Radioactive Dice Decay

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1 Radioactive Dice Decay Author(s) Maisha Murry Mathew Bye Subject(s) Math Grade Level 9 th Duration Two-Three 70 minute periods Rationale (How this relates to engineering) Radioactivity naturally occurs in our environment. Different radioisotopes are used for the production of electricity, sterilizing food, medical treatment, and etc. Students need to have some basic understanding of how radioactivity relates to them and their environment. Exponential decay based on the half-life of the isotope. The half-life Activity Summary Students will learn that radioactive decay is unpredictable and spontaneous. They will also learn that the decay of one atom to another is irreversible. (This principle can be illustrated using popcorn) Students will learn that exponential decay is when a quantity deceases at a rate proportional to its value. Students will learn how the half-life of a radioactive isotope is subject to exponential decay. Students will learn that the half-life of a radioactive isotope is the time required for a quantity of radioactivity to decay by half. These principles will be illustrated using dice. Objectives Upon completion of this lesson, students will be able to 1. Understand the unpredictability and spontaneity of radioactive decay. 2. Understand that the decay of one atom to another is irreversible 3. Understand exponential decay of radioactive isotopes Standards Mathematics Patterns, Functions, and Algebra Standards (Pg 170) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

2 Physical Science Nature of Matter (Pg 137) Describe radioactive substances as unstable nuclei that undergo random spontaneous nuclear decay emitting particles and/or high energy wavelike radiation. Background Knowledge Students should some general knowledge of radioactivity. Students should also be able to graph points. Materials Required Handout (Below) Popcorn Popper Popcorn Kernels Cooking oil 50 dice for each students (A total of 1250 dice are needed for a group of 25 students) 50 Ziploc Bags 25 boxes (The tops of printer paper boxes would work best) Black Marker Graphing Paper Geiger Counter for Alpha Geiger Counter for Beta Mental Lanterns containing thorium (Alpha-α Source) Uranium Glazed Pottery (Alpha-α, Beta-β, Gamma-γ Source) Pencils Activities Teacher Information The teacher will introduce Radiation and Radioactive decay. First probe students with questions like what is radiation to gage your students understanding of the subject. Radiation is energy in the form of waves or moving subatomic particles. Explain the most commonly known sources of radiation (Note: Constantly ask your students question about each of the different area before you tell them the answer.) o Alpha-α particle (A Helium Atom-2 Protons & 2-Neutrons) o Beta particle (An Electron) o Photons-Gamma- γ Rays (Come from inside the nucleus), X-Rays (Come from outside the nucleus) Radioactive decay is a process when an unstable atom loses energy by emitting radiation Using a popcorn popper (or hotplate, skillet), cooking oil and popcorn demonstrate the following The unpredictability and spontaneity of radioactive decay by popping popcorn. That the decay of one atom to another is irreversible by showing a popcorn kernel un-popped and popped.

3 Using a Geiger Counter (one for alpha and beta) demonstrate the different shielding methods for alpha particles beta particles and gamma rays. Alpha particle can be shielded (stopped) by a sheet of notebook paper Lower energy Betas can be shielded (stopped) by aluminum foil. Gamma Rays can be shielded (stopped) by lead or H 2 O. Following the demonstration each student will be given 50 dice in a Ziploc bag, a box and additional Ziploc bag labeled Decayed Dice. Review the student handout procedure and have students the math lab.

4 Radioactive Dice Decay Student Handout Procedure 1. Obtain 50 dice, place them into a Ziploc bag and roll them out into the box. Please do not make too much noise, and be careful not to loose any. 2. Every time you roll the dice, some dice will decompose (decay) and you must remove them. Place them in the Ziploc bag marked Decayed Dice. 3. For the first trial, if an even number (2,4,6) is rolled, the dice has decayed and must be removed. Count the remaining dice and record this information the data table under the # of Dice. 4. Put the remaining dice in the container and roll again. Remove the even numbered dice, and record the number of dice remaining in the data table. 5. Continue rolling dice, removing even numbered dice and recording in the data table, until all the dice have been removed. You have d Trial # For Trial # 2 repeat steps 2-5, but this time the odd numbered (1, 3, 5) dice are radioactive and decay. 7. For Trial # 3 repeat steps 2-5, but this time only dice numbered 1 and 6 decay. 8. For Trial # 4 repeat steps 2-5, but this time dice numbered 1, 2, 3, 4 decay. 9. Make a graph of the results. On the x-axis goes the number of tosses, and on the y-axis goes the number of dice remaining. All data will go onto the same graph, so everyone shall use the same scale. Turn your paper sideways (landscape) and use the following scale: 1 Toss = 1 Line (x-axis) and 2 dice = 1 line (y-axis). 10. Answer the following post math lab questions in.

5 Radioactive Dice Decay Math Lab Name Date Trial # 1: Even Numbers Trial # 2: Odd Numbers

6 Radioactive Dice Decay Math Lab Name Date Trial # 3: Dice 1 & 6 Trial # 4: Dice 1,2,3,4

7 Radioactive Dice Decay Math Lab Answer the following post math lab questions in. 1. Describe any patterns that you see in the data. (Use words like increasing and decreasing, x-axis and y-axis) 2. For the first two trials (even and odd dice), how many tosses did it take for half of the dice to decay? Compare this number to the other two trials. 3. Based on questions number one and two, define in your own words what half life means. 4. Think about what would happen if you started with only 40 dice. Explain how you think the data and graph would look different.

8 Radioactive Dice Decay Math Lab 5. a. Try using 40 dice and repeat trial # 1 only. b. Do you agree with your answer for # 4 above? Why or Why not? Trial # 1: Even Dice Numbers 6. Suppose you were to start with 100 dice and redid all 4 trials. a. How would the data look different? b. How would the data look the same?

9 Radioactive Dice Decay Rubric Trials 1-4 Graphing Behavior Questions 1-4 Questions 5 & Students Student s 2 out s 3 of 4 of the Trials out of 4 of Student s 1 out of 4 of the Trials Students graphs 1 out of 4 trials neatly and correctly with the 1 Toss = 1 Line on the x-axis and 2 dice = 1 line Student needs improvement. Discipline is not acceptable 1 out of the 4 questions one part of questions 5 or 6 Students graphs 2 out of 4 trials neatly and correctly with the 1 Toss = 1 Line on the x-axis and 2 dice = 1 line Student is attentive while being somewhat disruptive 2 out of the 4 questions part a & b of questions 5 or 6 the Trials Students graphs 3 out of 4 trials neatly and correctly with the 1 Toss = 1 Line on the x-axis and 2 dice = 1 line Student is attentive and actively participating Student answers 3 out of the 4 questions Student answers all 3 out of 4 parts questions 5 & 6 correctly in Student s all 4 Trials Students graphs all 4 trials neatly and correctly with the 1 Toss = 1 Line on the x-axis and 2 dice = 1 line on the y-axis Student is very attentive and actively participating without disturbing others all 4 of the questions part a & b, in questions 5 & 6

Safety: Do not eat the radioactive candium until it has decayed into a safer element.

Safety: Do not eat the radioactive candium until it has decayed into a safer element. Name: Date: Period: CHEMISTRY LAB #23 Radioactive Candium Experiment 90 MINUTES Do Now Review: 1) How long will it take for 20 g of 222 Rn to decay to 5 g? 2) How many half-lives is this? 3) What type