads” and record your findings in the table below. Note: If a scale is not available, you can assume each penny weighs 1 g.
6. Place the remaining pennies back in the container and repeat steps 2-‐4 four more times. 7. Repeat steps 1-‐5 for Pennithium-‐80 and Pennium-‐30, beginning with 80 pennies for trial 2, and 30 pennies for
trial 3. 8. Graph your results from each experiment on one sheet of graph paper using different colored pens. Note: Make
sure you put your independent and dependent variables on the correct axis, include a graph title, and label your axes.
9. Using the information below, determine what type of trend line/regression type will produce the line of best fit
for your data. Record your answer below.
Linear: A linear trend line is used when data points resemble a straight line that increase or decrease at a steady rate.
Logarithmic: A logarithmic trend line is a curved line where the data increases or decreases at a steady rate and then levels outs. A logarithmic line can contain negative and/or positive values.
Exponential: An exponential trend line is a curved line that is used when values rise or fall at constantly increasing rates. An exponential trend line will approach zero or infinity, however data points will never include zero or negative values.
Polynomial: A polynomial trend line is a curved line that is used when data fluctuates (e.g., one or more bends in the data).
Power: A power trend line is a curved line that is best used when data increases at a specific rate. A power trend line cannot contain zero or negative values.
Shakes/rolls Pennicium-‐100 Mass (g) Pennithium-‐80
Mass (g) Pennium-‐30 Mass (g)
0 100 80 30 1 2 3 4 5
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10. Using a TI graphing calculator or the online Meta-‐Calculator 2.0 (http://bit.ly/HXcjnE), enter your data points (shakes/rolls and mass) for Pennicium-‐100 in the appropriate columns. If using a TI Calculator: select STAT, Edit, and enter data points in L1 and L2. If using the Meta-‐Calculator: select “Statistics Calculator” and then select the “Regression Analysis” tab; enter data points in the xi and fi columns. Determine the line of best fit using the regression type you chose above in question 8 (TI Hint: STAT, CALC; META Hint: select type of regression and click “Analyze”). Write the equation below.
11. Graph your equation from question 10 with the data points you entered in question 9. (TI Hint: Y=; enter equation; make sure Plot 1 is turned on; ZOOM; select 9; Meta Hint: “Plot Graph”, note: you may need to change the bounds to view full graph). How well does the line fit your data? If the line is not a good fit, review the definitions in question 8 to determine if there is another regression type that may produce a better fit.
12. Repeat steps 9 through 11 with Pennithium-‐80 and Pennium-‐30. Record the type of regression used and the equation for each line of best fit below.
13. Write the equations for the lines of best fit for Pennicium-‐100, Pennithium-‐80, Pennium-‐30 below. What does each of your equations have in common?
14. Thinking about the material (pennies) you began each experiment with, what does the similarity you identified in question 13 model?
.
15. If you were given a 200g sample of the isotope Pennercum-‐200, what would the data table and graph for its radioactive decay look like? Use the space below to sketch your data table and graph.
Radon Lesson 1
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Lab 2: Pennicium, Pennithium, & Pennium -‐Teacher Key
Guiding Question: How can the rate of radioactive decay be determined by using isotopes of Pennicium, Pennithium, and Pennium?
In this activity, you will be working with three distinct isotopes, Pennicium-‐100, Pennithium-‐80, and Pennium-‐30. Follow the directions below to determine the rate of radioactive decay for each isotope.
Student Directions 1. Obtain 100 pennies (i.e., Pennicium-‐100) and place them in a cup or Ziploc bag. 2. Shake the contents of your container and empty the pennies onto a flat surface. 3. Remove all of the pennies with the tails side facing up. 4. Record the number of “heads” that remain in the table below. Note: One or more heads must remain each time
to record an observation. If no heads remain, simply return the remaining pennies to your container and repeat steps 2-‐4.
5. Weigh each group of “heads” and record your findings in the table below. Note: If a scale is not available, you can assume each penny weighs 1 g.
6. Place the remaining pennies back in the container and repeat steps 2-‐4 four more times. 7. Repeat steps 1-‐5 for Pennithium-‐80 and Pennium-‐30, beginning with 80 pennies for trial 2, and 30 pennies for
trial 3. 8. Graph your results from each experiment on one sheet of graph paper using different colored pens. Note: Make
sure you put your independent and dependent variables on the correct axis, include a graph title, and label your axes.
*Examples of student-‐derived data are shown above in red. Results will vary.
9. Using the information below, determine what type of trend line/regression type will produce the line of best fit for your data. Record your answer below.
Linear: A linear trend line is used when data points resemble a straight line that increase or decrease at a steady rate.
Logarithmic: A logarithmic trend line is a curved line where the data increases or decreases at a steady rate and then levels outs. A logarithmic line can contain negative and/or positive values.
Exponential: An exponential trend line is a curved line that is used when values rise or fall at constantly increasing rates. An exponential trend line will approach zero or infinity, however data points will never include zero or negative values.
Polynomial: A polynomial trend line is a curved line that is used when data fluctuates (e.g., one or more bends in the data).
Power: A power trend line is a curved line that is best used when data increases at a specific rate. A power trend line cannot contain zero or negative values.
