Download Radioactive Curves and Aging

Radioactive Curves and Aging
Cindy So
Abstract
A radioactive curve is a graph that shows the decay or decrease of a radioactive
isotope, such as carbon or potassium, as time passes. This is curvebank project to draw a
radioactive curve. It is a useful program for users to experiment and learn about
radioactive decay. Our program begins with a radioactive curve. Given the proper
radioactive rates and the time range, the program will calculate the points and translate
them into the applet window. This will allow users to view the decay of an object as time
passes. One feature included in this program includes the ability to view three curves at
once without entering the necessary numbers again and having the program graph again.
Each curve is drawn in a different color, which allows a user to recognize which curve
belongs to which radioactive decay rate entered. Another option in this program is the
calculation of the age given the correct information. It is able to calculate three different
decays, so user can compare the ages of different objects given the same amount.
Introduction
Radioactive decay occurs when a parent isotope creates daughter isotopes. This is
done to maintain a more stable atom by readjusting the neutrons and protons within an
atom. As time passes, the amount of radioactive isotopes within a radioactive object
slowly decreases. One type of radioactive dating is carbon-14 dating, which uses carbon14 in objects to calculate the age of an object. Within living organisms is carbon-14.
Carbon-14 slowly decays into carbon-12 and N-14 as time passes. To measure the
amount of carbon-14, a small piece of fossil is burned and converted carbon dioxide gas.
Changing into a gas, scientists measure the amount of carbon-14 in the gas. The age of
the fossil is calculated by comparing the amount of carbon-14 in the original amount with
the remaining amount of carbon-14 in the current object.
The purpose of the radioactive curve is to tell how old an object is based on the
amount of radioactive isotope remaining in the object after a certain amount of time. A
radioactive curve is also known as radioactive dating. It can also be named after the
isotope that is being measured. For example, if carbon-14 is being measured it can be
called carbon-14 dating. At the beginning, an object contains a certain amount of
radioactive isotope. As time passes, the amount of radioactive isotope in the object
reduces until it reaches zero. The rate of the decrease of the amount of radioactive
isotope is known as the radioactive decay rate.
The formula for calculating the
radioactive curve is A=Aoekt where A is the current amount of radioactive isotope, Ao is
the original amount of radioactive isotope, k is the radioactive decay rate and t is the time.
To graph the curve, Ao and k needs to be known. The maximum time range is also
required because the program needs to know when to stop graphing the curve. To
calculate the age of an object, the equation needs to be modified so that the time is the
only unknown factor. Therefore the equation for calculating the age of the object is
t= ln(
A
)( k ) .
Ao
The reason we choose this project is because radioactive decay is
interesting. Being able to determine the age of an object by the amount of isotope it
contains is important. This helps scientist, archaeologists and other professions use this
equation and find the age object that they may find. For example, in 1964 scientists
found bones of a Deinochus, a dinosaur, and wanted to know the age of the object.
However, the bones were too old to estimate the age. Therefore, the used the volcanic
debris in the surrounding rocks to estimate the age of the dinosaur. The rocks were
analyzed using potassium-argon dating and the result is the dinosaur lived approximately
107 million years ago.
This project is written for Curvebank, the website address for cuvebank is
http://curvebank.calstatela.edu/home/home.html.
It is website that contains many
information about curves that is related to math. For some curves there is a type of
animation or applet to accompany the explanation. We have been working with Shirley
Gray to create the radioactive curve for this website.
Technological Background
The program is written in Java using JBuilder. The classes that we used are:
java.awt.*;
java.awt.event.*;
java.applet.*;
javax.swing.*;
Each of these classes is needed to build each component of our program.
Java.applet is used to enable the java program to run on a browser and be viewed
on the internet. All that is required is inserting the applet tag with information such as
path to the java class file, size and height of the applet into the html file.
<APPLET
CODEBASE
CODE
NAME
ARCHIVE
WIDTH
HEIGHT
HSPACE
VSPACE
ALIGN
>
</APPLET>
=
=
=
=
=
=
=
=
=
"."
"radioactive.RadioactiveCurve.class"
"Radioactive Curve"
"radioactive.jar"
700
400
0
0
middle
In the above code, the class that it references is RadioactiveCurve.class within the
package radioactive. Since JBuilder created some files that were too long and had
strange symbols, the files had to be placed into a jar file. To create a jar file, we needed
to type “jar cd radioactive.jar radioactive” into a command prompt. In my program the
jar file is called radioactive.jar. The last word is the folder where all the classes were
stored. Since, we created a package for the java files, the folder also needs to be
packaged into the jar file. A jar file is like a zip file where several files are put together
into one file. To be able to read a jar file instead of folders, archive must be added and
needs to reference the jar file.
