Exploring Radioactive Decay in Excel

8/17/2019 Exploring Radioactive Decay in Excel

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Exploring Radioactive Decay in Excel: An Interactive Visual Thinking Tool

Scott A. Sinex

Prince eorge!s "o##unity "ollege

A$stract

An interactive Excel spreadsheet investigation o% radioactive decay kinetics andassociated #easure#ent error is presented %or use in general che#istry. Students

are engaged in nu#erous higher&order thinking and science process skills as they

'ork through the activity.

(ey'ords

Excel spreadsheet

discovery learning

radioactive decay

kineticsrando# and syste#atic

errors

Introduction )top o%

page*

Radioactive decay is a general che#istry topic+ usually covered late in the second

se#ester+ and a typical exa#ple used to illustrate exponential $ehavior in

#athe#atics text$ooks. Developing an interactive discovery&$ased activity %or

exa#ining aspects o% radioactive decay 'as acco#plished using the graphical and

nu#erical data display capa$ilities o% Excel. The $asics o% developing interactive

co#putational Excel spreadsheets including an Excel tutorial are discussed in Sinex

,-/0. 1urther Excel application support is also provided as links later in this article,Sinex+ -2a0. Discovery learning is in line 'ith national re%or# e%%orts ,Sie$ert

and 3cIntosh+ -40.

The tool consists o% a series o% 5uestions that allo' students to discover a nu#$er o%

aspects o% radioactive decay 'hile exa#ining an interactive #ulti&layered Excel

spreadsheet. There are %ive learning o$6ectives to $e addressed: ,40 introduce the

$asics o% radioactive decay kinetics including deter#ining hal%&li%e7 ,-0 exa#ine the

gro'th o% the sta$le daughter nuclide produced %ro# the parent nuclide7 ,80 exa#inethe $ehavior o% an unsta$le or radioactive daughter nuclide ,$ehavior o% consecutive

reactions0 including total radioactivity7 ,/0 investigate the counting error o% the

parent activity+ its e%%ects and correction+ and7 ,20 investigate $ackground radiation

http://academic.pgcc.edu/~ssinexhttp://academic.pgcc.edu/~ssinex/UCCEN_F05/#_tophttp://academic.pgcc.edu/~ssinex/UCCEN_F05/#_tophttp://i.cmpnet.com/techlearning/archives/2004/01/Tutorial.xlshttp://academic.pgcc.edu/~ssinex/UCCEN_F05/#_tophttp://academic.pgcc.edu/~ssinex/UCCEN_F05/#_tophttp://i.cmpnet.com/techlearning/archives/2004/01/Tutorial.xlshttp://academic.pgcc.edu/~ssinex


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and its e%%ect and correction on the #easure#ent. 9u#erous higher&order thinking

5uestions are posed throughout the activity along 'ith the application o% science

process skills. The interactive dyna#ic nature o% the technology e#ployed enhances

the discovery learning o% $oth che#ical and #athe#atical concepts in %resh#an

che#istry %or nona6ors. Recently+ i# ,-80 has outlined so#e advantages o%

using spreadsheets in che#istry+ 'here in 5uantu# che#istry the sy#$olic

#athe#atics is purposely hidden due to its #ore co#plicated nature.

This activity is done having covered che#ical kinetics earlier in the se#ester and

'ith an introduction to radioactive decay via the penny or 3;3 %lipping activity to

uncover the exponential nature o% decay and de%ine hal%&li%e. The statistical nature

o% the process is discovered and the appropriate #athe#atical relationships can $e

derived. Students have used Excel as a data handling+ graphing+ and analy


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1or novices to these interactive spreadsheets or si#ulations+ it is generallyreco##ended to ad6ust the varia$les in a syste#atic 'ay ,lo' to #ediu# to high or

vice versa0 and to explore the %ull range o% the varia$le. Excel!s data

validation %eature is used in so#e cases to set speci%ic li#its on varia$les. "onditional

%or#atting is used to enhance patterns ,cell $ackground color changes0 in nu#erical

data such as the rando# error and sa%e 'orksheets. Each 'orksheet has the Protect

Sheet... selected under the Tools to prevent students %ro# accidentally #odi%ying

%or#ulas. This can $e turned o%% $y selecting >nprotect Sheet... to allo'

#odi%ication or generation o% other plots. Pass'ord protection and the a$ility to hide

%or#ulas are also availa$le options.