Shakes/rolls Pennicium-‐100 Mass (g) Pennithium-‐80
Mass (g) Pennium-‐30 Mass (g)
0 100 261.49 80 209.06 30 79.12 1 61 158.64 39 102.86 15 39.88 2 13 34.28 22 58.06 9 13.79 3 12 32.50 11 29.96 2 5.54 4 9 24.96 5 11.20 2 5.64 5 2 6.16 1 2.52 1 3.11
Exponential
Radon Lesson 1
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1. Using a TI graphing calculator or the online Meta-‐Calculator 2.0 (http://bit.ly/HXcjnE), enter your data points (shakes/rolls and mass) for Pennicium-‐100 in the appropriate columns. If using a TI Calculator: select STAT, Edit, and enter data points in L1 and L2. If using the Meta-‐Calculator: select “Statistics Calculator” and then select the “Regression Analysis” tab; enter data points in the xi and fi columns. Determine the line of best fit using the regression type you chose above in question 8 (TI Hint: STAT, CALC; META Hint: select type of regression and click “Analyze”). Write the equation below.
Equations will vary (e.g., using sample data above ! = 249.5 ∗ (. 50),)
10. Graph your equation from question 10 with the data points you entered in question 9. (TI Hint: Y=; enter equation; make sure Plot 1 is turned on; ZOOM; select 9; Meta Hint: “Plot Graph”, note: you may need to change the bounds to view full graph). How well does the line fit your data? If the line is not a good fit, review the definitions in question 8 to determine if there is another regression type that may produce a better fit. The line should fit the data very well (similar to the graph shown in question 15 below). If not, the student
likely chose the incorrect type of regression.
11. Repeat steps 9 through 11 with Pennithium-‐80 and Pennium-‐30. Record the type of regression used and the equation for each line of best fit below.
Equations will vary. Examples shown use sample data above.
Exponential -‐ Pennithium-‐80: ! = 260.7 ∗ (. 43)-
Exponential -‐ Pennithium-‐30: ! = 65.6 ∗ (. 52)*
12. Write the equations for the lines of best fit for Pennicium-‐100, Pennithium-‐80, Pennium-‐30 below. What does each of your equations have in common?
Pennithium-‐100: ! = 249.5 ∗ (. 50),
Pennithium-‐80: ! = 260.7 ∗ (. 43)-
Pennithium-‐30: ! = 65.6 ∗ (. 52)*
13. Thinking about the material (pennies) you began each experiment with, what does the similarity you identified in question 13 model?
After each shake/roll (x), approximately half of the material (i.e., mass) remains.
14. If you were given a 200g sample of the isotope Pennercum-‐200, what would the data table and graph for its radioactive decay look like? Use the space below to sketch your data table and graph.
Shakes/Rolls Pennercum-‐200 (g) 0 200
1 100
2 50
3 25
4 12.5
5 6.25
Radon Lesson 1
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Calculating Half-‐Life (A)
Guiding Question: How are half-‐lives calculated?
The graph you developed in the Pennicium, Pennithium, & Pennium lab should resemble the graph below and illustrates the concept of half-‐life or the exponential nature of decay exhibited by radioactive materials. Radioactive decay is important in a variety of fields from medicine to energy production, astronomy, and geology. Some of the applications of the radioactive decay process include determining how long spent nuclear fuel poses an environmental danger and dating geological materials based on their half-‐lives.
When appropriate, use the graph to solve the following problems:
Example: Francium-‐223, one of the most unstable and reactive elements, has a half-‐life of approximately 22 minutes. If you initially had a 10.0 g of Francium-‐223, how many grams would remain after 55 minutes?
First, determine the number of half-‐lives that have occurred:
!!#$%&'()*)$*+ =
--#$%.'()*)$/+0 1ℎ34546789 = 55;6<× &'()*)$*+
!!#$% = 2.5ℎ34546789
Using the graph, determine what percent of the material remains after 2.5 half-‐lives.
10.0%×0.18 = 1.8%)*+,-./0-223*40+.,.,%
-‐ -‐ -‐
-‐ -‐
Radon Lesson 1
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1. Iodine-‐131 (I-‐131) has a half-‐life of approximately 8.0 days. If you started with an 80.0g sample, how many grams of I-‐131 would be left after 2 days?
2. There are 200.0 grams of an isotope with a half-‐life of 42 hours present at time zero. How much time will have elapsed when 76.0 grams remain?
3. After 15 days, approximately 70% of a sample of a radioactive isotope remains from the original material. What is the half-‐life of the sample?
15. The half-‐life of the radioactive isotope phosphorus-‐32 is approximately 14.3 days. How long until a sample loses 98% of its radioactivity?
16. Uranium-‐238 has a half-‐life of 4.46 x 109 years. How much U-‐238 should be present in a sample 2.5 x 109 years old, if 2.00 grams was present initially?
Radon Lesson 1
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Calculating Half-‐Life (A)-‐ Teacher Key
1. Iodine-‐131 (I-‐131) has a half-‐life of approximately 8.0 days. If you started with an 80.0g sample, how many grams of I-‐131 would be left after 2 days?
2 days represents ¼ or 0.25 half-‐lives.
According to the graph, at 0.25 half-‐lives, approximately 80% of the original material will remain:
80.0%×0.80 = 64.0%*-131./012323%.
2. There are 200.0 grams of an isotope with a half-‐life of 42 hours present at time zero. How much time will have elapsed when 76.0 grams remain?
First, solve for the percentage of the isotope remaining after time, t.
%#$%&'('() = 76.0) ÷ 200.0) = 0.380 = 38%.
According to the graph, 38% remaining represents 1.4 half-‐lives:
!"#$$&'()$* = 1.4ℎ'&0&"1$)× 34567589:9;:< = 59ℎ?) .
