Roll # Decayed Undecayed Natural Log e ^-kt slope = k (decay constant) O 0 26 3.258096538 k = 0.53 Half Lives 9 17 2.833213344 0.5886049729 2.09 16 10 2.302585093 0.3464558142 decay = kernals landing on black sections 1.31 20 6 1.791759469 0.2039256151 1.7 O U A W N - 23 3 1.098612289 0. 1200316312 1.307824869 =half life 1.35 24 2 0.6931471806 0.07065121502 Mean 1.6125 26 0 #NUM! 0.04158565651 Standard Dev 0.3633524461) You can use it to estimate the amount of Carbon or Uranium left and can estimate age using the half life. Radioactive Dating Game [3.27) file nlp iinuulElhm i i Report the value for the half-life you found by rolling 100 dice. Also report the average half-life and the standard deviation calculated from the whole class multiple trials. If you need help doing this calculation, go back to the very first popcorn lab module and review the definitions and how to use Excel for statistics. By what factor are the statistics for the whole class sample larger than your individual measurement? In what way is the result better for the whole class sample? How many sigmas away is your individual measurement from the class average? Comment on whether the whole class sample is more precise or more accurate or both. How would the half-life of this experiment have changed if you had used a 20-sided dice? Is a 20-sided dice a model for a longer or a shorter decay time? Attach your answers to Part II to your lab report or as a second pdf file Part I You and your lab partners are studying the radioactive decay of an isotope. To find the half life, you must ascertain how many decays occur every second, as measured by the rate on a Geiger Counter. You will simulate this experiment by rolling dice, where each roll corresponds to an interval of time and every dice that lands with the 6 showing on the top face is one that decayed (and was counted by the Geiger Counter). Prepare a spreadsheet (Microsoft Excel preferred) in which you will write down the number that "decayed" and the number that remained un-decayed for each throw, starting with roll 0 (the 100 not-yet-decayed dice you start with). After each roll, remove all that have a 6 face-up, and roll again with those that are left until all the dice are removed. For the purposes of this experiment, assume each throw is a one second time interval. Part II - You can work on this while the TA is compiling the class spreadsheet. Now, you will use your knowledge of how radioactive decay works to date archaeological objects. Radioactive dating is a powerful tool to determine how old something is, from old dinosaur bones to human artifacts (made from organic materials). This is because things like radioactive carbon are constantly being produced in our atmosphere, and we can determine the date of these molecules very precisely using the equations from Part 1 of the lab. This carbon will enter biological systems by means of photosynthesis soon after they are produced. Then, the radioactive carbon will be consumed by an animal and end up in their bones. To practice dating some materials mentioned above and more, go back to this link: simulation=radioactive-dating:game