*Using
Computers in Chemical Education Newsletter -
Fall 2005*

Exploring Radioactive
Decay in Excel: An Interactive Visual
Thinking Tool

__Abstract__

An interactive Excel spreadsheet investigation of radioactive decay kinetics and associated measurement error is presented for use in general chemistry. Students are engaged in numerous higher-order thinking and science process skills as they work through the activity.

__Keywords__

Excel spreadsheet

discovery learning

radioactive
decay kinetics

random
and systematic error

Student
Feedback and Assessment

Printable pdf version

Radioactive decay is a general chemistry topic, usually covered late in the second semester, and a typical example used to illustrate exponential behavior in mathematics textbooks. Developing an interactive discovery-based activity for examining aspects of radioactive decay was accomplished using the graphical and numerical data display capabilities of Excel. The basics of developing interactive computational Excel spreadsheets including an Excel tutorial are discussed in Sinex (2004). Further Excel application support is also provided as links later in this article (Sinex, 2005a). Discovery learning is in line with national reform efforts (Siebert and McIntosh, 2001).

The tool consists
of a series of questions that allow students to discover a number of aspects of
radioactive decay while examining an interactive multi-layered Excel
spreadsheet. There are five learning
objectives to be addressed: (1) introduce the basics of radioactive decay
kinetics including determining half-life; (2) examine the growth of the stable
daughter nuclide produced from the parent nuclide; (3) examine the behavior of
an unstable or radioactive daughter nuclide (behavior of consecutive reactions)
including total radioactivity; (4) investigate the counting error of the parent
activity, its effects and correction, and; (5) investigate background radiation
and its effect and correction on the measurement. Numerous higher-order thinking questions are
posed throughout the activity along with the application of science process
skills. The interactive dynamic nature
of the technology employed enhances the discovery learning of both chemical __and__
mathematical concepts in freshman chemistry for non-majors. Recently, Lim (2003) has outlined some
advantages of using spreadsheets in chemistry, where in quantum chemistry the
symbolic mathematics is purposely hidden due to its more complicated nature.

This activity is
done having covered chemical kinetics earlier in the semester and with an
introduction to radioactive decay via the
penny
or
M&M
flipping activity to uncover the exponential nature of decay and define
half-life. The statistical nature of the
process is discovered and the appropriate mathematical relationships can be
derived. Students have used Excel as a
data handling, graphing, and analyzing tool in their general chemistry
experience and we provide support documentation (Sinex and Gage, 2001). Experience with Excel is not really necessary
to use this spreadsheet; although students should be introduced to using an
interactive spreadsheet. A large
percentage of our students come into general chemistry with Excel experience;
however, it generally does not involve plotting scientific data.

Here are the links
to the files:

__Interactive
Excel Spreadsheet__ [top of
page]

The approach of
questioning drives the student to discover concepts as they explore the
interactive spreadsheet. Students are going
to perform numerical experiments and address many "what if" scenarios; hence,
they are engaging in science process while learning. The questions are keyed to the tabs (lower
left of screen) on the Excel spreadsheet as shown below in Figure 1.

A number of adjustable variables, where values are typed in (shown as yellow cells) or adjusted with sliders (scroll bars as referred to in Excel on the Forms toolbar), are included on each worksheet. As they are adjusted, the graphs and data in columns respond and regressions are re-evaluated as well. Comment cells, indicated by a small red triangle in the upper right corner of the cell, are included to offer explanation. A number of these features are illustrated on the screen shot (Figure 2) from the counting error tab worksheet given below.

For novices to these interactive spreadsheets or simulations, it is generally recommended to adjust the variables in a systematic way (low to medium to high or vice versa) and to explore the full range of the variable. Excel's data validation feature is used in some cases to set specific limits on variables. Conditional formatting is used to enhance patterns (cell background color changes) in numerical data such as the random error and safe worksheets. Each worksheet has the Protect Sheet... selected under the Tools to prevent students from accidentally modifying formulas. This can be turned off by selecting Unprotect Sheet... to allow modification or generation of other plots. Password protection and the ability to hide formulas are also available options.

The unstable
daughter situation allows the introduction of consecutive reactions (A --> B -->
C). From the graphical
display students can discover that the slower step (longer half-live) controls
the overall rate. Use of the total
radioactivity or the sum of the parent plus radioactive daughter makes this
easy to follow as illustrated in Figure 3.

The investigation
of counting error and background uses adjustable random noise added to the data
via the
RANDBETWEEN
function available in the
Analysis
ToolPak of Excel (loading instructions included on spreadsheet, see the
last tab). The equation given below
illustrates how adding error to the activity, A_{measured}, was
accomplished:

The RANDBETWEEN function is set to generate random numbers between -10 to 10 in
this case. The "x" variable is then tied
to an adjustable slider that can be adjusted from zero to some upper
limit. A_{theoretical} is simply
based on exponential decay, A_{o}e^{-kt}. Hence, the noise can be removed (set x = 0)
or increased to examine its consequence. If your students are not used to dealing with scatter and its effects in
data analysis, see Sinex (2005b). The
%Error graph in Figure 2 shows how relative error grows larger at later
times. Students can discover that
increasing initial activity, A_{o}, can reduce the random counting
error.