The other files are used for creating the gui for the project.
The first is
javax.swing, which is needed to build the gui with text fields, labels, JPanel and buttons.
Java.awt.event allows us to do some action on the gui. For example, when a button is
clicked the program will recognize the button has been clicked and will do some action.
The final class that was needed is java.awt which is where all the drawing tools are stored.
For our program, we used mostly drawLine to draw the x-axis and y-axis. DrawLine was
also used to draw the curve of the radioactive decay curve by calculating the points then
connecting each of the points with lines. For example, the points will start with 0 to the
time range specified by the user. This range will be split into segments and the points for
the graph will be calculated based on those segments. This will result in x and y
coordinates for the curve. The final step is to connect the points and depending on the
number of segments, the multiple lines will form a smooth curve. This program will run
on any browser that has java runtime environment, otherwise, the applet will not load.
System Overview
The main function of the curve is to draw the radioactive curve based on the
inputs for time range, original amount and radioactive decay rate given by the user.
However, a curve is plain and is available on many other websites by searching for
radioactive decay. To make my program different, we needed to add more features.
The first feature added is the ability to graph up to three curves at once. This will allow
the user to compare each of the radioactive decay rates given. By looking at the different
curves, the user will be able to tell which curve is decreasing faster and which is not. For
example, carbon-14 has a radioactive decay rate of -1.21 x 10-4 and iodine-131 has a
decay rate of –0.08664 and xenon-133 has a decay rate of –0.13862.
Carbon-14
decreases slower than the other two isotopes. Iodine-131 has the fastest decay rate and
gets closer 0 as time progresses. The decay rate of the three isotopes can be seen in the
screenshot above. The range of the graph has been set to 100 years. In the screenshot
above, the green line is carbon-14, the red line iodine-131 and blue is xenon-133. When
users see the graph, they can compare the three decay rates and see that they each decay
differently.
When the applet is loaded, some sample radioactive rates have been inserted to
give users an example of that to expect from this applet. The amount of the objects is not
needed. Instead the amount of the object will be show in percentages. At the top is 100
percents which means the current amount is the same as the original amount. As time
moves, the amount will decrease. Next is the time range will tell the applet how far to
calculate the points, which will affect how far in time to view the decay of the isotope.
This number will affect the x-axis on the graph. Depending on the decay type, either year,
day, hour or seconds, it will graph the decay based on the time. For example, in the
above screenshot, all three decay in years, so their type is year. If a day decay type is
inserted, the graph will not be visible because decays so fast that it will not be seen.
However, changing the range to days or lowering the year will make the graph visible.
The next three text fields are for inputting the decay rate or three radioactive isotopes.
The font of the letters have been given a color to match the curve that will be draw so the
user can match the radioactive curve to its radioactive decay rate. Below each text field
for inputting radioactive decay is a drop down box to choose what the decay type is.
They decay type will tell the program how fast the radioactive will decay. The possible
choices are: years, days, hours and seconds. Decay types with years will decay in terms
of years, while decay types with days will decay in terms in days. The graph will graph
based on the range given, radioactive decay type and the radioactive decay.
The final feature is the calculation of the age of an object. Assuming the user has
inputted the original amount of radioactive isotope, current amount, and the radioactive
decay rate with its type, the age of the object will be displayed.
Similar to the graph section, the input for radioactive decay will have the decay rate and
the decay type. At the top is the “calculate by”, which tells the program how to display
the answer. It can display the answer in terms of years, days, hours or seconds. The
program will calculate the answer and convert it to the type of answer desired. This
section can also calculate the half-life of an object. The half-life is the time needed for an
object to decay to half the amount. To calculate half-life, enter any number into the
remaining amount and enter double the amount in the original amount field.
Design and Implementation
To create this program, many java.swing components are put together.
JTextFields, Labels, JComboBox and Jbuttons are put together to create the design of the
program. For the graphing area, Jpanel is used. When calculating the points for the
radioactive curve, the points need to be translated into the x and y coordinates for the
Jpanel window. To accomplish that, another set of equations need to be inserted into the
program to translate the graph point into the window points.