3. After 15 days, approximately 70% of a sample of a radioactive isotope remains from the original material. What is the half-‐life of the sample?
According to the graph, 70% remaining represents 0.5 half-‐lives:
ℎ"#$#&$' = 15+",-× /0.234565789: = 30+",-
4. The half-‐life of the radioactive isotope phosphorus-‐32 is approximately 14.3 days. How long until a sample loses 98% of its radioactivity?
If the sample loses 98% of its radioactivity, then there will be 2% of the original sample of P-‐32 remaining. According
to the graph, 2% remaining represents approximately 5.6 half-‐lives.
!"#$ = 5.6ℎ"+,+-./$× 12.345671859:9;:< = 80?"#$.
5. Uranium-‐238 has a half-‐life of 4.46 x 109 years. How much U-‐238 should be present in a sample 2.5 x 109 years old, if
2.00 grams was present initially?
!". ℎ%&'&)*+, = .../0123456789.:012345678 = 0.56ℎ%&'&)*+, .
According to the graph, approximately 68% of U-‐238 will remain after 0.56 half-‐lives.
!#-238 = 2.00!×0.68 = 1.36! .
-‐ -‐
-‐ -‐
-‐ -‐
-‐ -‐
Radon Lesson 1
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Calculating Half-‐Life (B)-‐Teacher Key Guiding Question: How are half-‐lives calculated?
The equations you calculated in the Pennicium, Pennithium, & Pennium experiment should resemble ! = # $%&where a
equals the number of pennies in the beginning, x is the number of shakes/rolls, and y is the number of pennies remaining after that throw. This equation illustrates the concept of half-‐life or the exponential nature of decay exhibited by radioactive materials. Radioactive decay is important in a variety of fields from medicine to energy production, astronomy, and geology. Some of the applications of the radioactive decay process include determining how long spent nuclear fuel poses an environmental danger and dating geological materials based on their half-‐lives. A common equation that is used for the exponential decay process (shown below) is very similar to the equation you developed and can also be used to solve half-‐life or radioactive decay problems.
*Note to Teacher: The following problems are optional, as they require advanced mathematical solutions. For example, some of the solutions require the use of logarithms and therefore a minimum of an Algebra II background. Team teaching this exercise with a math teacher is an option. To guide students in the right direction, provide the following logarithmic property (shown in red text in the box below). Student worksheet follows this key.
! " = !$ %&
()*/,
Where: • ! " = "ℎ%'()*+"),'-*.-"'+/%"ℎ'"0%('1+-',"%0'-2%/1,1/"1(% " ),3%/'4 • !" = $ℎ&"()*+,-,."/+$"0$ℎ&1/21$,+3&$ℎ,$4)--5&3,6 • ! = !#$% • !"/$ = ℎ'()(+),-).ℎ,/,0'1+234564.'20,
Using the equation above, solve the following problems:
Example: There are 200.0 grams of an isotope with a half-‐life of 42 hours present at time zero. How much time will have elapsed when 76.0 grams remain?
!"#$%'ℎ)*+,#-+.'#/),).+0)12+'#-$, 4 ' = 4- 12
89:/< '-"-=/)>-*':
76# = 200# '( *+,-./01 ! To solve for t, you need to take the log of each side.
!"# $%&'((& = *
+'-./01 !"# 2' ! !"# $%&
'((& =-‐.420 ! !"# $% =-‐.301
-.#$%-.&%' *42ℎ-./0 = t ! t = 58.6 hours
1. Iodine-‐131 (I-‐131) has a half-‐life of 8.0197 days. If you started with an 80.0g sample, how many grams of I-‐131 would be left after 2 days? Use the radioactive decay equation to solve the problem then compare your result with the original result derived from using the graph.
! " = 80.0 '( *+.,-./ ! ! " = 67.3(
The following logarithmic property is needed to correctly solve some of the problems in this activity.
Log Un = n*Log (U)
According to the graph, 2 days represents 0.25 of a half-‐life of 8 days. After 0.25 half-‐lives, approximately 80% of the original material remains -‐ 80.0g × 0.80 = 64.0g. The two answers are reasonably similar.
-‐
Radon Lesson 1
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2. After 15 days, two-‐thirds of a sample remains. If the original sample was 87mg, what is the half-‐life of the sample?
3.
23 87% = 58%à58% = 87% 1
2*+,-./0*/2
4. To solve for half-‐life, you need to take the log of each side.
5. !"# $%&%'& = )$+,-.
/0/2!"# )
3
! !"# $%&
%'& =.176 ! !"# $% =-‐.301
6. -.#$%-.&'# *)#/+ = 15 days ! !"/$= 15 days * 1.71
7. !"/$ = 25.7 days
8. Radon-‐222 has a half-‐life = 3.8235 days. How many grams of a 64.0 g sample of Rn-‐222 will remain after 11.5 days?
!"#$%'ℎ)*+,#-+.'#/),).+0)12+'#-$, 4 ' = 4- 67 89:/< à4 ' = 64.0 6
7 ::.ABCDEF.G<FABCDE
! " = 7.96(
9. The isotope Radium-‐226 has a half-‐life of 1640 years. Chemical analysis of a certain chunk of concrete from an
atomic-‐bombed city, preformed by an archaeologist in the year 6264 AD, indicated that it contained 2.50 g of Ra-‐226. By comparing the amount of Ra-‐226 to its end product Lead-‐206, it was determined the original amount of Ra-‐226 was 9.962 g. What was the year of the nuclear war?