The unsta$le daughter situation allo's the introduction o% consecutive reactions ,A

&&? @ &&? "0. 1ro# the graphical display students can discover that the slo'er step

,longer hal%&live0 controls the overall rate. >se o% the total radioactivity or the su#

o% the parent plus radioactive daughter #akes this easy to %ollo' as illustrated in

1igure 8.

http://academic.pgcc.edu/~ssinex/excelets/data_validation.pdfhttp://academic.pgcc.edu/~ssinex/excelets/data_validation.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Conditional_Formatting.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Conditional_Formatting.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Protect_Sheet.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Protect_Sheet.pdfhttp://academic.pgcc.edu/~ssinex/excelets/data_validation.pdfhttp://academic.pgcc.edu/~ssinex/excelets/data_validation.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Conditional_Formatting.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Conditional_Formatting.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Protect_Sheet.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Protect_Sheet.pdf


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The investigation o% counting error and $ackground uses ad6usta$le rando# noise

added to the data via the RA9D@ETEE9 %unction availa$le in the Analysis

ToolPak o% Excel ,loading instructions included on spreadsheet+ see the last ta$0. Thee5uation given $elo' illustrates ho' adding error to the activity+ A#easured+ 'as

acco#plished:

The RA9D@ETEE9 %unction is set to generate rando# nu#$ers $et'een &4 to 4

in this case. The =x= varia$le is then tied to an ad6usta$le slider that can $e ad6usted%ro#


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co##on ,/80 valua$le aspect. The $ackground and counting errors proved to $e the

#ost di%%icult ,820 as this 'as totally ne' #aterial not discussed in class. Hne

student co##ented =I learned through #y o'n actions and got to #anipulate #y o'n

data. I %elt #ore like an active learner+= 'hile another suggested to =do 'ithout the

Excel.= hen the students 'ere asked to have the option o% the interactive activity

or lecture+ 2 'anted their instructor to 6ust lecture. Bo'ever+ research such as

Hliver&Boyo and others ,-/0 has sho'n other'ise.

Assess#ent is acco#plished $y having students analy


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As students 'ork through this learner&centered activity+ discussion o% che#ical

concepts is included at a nu#$er o% points and the connections to the #athe#atics

are e#phasi+ or radioactive generators in nuclear #edicine. The

discussion also distinguishes $et'een rando# and syste#atic errors. Error isintroduced earlier as part o% the la$oratory to this course7 see Sinex ,-2c0 %or

%urther discussion. "ounting error is rando# in nature. This rando# variation in the

counts $eco#es a serious pro$le# 'hen the total counts are s#all nu#$ers at later

ti#es. arger percent errors can greatly in%luence the exponential regression

results. @ackground radiation induces a syste#atic error+ 'hich has the largest

e%%ect at lo' activities and has a #a6or in%luence on the resulting exponential

regression i% le%t uncorrected. They also research in%or#ation on $ackground

radiation 'ith proper citation o% their sources. An instructor can generate a ne' seto% data %or assess#ent using the $ackground ta$ 'orksheet and ad6usting the hal%&

li%e+ starting activity+ counting error+ and $ackground level. Data generated $y the

instructor can $e copied %ro# Excel and pasted into a ord docu#ent as a ta$le %or

students to analy


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Students are exposed to the topic o% radioactive decay via a hands&on #inds&on

investigation using availa$le technology that enhances the graphical and nu#erical

nature o% the kinetic $ehavior. The nature o% radioactive decay and its #easure#ent

error are explored through a #athe#atical #odeling approach+ 'hich is in itsel% good

science process. ith the proper #ode o% 5uestioning+ a little si#ulation can

generate a 'ealth o% reasoning $y students. The dyna#ic nature o% interactive

spreadsheet $rings the #athe#atics =alive= %or students+ as novice learners do notreadily see this in #athe#atical e5uations. This approach 'orks to strengthen the

=rule o% %our+= through 'hich #athe#atics educators ,A3ATK"+ -27 9"T3+ -0

are trying to e#phasi

Exploring Radioactive Decay in Excel

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