The new points are
calculated as follows:
new.x = Ax + C
new.y = By + D
where A, B, C and D are calculated as follows:
window.right  window.left
graph.right  graph.left
window.top  window.bottom
B
graph.top  graph.bottom
C = window.left – A * graph.left
D = window.bottom – B * graph.bottom
A
Each of the points are the points for the top, bottom, left and right point of the graph area.
The graph points refers to the original graph and the window points refers to the points in
the JPanel screen. Using these equations to translate the points will allow the graph in
the window screen to correctly display.
This program is useful to many users; however, users who are studying
radioactive decay or have an interest in radioactive decay will find the program more
useful. This program was designed to improve the user experience in using a radioactive
decay applet. This program contains features that we believe will help the user in
comparing different radioactive curves with each other. Other applets that we have seen,
graphs one curve and that is the end of its abilities. If a user wanted the age calculated,
they will need to locate another website that contains an applet that will calculate age of
the object or the half-life of an object. The result of the project can be seen in the
screenshots above. In comparison to other applets for radioactive decay, we believe our
program is the most useful because of its features. Other applications that we have seen,
graphs one curve so the user is required to input another set of numbers to view a
different curve. After viewing two different curves, we preferred the ability to compare
the graphs without having to remember what the previous curve looked like. A direct
comparison feature has been added to this applet. This program allows users to compare
three radioactive decay curves in the same graph so it can be compared easily. The user
can view the curves and determine which decay rate decreases faster by comparing to the
other graphs. The user will be able to visually see the decrease of the curve. Some
curves will drop to approximately zero near 20,000 years such as carbon while others will
take more time. For example, potassium will take over five billion years, which will be
approximately 250,000 times longer than carbon.
System Evaluation
This is a curvebank project to draw a radioactive curve and is a useful program
for users to experiment and learn about radioactive decay. Our first goal was to draw the
radioactive curve. When the user enters a radioactive rate, the original amount and the
time range, the program will calculate the points and translate them into the applet
window. One feature included in this program includes the ability to view three curves at
once without inputting numbers again and graphing the curve a second time. Each curve
is drawn in a different color, which allows a user to recognize which curve belongs to
which radioactive decay rate entered since they will have matching colors. Another
option in this program is a calculator that will give the year of the object if provided with
enough information. It will calculate using all three radioactive decay rates so the user
will not have to input another number to see another calculation. This also allows the
user to compare the three years of the object, so the user can relate the radioactive isotope
rates with the year of an object at that certain time. This feature can also be used to
calculate points on the graph. If the user wants to know the half-life of an object, the user
can input half of the original amount entered to have the half-lives calculated. This
feature also allows the user to calculate points on the curve. For example, if the user
wants to know the year when it reaches twenty percent of the original amount, the user
will just have to input the amount into the text field.
This program has been tested to work on many browsers. To view the applet,
JRE is needed to run applets on a browser. This program has been tested on two
machines, a PC and a Macintosh. On a PC, internet explorer and firefox will work
perfectly. However, on a Macintosh machine the tabbed panes appear to overlap each
other. After loading each tab a few times, the applet will begin to correctly show. Matt,
who works with Shirley Gray on uploading the files on the server, says that it has
something to do with the Macintosh machines not displaying the GUI correctly.
Conclusion
From this project, the most important lesson that we have learned is java 2D.
Java 2D allows the programmer to draw various shapes such as circles, rectangles and
lines. To learn the more advanced java 2D functions, we must start at the beginning.
This program allowed me to learn a new feature of java that we never had the time to
learn. The beginning of any learning process is hard until a person become accustomed
to it. Afterwards, it becomes slightly easier. Another lesson we learned is applets.
Before beginning this project, we did not know how to create any applet programs. The
only thing we knew is that some internet programs use applets to run applications such as
yahoo games.
References
Deitel, H.M and P.J. Deitel. Java How to Program. New Jersey: Prentice Hall, 1999.
Java 2D API. Sun Microsystems. <http://java.sun.com/products/java-media/2D/>.
Keeton, Brian, Chuck Carvaness and Geoff Frieses. Special Edition Using Java 2
Standard Edition. Indiana: QUE. 2001.
Lesson: Packaging Programs in JAR Files. Sun Microsystems. 1 May 2006
<http://java.sun.com/docs/books/tutorial/deployment/jar/>
Radioactive decay. 4 June 2006. Wikipedia. 1 May 2006. <http://en.wikipedia.org/
wiki/Radioactive_decay>