!"#$%'ℎ)*+,#-+.'#/),).+0)12+'#-$:4 ' = 4- 12
89:/< , "->/)?-*'.
2.50% = 9.962% )* ,-./012345 ! To solve for t, you need to take the log of each side.
!"# $.&'().)*$( = ,
-*.'01234 !"# -$ ! !"# $.&'(
).)*$( =-‐.600 ! !"# $% =-‐.301
-.#$$-.%$& *1640-./01 = t ! t = 3271 years
!"#$ = 6264)*-3271/01 = 2993)*
10. Carbon-‐14 has a half-‐life of 5730 years making it useful for dating organic materials. A piece of charcoal found by an archaeologist at an excavation of an ancient campsite was found to have 30.0% of that in living trees. What is the approximate age of the piece of charcoal?
!"#$%'ℎ)*+,#-+.'#/),).+0)12+'#-$:4 ' = 4- 12
89:/< , "->/)?-*'.
. 30 = 1.00 &' )*+,-./012 ! To solve for t, you need to take the log of each side.
!"# $.&$'(.$$' = *
+,&$./012 !"# (3 ! !"# $.&$'
(.$$' =-‐.523 ! !"# $% =-‐.301
-.#$%-.%&' *5730./012 = t ! t = 9956 years
Radon Lesson 1
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Calculating Half-‐Life (B)
Guiding Question: How are half-‐lives calculated?
The equations you calculated in the Pennicium, Pennithium, & Pennium experiment should resemble where a
equals the number of pennies in the beginning, x is the number of shakes/rolls, and y is the number of pennies remaining after that throw. This equation illustrates the concept of half-‐life or the exponential nature of decay exhibited by radioactive materials. Radioactive decay is important in a variety of fields from medicine to energy production, astronomy, and geology. Some of the applications of the radioactive decay process include determining how long spent nuclear fuel poses an environmental danger and dating geological materials based on their half-‐lives. A common equation that is used for the exponential decay process (shown below) is very similar to the equation you developed and can also be used to solve half-‐life or radioactive decay problems.
! " = !$ %&
()*/,
Where:
• ! " = "ℎ%'()*+"),'-*.-"'+/%"ℎ'"0%('1+-',"%0'-2%/1,1/"1(% " ),3%/'4 • !" = $ℎ&"()*+,-,."/+$"0$ℎ&1/21$,+3&$ℎ,$4)--5&3,6 • ! = !#$% • !"/$ = ℎ'()(+),-).ℎ,/,0'1+234564.'20,
Using the equation above, solve the following problems:
Example: There are 200.0 grams of an isotope with a half-‐life of 42 hours present at time zero. How much time will have elapsed when 76.0 grams remain?
!"#$%'ℎ)*+,#-+.'#/),).+0)12+'#-$, 4 ' = 4- 12
89:/< '-"-=/)>-*':
76# = 200# '( *+,-./01 ! To solve for t, you need to take the log of each side.
!"# $%&'((& = *
+'-./01 !"# 2' ! !"# $%&
'((& =-‐.420 ! !"# $% =-‐.301
-.#$%-.&%' *42ℎ-./0 = t ! t = 58.6 hours
1. Iodine-‐131 (I-‐131) has a half-‐life of 8.0197 days. If you started with an 80.0g sample, how many grams of I-‐131 would be left after 2 days? Use the radioactive decay equation to solve the problem then compare your result with the original result derived from using the graph.
-‐
Radon Lesson 1
28
2. After 15 days, two-‐thirds of a sample remains. If the original sample was 87mg, what is the half-‐life of the sample?
3. Radon-‐222 has a half-‐life = 3.8235 days. How many grams of a 64.0 g sample of Rn-‐222 will remain after 11.5
days?
4. The isotope Radium-‐226 has a half-‐life of 1640 years. Chemical analysis of a certain chunk of concrete from an atomic-‐bombed city, preformed by an archaeologist in the year 6264 AD, indicated that it contained 2.50 g of Ra-‐226. By comparing the amount of Ra-‐226 to its end product Lead-‐206, it was determined the original amount of Ra-‐226 was 9.962 g. What was the year of the nuclear war?
5. Carbon-‐14 has a half-‐life of 5730 years making it useful for dating organic materials. A piece of charcoal found by an archaeologist at an excavation of an ancient campsite was found to have 30.0% of that in living trees. What is the approximate age of the piece of charcoal?
Radon Lesson 1
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COMPREHENSION 2
How does Radioactive Decay Occur? HALF-‐LIFE OF RADIOACTIVE ISOTOPES
We cannot determine when radioactive materials will decay and give off radiation. However, there is a pattern we can use to estimate how long it takes for an isotope to lose half of its radioactivity. This pattern is known as half-‐life. For example, if an isotope has a half-‐life of 20 years, half of the original substance will decay in 20 years. Then in another 20 years, half of the substance that remained will decay. This process will continue every 20 years. It is important to note that a radioactive substance will never completely decay, no matter how insignificant or small of an amount is left.
The half-‐life of a radioactive isotope is important as it dictates its behavior, its effects on the environment, and the amount of radiation it emits. For example, a radioactive isotope with a long half-‐life will emit its radiation infrequently. However, a radioactive isotope with a short half-‐life will emit its radiation repeatedly in a short period of time.
Not only is radiation emitted when the radioactive isotope decays, but the decay products of an isotope can also give off radiation. As discussed earlier, these decay products are referred to as daughters or progeny.
