Contributed by: Council of Chief State School Officers (CCSSO)
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 (yaxis) and the sample number (xaxis).
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 halflife.
The students are given 100 green beads that represent radioactive
atoms and 100 white beads that represent stable, nonradioactive
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 yaxis and the sample number on the xaxis. 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
halflife 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 halflife. 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 halflife (Q2). 
Rubric
Criterion 1: 

Two of the following must be met (Question
1):
 1. Scale marked on each axis.
OR
2. Axes are labelled correctly.
 yaxis: number of green beads remaining in the cup
xaxis: 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 (halflives) x 100 years
NOTE: For the sample to decay to 1/16 of its original amount,
4 halflives 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 510 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 halflife. This can be shown by any of the following:
 Calculations in question 2 (1) show four halflives 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
halflife, 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 halflife.

