The Item:

Question #1: On the graph paper below, make a graph for each of your samples showing the relationship between the number of green beads remaining in the cup (y-axis) and the sample number (x-axis). Construct both graphs using the same axes. Be sure to label your axes and provide a legend. The graphs represent the decay curve for your samples.
Question #2: Assume that one minute equals 100 years and that the sample needs to decay to 1/16 of its original amount to be considered "safe." You now have to safely dispose of your radioactive samples. Choose one of your samples. Explain (1) how many years you would have to be concerned about the radioactivity of the sample, and (2) how you would dispose of this material. Be sure to justify your responses.

Item Description:

The objective of the event is to help the students understand radioactive decay and be able to relate it to the concept of half-life.
The students are given 100 green beads that represent radioactive atoms and 100 white beads that represent stable, non-radioactive daughter atoms. The green beads are placed in one cup and the white beads in another. They are asked to do two trials, one sampling 8 beads at a time and the other sampling 4 beads at a time. The number of green beads removed in each sample should be recorded and replaced with an equal number of white beads. Any white beads removed in a sampling event should be returned to the cup that originally began with all green beads. Once 50 green beads are removed from the cup the elapsed time should be recorded.
Question 1 asks the students to graph each of the samples to show the relationship between the number of green beads remaining in the cup on the y-axis and the sample number on the x-axis. The graphs represent the decay curves for the samples.
A good response will have labeled the axes correctly and provided a legend, and show two curves based on the data collected.
Question 2 tells the student to assume one minute equals 100 years and that the sample needs to decay to 1/16 of its original amount to be considered "safe." To safely dispose of the samples, they must explain how many years before the sample will be considered "safe" and how they would dispose of the material.
A good response will show the student understands the concept of half-life and can use this concept to determine when their sample will be "safe." From the experiment they may also note that sampling 8 beads at a time will become safer in less time than when they sampled 4 beads at a time because it has a shorter half-life. A method of disposal must include limiting exposure of the radioactive material to the environment.

SUMMARY TABLE

Criterion
1	Question 1 - Two of the following are met: scale on axes legend graph
2	Number of years before sample is "safe" is determined. (Q2)
3	Method of disposal described. (Q2)
4	All of Criterion 1 are met, data is plotted correctly (Q1) AND student understands half-life (Q2).

Criterion 1:		Two of the following must be met (Question 1): 1. Scale marked on each axis. OR 2. Axes are labelled correctly. y-axis: number of green beads remaining in the cup x-axis: sample number A legend is provided indicating which line or points represent sampling 8 at a time and which one represents sampling 4 at a time. An attempt is made graph the two samples on one graph. Two lines may be drawn. OR Data points are plotted for the two samples.
Criterion 2:		An attempt is made to determine how many years you would need to be concerned about the radioactivity of the sample. (Q2) If no calculations are shown, the number of years must be "reasonable", i.e. using the elapsed time for either of the two samples, the number of years should be approximately: # minutes x 4 (half-lives) x 100 years NOTE: For the sample to decay to 1/16 of its original amount, 4 half-lives are necessary because (1/2)(1/2)(1/2)(1/2) = 1/16. The number of minutes x 100 years is acceptable if the answer is given in years. NOTE: The majority of students had elapsed times of 5-10 minutes. Answers of 2,000 to 4,000 years are acceptable if no elapsed time is shown or can be determined.
Criterion 3:		Student describes a method of disposal (Question 2 (2)). The method must include limiting the exposure of the radioactive material to the environment and/or humans. For example: Store the material away from man until it is safe. Place it in sealed containers and bury it. Ship it to the moon so it will be away from people. The following are not acceptable: Stop manufacturing it. (This is a comment - it doesn't attempt to answer the question.) Inject it into someone so they are mutant.
Criterion 4:		All the condition in Criterion 1 are met (A1, A2, B, C1, C2), the data must be plotted correctly, AND the student shows they understand radioactive decay and the concept of half-life. This can be shown by any of the following: Calculations in question 2 (1) show four half-lives are necessary for the sample to decay to 1/16 of its original amount. The number of years calculated to answer question 2 (1) is used to answer question 2 (2) as follows: "The samples should be stored in barrels away from human contact for 4,000 years because it will take that long before it is considered safe." NOTE: The number of years must show some understanding of half-life, not simply the number of minutes times 100 years, i.e., if Criterion 2 (1) is met, Criterion 4 is not met automatically. Some calculations must be shown or the student must attempt to determine the number of years, not simply multiply the number of minutes x 100 years or put down a number, even if it is "reasonable." The student notes that sampling 8 at a time will become "safe" in less time than sampling 4 at a time because it has a shorter half-life.