Alpha, Beta, and Gamma Radiation. Although there are several forms of ionizing radiation (i.e., when the energy produced is strong enough to knock electrons out of molecules and create ions or free radicals, we will concentrate on just three. These three types of radiation -‐ alpha, beta, and gamma -‐ result from the decay of radioactive isotopes.
An alpha particle, beta particle, or gamma ray is emitted during radioactive decay. Each time an alpha particle is emitted the number of protons decreases by 2 and the number of neutrons decreases by 2. This is always the same because an alpha particle is made up of 2 protons and 2 neutrons, identical to a helium nucleus (i.e., He+). A beta particle is formed when a neutron breaks apart into a proton and an electron. A beta particle is essentially an electron emitted from a nucleus. When a beta particle (i.e., the newly formed electron) is emitted, the atomic number increases by one. This can be thought of as a conversion of one neutron into one proton to account for the loss of the negatively charged beta particle. Although the atomic number changes during beta emission (thus creating a new element), the mass number stays the same.
Alpha particles are comparatively larger particles with an electrical charge (+2). For these reasons, alpha particles travel at relatively slow velocities and have low penetration depths. Alpha particles can be stopped by one to two
Alpha particle
Beta particle
Gamma ray
Radon Lesson 1
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inches in air, a thin sheet of paper, or the body’s outer layer of skin. Outside of the human body, alpha particles are not considered a hazard because they are stopped by our body’s first line of defense – the skin. However, when alpha particles are inhaled or swallowed, they interact with live tissues and cells. When this occurs, alpha particles can produce large amounts of ionizing radiation, thus causing internal tissue and cell damage.
Compared to alpha particles, beta particles are much faster and lighter. Beta particles can also travel farther (~ 10 feet in air) and can penetrate past the most outer (dead) layer of skin. Since beta particles can cause damage to the skin, they are considered both an internal and external hazard. Solid materials such as clothing or a thin layer of metal or plastic can stop these particles and the effects of damaging radiation.
Gamma rays are high energy, electromagnetic waves that travel at the speed of light. Gamma rays have no mass and can travel farther distances than alpha and beta particles, reaching distances up to thousands of yards in air. Gamma rays can pass through human tissue and can only be stopped by dense materials such as lead, cement, or steel. X-‐rays, another type of electromagnetic radiation, are similar to gamma rays and also produce penetrating radiation (i.e., radiation capable of penetrating the skin and reaching internal organs and tissues.)
The ionizing radiation produced from alpha, beta, or gamma decay can be especially harmful because it can change the chemical makeup of many things, including the chemistry of the human body and other living organisms. X-‐rays and CT scans are good examples of ionizing radiation. If possible, it is good to avoid any unnecessary exposure to ionizing radiation.
Balancing Radioactive Equations. Another way to understand radioactive decay is to understand how to describe the process in the form of an equation. Writing and balancing an equation for radioactive decay is different than writing and balancing an equation for a chemical reaction. In addition to writing the symbols for various chemical elements, the protons, neutrons, and electrons associated with that element or isotope are also included in the equation.
Radon Lesson 1
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The accepted way of denoting the atomic number (i.e., protons or p) and mass number (i.e., protons plus neutrons or p + n) of Uranium is shown below:
##
MassAtomic U238
92 or ! + #! $
As we discussed before, alpha decay occurs when a particle with two protons and two neutrons is emitted. This alpha particle is identical to a helium nucleus or 42#$. As shown below, the original element’s (E1) mass decreases by four, and it’s atomic number decreases by two. This results in a new element (E2) and a helium nucleus.
! + #! $1 →(! + #) − 4!-2 $2 +42./
Now let’s look at a real-‐world example of alpha decay, such as Radium-‐226. When Radium-‐226 decays, the resulting products are Radon-‐222 and an alpha particle (or He). Notice in the equation below, that the same number of protons and neutrons exist on both sides of the equation, resulting in a balanced equation.
22688 $% →
22286 $(+ 4
2+, In beta decay, an unstable neutron turns into a proton and an electron. This results in a gained proton, while a neutron is lost. The beta particle is actually the newly formed electron being emitted from the nucleus. This decay process results in a new atomic number (i.e., from gaining a new electron), while the mass actually stays the same (i.e., a neutron was turned into a proton).
! + #! $1 →(! + 1) + (#-1)! + 1 $2 + 0-1-
Another example of beta decay is when Cesium decays to Barium, resulting in the emission of an electron. This reaction is shown below. Notice once again, the equation is balanced and the number of protons and neutrons on the left equals the number on the right.
13755 %& →
13756 *++ 0
-1/ The last type of decay we discussed, gamma decay, is very different from alpha and beta decay. In gamma decay, the number of protons and neutrons does not change and it is not possible to show the decay process in the form of an equation. Essentially, the protons and neutrons reconfigure themselves within the nucleus, and release high levels of energy in the form of electromagnetic rays or gamma rays.
Radon Lesson 1
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Application: Balancing Radioactive Equations
Balance the following reactions, identify product X, and determine what type of decay occurs.
A) 21482 %& →21483 *++-. = 012ℎ4567489:*6;456748
B) 23892 % → (+ 4
2+,- = /01ℎ34,536789,:34,536
C) 2411$% → (+ 0-1,- = /01ℎ%3,4%5678,9%3,4%5
D) 5226$% →5227)* +,- = /01ℎ34%536*78%934%536
E) 23290 %ℎ →22888 *++-. = 012ℎ+345+67894:+345+6
Extensions: Distribute suggested readings about beneficial uses of radiation, Marie Curie, and Mars travel.