__Student____ Feedback and Assessment__
[top of
page]

A survey of 23
students that used this activity in spring 2005 showed that 74% had no difficulty
in usage and 65% thought it helped them understand the concepts, due to its
interactive and/or visual nature. The
graphs were indicated as the most common (43%) valuable aspect. The background and counting errors proved to
be the most difficult (35%) as this was totally new material not discussed in
class. One student commented "I learned
through my own actions and got to manipulate my own data. I felt more like an active learner," while
another suggested to "do without the Excel." When the students were asked to have the option of the interactive
activity or lecture, 57% wanted their instructor to just lecture. However, research such as Oliver-Hoyo and
others (2004) has shown otherwise.

Assessment is
accomplished by having students analyze a set of data (which can be easily
modified from semester-to-semester or even student-to-student) to evaluate the
half-life of a radioactive isotope and examine experimental error. Figure 4 illustrates the scoring (out of 25
points) for the assessment, labeled as project, and a follow-up set of similar
questions with different data on the final exam. The project is an out-of-class assignment and
may be worked on in groups with each student submitting results. Of the 24 students that completed both, 42%
showed an increase or achieved maximum points, while 17% (four large negative
differences) showed that learning should be stressed in cooperative learning
activities.

As students work
through this learner-centered activity, discussion of chemical concepts is
included at a number of points and the connections to the mathematics are
emphasized as well. We deal with the
daughter nuclide and the "conservation of nuclides" to remind students of the
product in the decay reaction. The
unstable daughter is an introduction to consecutive reactions and useful for
discussion of decay series, such as ^{238}U, or radioactive generators
in nuclear medicine. The discussion also
distinguishes between random and systematic errors. Error is introduced earlier as part of the
laboratory to this course; see Sinex (2005c) for further discussion. Counting error is random in nature. This random variation in the counts becomes a
serious problem when the total counts are small numbers at later times. Larger percent errors can greatly influence
the exponential regression results. Background radiation induces a systematic error, which has the largest
effect at low activities and has a major influence on the resulting exponential
regression if left uncorrected. They
also research information on background radiation with proper citation of their
sources. An instructor can generate a
new set of data for assessment using the background tab worksheet and adjusting
the half-life, starting activity, counting error, and background level. Data generated by the instructor can be
copied from Excel and pasted into a Word document as a table for students to
analyze.

The advantages of
the interactive Excel spreadsheet in general chemistry are numerous and include
the following:

● readily available off-the-shelf
software;

● students have previous experience with
Excel;

● disguises
the mathematical computations to allow easier integration of the mathematical
aspects with less anxiety;

● provides
visual display of graphs with multiple variables plotted along with numerical
data and symbolic relationships;

● emphasizes
data modeling with analysis and interpolation;

● strengthens
the connection between science and mathematics;

● interactivity
allows comparison and exploration of variables (a poor man's simulation
package) through numerical experimentation;

● easily modified, and;

● enhances discovery-based learning
through "what if" scenarios.

Other topics
explored by students in Excel include a
review of
mathematical functions for modeling,
investigating the gaseous
state of matter,
velocity
distribution for gases,
acid
distribution diagrams (monoprotic, diprotic, and triprotic acids),
chemical kinetics,
consecutive and competing
reactions, and
Beer's
Law (Beer's Law activity).

Students are
exposed to the topic of radioactive decay via a hands-on minds-on investigation
using available technology that enhances the graphical and numerical nature of
the kinetic behavior. The nature of
radioactive decay and its measurement error are explored through a mathematical
modeling approach, which is in itself good science process. With the proper mode of questioning, a little
simulation can generate a wealth of reasoning by students. The dynamic nature of interactive spreadsheet
brings the mathematics "alive" for students, as novice learners do not readily
see this in mathematical equations. This
approach works to strengthen the "rule of four," through which mathematics
educators (AMATYC, 2005; NCTM, 2000) are trying to emphasize and relate
graphical, numerical, symbolic, and verbal descriptions. In the end, the technology helps students
develop an understanding of concepts involving radioactive decay (Sherman and
Kurshan, 2004).

AMATYC
(2005). *
Beyond Crossroads: **
Implementing Mathematics Standards in the First Two
Years of College*.
American Mathematical Association of Two Year Colleges (online).

<http://http://amatyc.org/Crossroads/CROSSROADS> Accessed
17 November 2005.

Lim,
K. (2003)
Using
Spreadsheets in Chemical Education to Avoid Symbolic Mathematics, *Using Computers in Chemical Education
Newsletter*, Spring 2003. Accessed
17 November 2005.

NCTM
(2000). *Principles and Standards for
School Mathematics*. National Council of Teachers of Mathematics (NCTM),

Oliver-Hoyo,
M.T., Allen, D., Hunt, W.F., Hutson, J., and Pitts, A. (2004) Effects of an
Active Learning Environment: Teaching
Innovations at a Research I Institution, *Journal
of Chemical Education 81* (3): 441-448.

Sherman,
T., and Kurshan, B. (2004). Teaching for Understanding. *Learning and Leading with Technology 32 *(4): 6-11.

Siebert, E.D. and
McIntosh, W.J. (2001) *College Pathways to
the Science Education Standards*, National Science Teachers Association
(NSTA)
Press,

*TechLearning
Educator's Outlook. *Accessed
17 November

*Journal
of Online Mathematics and Its Applications 5.* Accessed 17
November

Sinex, S.A. (2005)
Investigating Types
of Errors, *Spreadsheets in Education 2*** **(1) 115-124. Accessed
17 November 2005.

__
Using Excel for Handling,
Graphing, and Analyzing Scientific Data: A Resource for Science and
Mathematics Students__. Accessed
17 November

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Using
Computers in Chemical Education Newsletter -
Fall 2005*