Hot Dice Labettini PURPOSES: To illustrate the random nature of radioactive decay To define radioactive “half-life” To demonstrate that less stable elements decay faster and have shorter half-lives MATERIALS (per team — 12 teams REQUIRED): 32 dice Tray

Hot Dice Labettini INTRODUCTION: A radioactive atom can change into another element. It “decays” by spitting out a bit of its nucleus. Example: 210Po  206Pb + alpha A radioactive atom has a certain probability of decaying within a certain time. Example: Any atom of 210Po has a 50% chance of decaying in the next 138 days That probability never changes. Even if a 210Po atom has already survived a gazillion years, it still has just a 50% chance of decaying in the next 138 days. The time it takes for half of the atoms of a radioactive element to decay is called the “half life”. Duh.

Hot Dice Labettini We will simulate radioactive decay using dice instead of atoms. We’ll pretend that one of our atomic dice decays if it shows a certain number. EXAMPLE: An “atom” decays if it’s an even number. So, on any given roll, the “atom” has a 50% chance of decaying. Even if that atom comes up odd a gazillion times in a row, it still only has a 50-50 chance of being even (and decaying) on the next roll. Put another way, if we roll a bunch of “atoms”, we expect about half to decay and half to survive. Put yet another way, those “atoms” have a half life of “one roll”

Hot Dice Labettini We will simulate radioactive decay using dice instead of atoms. We’ll pretend that one of our atomic dice decays if it shows a certain number. EXAMPLE: An “atom” decays if it’s an even number. So, on any given roll, the “atom” has a 50% chance of decaying. Even if that atom comes up odd a gazillion times in a row, it still only has a 50-50 chance of being even (and decaying) on the next roll. Put another way, if we roll a bunch of “atoms”, we expect about half to decay and half to survive. Put yet another way, those “atoms” have a half life of “one roll” Understand this now so you don’t make stupid gambling bets later! Dice, like atoms, don’t have a memory!

Hot Dice Labettini SIMULATION 1: LESS STABLE ELEMENT To simulate an unstable element that decays quickly, we’ll pretend that an “atom” decays if it’s even after a roll. If it’s odd, it will survive for another roll. So, half of the “atoms” should decay after each roll, and half should survive. Each group will start with 32 “atoms” and roll them. After the first roll, remove the “atoms” that are even. Record how many remain for your group and for the class as a whole. Roll the remaining “atoms”. Repeat for six rolls, or until all “atoms” have decayed. Roll Remaining Atoms Predicted Yours Class 384 32 1 192 2 96 3 48 4 24 5 12 6

Hot Dice Labettini SIMULATION 2: MORE STABLE ELEMENT To simulate a more stable element, we’ll pretend that an “atom” decays if it equals 1 after a roll. So, 1/6 of the “atoms” should decay after each roll, and 5/6 should survive. (These fractions are not forbidden!) Each group will start with 32 “atoms” and roll them. After the first roll, remove the “atoms” that are 1’s. Record how many remain for your group and for the class. Roll the remaining “atoms”. Repeat for 15 rolls or until all “atoms” have decayed. Roll Remaining Atoms Predicted Yours Class 384 32 1 320 2 266.7 3 222.2 4 185.2 … 15 25.0

Hot Dice Labettini ANALYSIS: Plot the class data for both radioactive elements, but pretend that each roll represents 1 year. Use the graphs to estimate the half-life of each element in years. Remember, the half-life is the time it takes for half of the atoms to decay! Record your estimates.

Hot Dice Labettini QUESTIONS: Half gone, half left Unstable half-life Pick up one die. How many times in the life of the Universe has that die been rolled? What are the odds that it will be “even” if you roll it now? Will the odds of rolling “even” ever change — no matter how many times you roll that die? Likewise, the half-life of an atom never changes. No matter how long it has survived, it still has the same chance of making it through another day as any other atom of the same element. 400 Half gone, half left 300 200 100 Unstable half-life Stable half-life

Hot Dice Labettini SUMMARY: Radioactive decay is RANDOM and does NOT depend on history! Half of the atoms of a radioactive element will decay within a half life. Less stable elements have shorter half lives.