Have students view the Khan Academy’s video “Types of Decay” available at: http://bit.ly/S9Rmav
Students can calculate their personal annual radiation dose by completing the “Annual Radiation Dose Worksheet” or visiting: http://bit.ly/PMU9w4
Radon Lesson 1
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Comprehension 2 – Guiding Questions
1. Does radioactive decay proceed at the same rate for every radioactive isotope? How do nuclear scientists determine how long it takes for a radioactive isotope to decay? Why is the rate of decay important?
2. Will a radioactive element with a relatively short half-‐life emit more or less radiation than a radioactive element with a relatively long half-‐life?
3. When comparing alpha and beta radiation to gamma radiation, what is the basic difference?
4. When balancing radioactive chemical equations, how is alpha decay different from beta decay?
5. When balancing radioactive chemical equations, how is alpha decay the same as beta decay?
6. What are the biological hazards associated with alpha and beta particles, and gamma rays respectively?
Radon Lesson 1
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Comprehension 2 – Guiding Questions Teacher Key
1. Does radioactive decay proceed at the same rate for every radioactive isotope? How do nuclear scientists determine how long it takes for a radioactive isotope to decay? Why is the rate of decay important? Each radioactive isotope decays at its own signature rate, known as the half-‐life. The rate of decay is important because it determines how and when a radioactive isotope will emit radiation.
2. Will a radioactive element with a relatively short half-‐life emit more or less radiation than a radioactive element with a relatively long half-‐life?
Elements with a short half-‐life rapidly emit their radiation more intensely over a short period of time, while those with a long half-‐life emit their radiation very slowly.
3. When comparing alpha and beta radiation to gamma radiation, what is the basic difference?
Alpha and beta decay both involve the emission of a particle, where as gamma decay does not.
4. When balancing radioactive chemical equations, how is alpha decay different from beta decay?
Alpha decay must be balanced based on the emission of helium nucleus (2 protons and 2 neutrons). Beta decay involves the emission of an electron.
5. When balancing radioactive chemical equations, how is alpha decay the same as beta decay?
The number of particles present must be taken into consideration for both.
6. What are the biological hazards associated with alpha and beta particles, and gamma rays respectively?
Alpha particles can be stopped by one to two inches in air, a thin sheet of paper, or the skin. Outside of the human body, alpha particles are not considered a hazard because they are stopped by the skin. However, when alpha particles are inhaled or swallowed, they interact with live tissues and cells, thus causing internal tissue and cell damage.
Beta particles can travel farther than alpha particles (~ 10 feet in air) and can penetrate past the most outer (dead) layer of skin. Since beta particles can cause damage to the skin, they are considered both an internal and external hazard. Solid materials such as clothing or a thin layer of metal or plastic can stop these particles and the effects of damaging radiation.
Gamma rays have no mass and can travel farther distances than alpha and beta particles, reaching distances up to thousands of yards in air. Gamma rays can pass through human tissue and can only be stopped by dense materials such as lead, cement, or steel. The ionizing radiation produced from alpha, beta, or gamma decay can be especially harmful because it can change the chemical makeup of many things, including the chemistry of the human body and other living organisms.
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Retrieved from: http://www.nrc.gov/reading-‐rm/basic-‐ref/teachers/average-‐dose-‐worksheet.pdf
Annual Radiation Dose Worksheet
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‘What is Radioactivity?’ Evaluation Questions
For questions 1-‐5, write the letter of the best answer in the space before the question. 1. ____ Radiation and radioactivity are synonymous terms.
A. true B. false
2. ____ U-‐238 and U-‐234 are examples of _____.
A. allotropes B. complementary ions C. progeny D. isotopes
3. ____ Which of the following would represent the penetrating power of alpha, beta, and gamma radiation ranked from highest penetrating power to the lowest?
A. alpha, beta, gamma B. beta, gamma, alpha C. gamma, beta, alpha D. none of the above
4. ____ Which of the above mentioned types of radiation does not involve the emission of a particle?
A. alpha B. beta C. gamma D. none of the above
5. ____ The vapor trail produced by alpha radiation is longer than that produced by beta radiation.
A. true B. false
6. Using the blank graph below, draw a radioactive decay curve, be sure to label both axes, then use your decay curve to answer questions 7-‐12 below.
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7. What radioactive isotope does your decay curve describe?
8. Using the radioactive decay curve, what percentage of your radioactive isotope exists after three half lives?
9. Carbon 14 has a half-‐life of 5,730 years. If you have a .01 gram sample of carbon 14, what is the mass of carbon 14 remaining after two half-‐lives?
10. The element Osmium-‐182 has a half-‐life of 21.5 hours. How much time would have elapsed if a 10.0 g sample of Os-‐182 decays so that a 1.8 g sample remains?
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11. In a galaxy far, far away there exists a material known as Confusium-‐406, Cn-‐406. Over a 24.0 day period, 128.0 g of Cn-‐406 will decay so that 5.12 g of the original material remains. What is the half-‐life of Cn-‐406?
Use the half-‐life equation ! " = !$ %&
()*/, to answer questions 12-‐17:
12. At time zero, there are 10.0 grams of Tungsten-‐187. If the half-‐life is 23.9 hours, how much W-‐187 will be present at the end of two days?
13. The half-‐life of Hydrogen-‐3, also known as tritium, is 12.26 years? How much time will be required for a sample of tritium to lose 75% of its radioactivity?
14. The bristle cone pine, found in the White Mountains of California, is the oldest living thing on earth and they are unusual in that their cones are blue. Some samples of these blue cones dating back 10,000 years have been identified. Suppose you have a sample from such a cone that presently contains 5.00 g of Carbon-‐14, half-‐life=5730 yrs. Determine the amount of C-‐14 that was present in the cone sample 10,000 years ago.
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15. In the equation above, what kind of decay particle is produced?
16. What kind of radioactive decay produces a helium nucleus?
17. For the decay chart of uranium 238 to lead 206, provide 2 examples of transition to a different element that produce beta particles.
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‘What is Radioactivity?’ Evaluation Questions: Teacher Key
For questions 1-‐5, write the letter of the best answer in the space before the question. 1. ____ Radiation and radioactivity are synonymous terms.
A. true B. false
2. ____ U-‐238 and U-‐234 are examples of _____.
A. allotropes B. complementary ions C. progeny D. isotopes
3. ____ Which of the following would represent the penetrating power of alpha, beta, and gamma radiation ranked from highest penetrating power to the lowest?
A. alpha, beta, gamma B. beta, gamma, alpha C. gamma, beta, alpha D. none of the above
4. ____ Which of the above mentioned types of radiation does not involve the emission of a particle?
A. alpha B. beta C. gamma D. none of the above
5. ____ The vapor trail produced by alpha radiation is longer than that produced by beta radiation.
A. true B. false
6. Using the blank graph below, draw a radioactive decay curve, be sure to label both axes, then use your decay curve to answer questions 7-‐12 below.
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7. What radioactive isotope does your decay curve describe?
The graph from question 1 is not specific for any single radioactive isotope because it does not consider the length of a half-‐life. All radioactive isotopes will have the same percentage of material remaining at the end of each half-‐life.
8. Using the radioactive decay curve, what percentage of your radioactive isotope exists after three half lives?
There would be approximately 17% of the original material remaining after three half-‐lives.
9. Carbon 14 has a half-‐life of 5,730 years. If you have a .01 gram sample of carbon 14, what is the mass of carbon 14 remaining after two half-‐lives?
According to the graph in question 1, there would be 25% of the original material remaining after two half-‐lives: grams C = 0.01 g x 0.25 = 0.0025 g C.
10. The element Osmium-‐182 has a half-‐life of 21.5 hours. How much time would have elapsed if a 10.0 g sample of Os-‐182 decays so that a 1.8 g sample remains?
According to the graph, 18% of the material remaining represents approximately 2.5 half-‐lives.
-‐ -‐
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11. In a galaxy far, far away there exists a material known as Confusium-‐406, Cn-‐406. Over a 24.0 day period, 128.0 g of Cn-‐406 will decay so that 5.12 g of the original material remains. What is the half-‐life of Cn-‐406?
According to the graph, 4.00% of the original material remaining represents approximately 4.7 half-‐lives.
Use the half-‐life equation ! " = !$ %&
()*/, to answer questions 12-‐17:
12. At time zero, there are 10.0 grams of Tungsten-‐187. If the half-‐life is 23.9 hours, how much W-‐187 will be present at the end of two days?
13. The half-‐life of Hydrogen-‐3, also known as tritium, is 12.26 years? How much time will be required for a sample of tritium to lose 75% of its radioactivity?
14. The bristle cone pine, found in the White Mountains of California, is the oldest living thing on earth and they are unusual in that their cones are blue. Some samples of these blue cones dating back 10,000 years have been identified. Suppose you have a sample from such a cone that presently contains 5.00 g of Carbon-‐14, half-‐life=5730 yrs. Determine the amount of C-‐14 that was present in the cone sample 10,000 years ago.
-‐ -‐
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15. In the equation below, what kind of decay particle is produced?
Beta decay is represented in the equation above where a neutron from carbon is converted into a proton and an electron, , or beta particle.
16. What kind of radioactive decay produces a helium nucleus?
Alpha decay produces a helium nucleus as part of the radioactive decay process as in the radioactive decay of radium-‐226:
17. For the decay chart of uranium 238 to lead 206, provide 2 examples of transition to a different element that produce beta particles.
During the radioactive decay of U-‐238 to Pb-‐206, beta particles, electrons -‐ , are produced when
thorium-‐234 decays to protactinium-‐234 and when proctactinium-‐234 decays to uranium-‐234.
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Radon Lesson 1: Specific Learning Objectives and Standards Specific Learning Objectives Upon completion of this lesson, students will be able to:
• define terms related to radioactivity and radioactive decay.
• describe the process of radioactive decay.
• draw the basic structure of a commonly known atom
• calculate the half-‐life of elements.
• summarize what makes atomic nuclei unstable and recognize how unstable nuclei react.
• identify common sources of radiation, both natural and manmade.
• explain the difference between ionizing radiation and penetrating radiation.
• identify potential biological hazards related to alpha and beta particles and gamma rays.
• explain the differences between how alpha and beta particles, and gamma rays act in the environment and in the human body.
• balance radioactive reactions.
NEXT GENERATION SCIENCE STANDARDS Students who demonstrate understanding can:
HS-‐PS1-‐8 Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay.
HS-‐PS1-‐7 Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.
HS-‐LS3-‐2 Make and defend a claim based on evidence that inheritable genetic variations may result from: (1) new genetic combinations through meiosis, (2) viable errors occurring during replication, and/or (3) mutations caused by environmental factors.
MONTANA STATE SCIENCE STANDARDS A proficient student will (upon graduation):
Science Content Standard 1: Students, through the inquiry process, demonstrate the ability to design, conduct, evaluate, and communicate the results and form reasonable conclusions of scientific investigations.
1.2 select and use appropriate tools including technology to make measurements (in metric units), gather, process and analyze data from scientific investigations using appropriate mathematical analysis, error analysis and graphical representation.
Science Content Standard 2: Students, through the inquiry process, demonstrate knowledge of properties, forms, changes and interactions of physical and chemical systems.
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2.1 A proficient student will describe the structure of atoms, including knowledge of (a) subatomic particles and their relative masses, charges and locations within the atom, (b) the electrical forces that hold the atom together, (c) fission and fusion, and (d) radioactive decay.
ALASKA STATE SCIENCE STANDARDS SB3 Students develop an understanding of the interactions between matter and energy, including physical, chemical, and nuclear changes, and the effects of these interactions on physical systems.
(9) SB3.3 The student demonstrates an understanding of the interactions between matter and energy and the effects of these interactions on systems by recognizing that atoms emit and absorb electromagnetic radiation.
(10) SB3.2 The student demonstrates an understanding of the interactions between matter and energy and the effects of these interactions on systems by recognizing that radioactivity is a result of the decay of unstable nuclei.
SA1 Students develop an understanding of the processes of science used to investigate problems, design and conduct repeatable scientific investigations, and defend scientific arguments.
(10) SA1.1 The student demonstrates an understanding of the processes of science by asking questions, predicting, observing, describing, measuring, classifying, making generalizations, analyzing data, developing models, inferring, and communicating.
IDAHO STATE STANDARDS Chemistry:
Goal 1.2: Understand Concepts and Processes of Evidence, Models, and Explanation 11-‐12.C.1.2.2 Create and interpret graphs of data.
Goal 1.6: Understand Scientific Inquiry and Develop Critical Thinking Skills 9-‐10.B.1.6.3 Use appropriate technology and mathematics to make investigations.
Goal 1.8: Understand Technical Communication 11-‐12.C.1.8.2 Communicate scientific investigations and information clearly.
Goal 2.4: Understand the Structure of Atoms 8-‐9.PS.2.4.2 Explain the processes of fission and fusion.
Goal 5.3: Understand the Importance of Natural Resources and the Need to Manage and Conserve Them
11-‐12.C.5.3.1 Evaluate the role of chemistry in energy and environmental issues.
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Resources LESSON 1: RADIOACTIVITY Chemistry. By Raymond Chang, 1984 (Second Edition). Random House, Inc., New York, NY. Cloud Chamber. American Nuclear Society, Michigan Section, Radiation Resources CD-‐ROM Index. Available online at: http://local.ans.org/mi/Teacher_CD/Activities/Cloud_Chamber.pdf Designing Effective Projects: What Does This Graph Tell You? Intel, Designing Effective Projects: Project-‐Based Units to Engage Students. Available online at: http://educate.intel.com/en/ProjectDesign/UnitPlanIndex/WhatDoesThisGraphTellYou/graphing_trendlines.htm General Chemistry: An Active Learning Approach. By Mark S. Cracolice and Edward I. Peters, 2003. Brooks/Cole Publishing, Pacific Grove, CA. Lesson Plans -‐ Unit 1: Radiation. The United States Nuclear Regulatory Commission (U.S. NRC). Available online at: http://www.nrc.gov/reading-‐rm/basic-‐ref/teachers/unit1.html Pennium-‐123. American Nuclear Society. Michigan Section, Radiation Resources CD-‐ROM Index. Science, Society, and America's Nuclear Waste, Teacher Guide. Available online at: http://local.ans.org/mi/Teacher_CD/Activities/pennium-‐halflife-‐activity.pdf Personal Annual Radiation Dose Calculator. The United States Nuclear Regulatory Commission (U.S. NRC). Doses in Our Daily Lives. Available online at: http://www.nrc.gov/about-‐nrc/radiation/around-‐us/calculator.html Radiation Measurement Units -‐ International (SI) System. Table available at: http://www.civildefensemuseum.com/southrad/conversion.html Radiation Measurement. Idaho State University, The Radiation Information Network, Page 9. Available online at: http://www.physics.isu.edu/radinf/measure.htm Radiation Risk. Georgia State University, Department of Physics and Astronomy, HyperPhysics. Available online at: http://hyperphysics.phy-‐astr.gsu.edu/hbase/Nuclear/radrisk.html Radioactive Decay of M&Ms. US Department of Energy. Nuclear Energy Student Zone, Science Projects. Available online at: http://www.ne.doe.gov/students/activities_mmDecay.html The Basics of Radiation Science. Department of Energy (DOE). Office of Health, Safety and Security. DOE Openness: Human Radiation Experiments: Roadmap to the Project, ACHRE Report. Available online at: http://www.hss.doe.gov/healthsafety/ohre/roadmap/achre/intro_9.html The Discovery of Radioactivity. Nuclear Science Division and the Contemporary Physics Education Project (CPEP). Guide to the Nuclear Wall Chart. Available online at: http://www.lbl.gov/abc/wallchart/chapters/03/4.html Types of Decay. Khan Academy. Chemistry, Radioactive Decay. Available online at: http://www.khanacademy.org/science/chemistry/radioactive-‐decay