of atomic number vs. number of neutrons for the most stable isotopes in the first twenty elements. Use atomic number as your manipulated variable (independent) and the cross marker (+) to mark the points.
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1.1 Run the program ISOTOPE and select ACTIVITY ONE to set the calculator up to begin. When the calculator screen shows "Done" continue on to 1.2 below.
| 1.2 Using lists L1=atomic number, L2=number of neutrons and the enclosed chart of the isotopes, plot a scatter gram of atomic number vs. number of neutrons for the most stable isotopes in the first twenty elements. Use atomic number as your manipulated variable (independent) and the cross marker (+) to mark the points. |
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1.3 What does the scatter gram indicate about the relationship between the variables? hint: Is it linear or nonlinear?
| 1.4 Calculate the regression equation for the data. Enter the equation into Y1 and plot the line of "best fits". Record the regression equation and sketch the calculator screen in your lab report.
Regression Equation Y= |
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1.5
a. What does the linear relationship indicate about stable atomic nuclei for the first 20 elements?b. From the linear relationship, predict the trend for the relative masses in the first twenty elements.
1.6 Using the data for the Carbon-14 isotope, enter: L3 = atomic number and L4=neutron number. Create a second scatter gram using PLOT2 and a box marker  for the data in L3 and L4.
Note: This will plot only one point for PLOT2. |
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1.7 Update your sketch in question four to include the box point for the carbon-14 isotope.
a. What is the Carbon-14 isotope's position relative to the regression line?b. What does carbon-14's position relative to the regression line imply about the stability of it's nucleus?
1.8 Using the data for the two possible daughter nuclides, enter: L3 = atomic number and L4 for neutron number (overwrite the C-14 data). Create a scatter gram using PLOT2 and a box marker for the data in L3 and L4.
1.9 By using the  function, analyze the graph showing the possible daughter nuclides for the decay of carbon-14. Considering the established stability trend and the nuclear composition of each daughter nuclide, predict whether carbon-14 undergoes alpha or beta decay and write a nuclear equation describing the decay. |
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2.1 Run the program ISOTOPE and select ACTIVITY TWO. This program updates the data in L1 and L2 to include the remaining stable naturally occurring isotopes (up to atomic number 92). The data is stored as L1=atomic number, L2=neutron number on your calculator.
2.2 By interpreting the graph, what happens to the stability trend we established for the first twenty elements? Has it changed or stayed the same?
2.3 To find a "new" mathematical relationship for the remaining data, or the second piece of this "piece-wise" function, we need to find a regression equation. Does the data look like a line or a curve? If the trend looks to be linear, use the LinReg function. If the data looks to be a curve you must find the equation of best fits, by choosing between a log function (LnReg), an exponential function (ExpReg)and a power function (PwrReg). Use the value of the Pearson Correlation Coefficient (r) to judge which regression model "best fits" the new data. Remember the "best fits" model will have an (r) value closest to 1 or -1.
When you have determined the regression equation, store it to Y2 and graph the line of "best fits". Record the equation and sketch the graph in your lab report.
| Regression Equation Y2= |
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2.4
a. If we look at the proton/neutron data for the first twenty stable isotopes, what type of a mathematical function exists?b. What does the data indicate about stable nuclei as their atomic number increases?
c. As the atomic number of an atom increases, what changes in the nucleus would account for the difference in the mathematical stability function?
3.1 Run the program ISOTOPE and select ACTIVITY THREE. This program removes the data points for the stable naturally occurring isotopes but leaves the "band of stability" equation in Y1.
3.2 Some unstable nuclei cannot reach the "band of stability" by one nuclear decay. They undergo many decays in an effort to become stable. One such element is Uranium-238. Using the enclosed data series chart with L1 atomic number and L2=number of neutrons, enter the data for all of the daughter nuclides in Uranium-238's decay series.
3.3 Set up Stat Plot 1 for a line graph 
, with a cross marker (+), of L1,L2. Select
, ZoomStat.
| Sketch the calculator screen in your lab report. |
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3.4 Use thefunction on the calculator and trace the points on the screen that represent atoms in U-238's decay series.
3.6 Complete the chart below by identifying the types of nuclear changes needed in order for unstable atoms to reach the "band of stability". Each region, A, B and C, requires a different nuclear change in order to achieve stability.
Nuclear fission is a spontaneous process whereby a large nucleus splits into two or more smaller nuclei. This process is induced by bombarding large atoms, like U-235 with neutrons, forming a highly unstable nucleus. This unstable nucleus undergoes spontaneous decay into two small daughter nuclei and emits a number of neutrons. These neutrons are moving at a very high rate of speed and can bombard other U-235 atoms and initiate other fission reactions, continuing the process by chain reaction. Attached is a diagram showing the neutron bombardment and subsequent nuclear chain reaction for U-235.
Nuclear fission unleashes an enormous amount of energy. The fission of 1 Kg of uranium-235 releases an amount of energy equal to the energy generated in the explosion of 20,000 tons of dynamite. If the chain reaction of uranium fission is uncontrolled, the energy release is instantaneous. This is what happens in an atomic bomb explosion. But, nuclear fission can be controlled and the energy released can be used to heat steam and produce electricity.
Like all other stars our sun runs on nuclear power. What is new is human use of nuclear energy. The nuclear energy released from only a few grams of nuclear fuel is equal to that produced by burning thousands of gallons of gasoline. In 1989 nuclear power plants generated 5% of the nation's total energy needs, and generated nearly 20% of U.S. electrical power.
Are the risks of nuclear technology worth its benefits? Some uses of nuclear technology create greater risks than others, and some offer greater benefits than others. As a voting citizen you will help influence nuclear technology's future. To better understand the risks of nuclear energy production we need a better understanding of fission. So let's go fission!!
4.1 Run the program ISOTOPE and select ACTIVITY FOUR. This program removes the data points for the stable naturally occurring isotopes but leaves the "band of stability" equation in Y1.
4.2 Using the enclosed fission chart with L1=atomic number and L2=number of neutrons, enter the data for all of the daughter nuclides shown.
4.3 Set up Stat Plot 1 for a scatter gram, with a box marker, of L1,L2. Select, ZoomStat.
| 4.4 Sketch the plot into your lab notebook. Explain what the plot tells you and why you think this pattern occurs. |
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4.5 Make a hypothesis concerning the stability of the fission daughter nuclides.
4.6 If these daughter products are radioactive, what type of nuclear changes need to occur for them undergo to become stable? (Which zone are they in?)
4.7 Update lists L1 and L2 to include the data for the U-235 parent isotope. Set up Stat Plot 1 for a scatter gram, with a box marker, of L1,L2. Select, ZoomStat.
| 4.8 Is there a mathematical relationship here for the points plotted? Figure the line of regression for the data in L1, L2. Sketch the graph and record the regression equation.
4.9 What is the significance of the slope of this line? |
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The daughter nuclides are physiologically important to humans because they can accumulate in the body. The following table illustrates areas of accumulation and stability for some of the fission daughters:
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Let's look further at one of the fission products, Kr-92. We established above that Kr-92 is unstable and will decay via beta decay. But will Kr-92 become stable with one decay, or will it decay by a series?
4.10 If each decay from Kr-92 requires the conversion of a neutron to a proton, determine the nuclear composition of the first three daughter products.
4.11 Using the data from 4.10 above, construct a mathematical equation describing the relationship of number of neutrons in each daughter's nucleus versus the number of protons. Make the equation of the form Y=AX+B.
4.12 What is the "atomic significance" of your coefficients for A and B in the equation you have created in 4.11?
4.13 Enter the equation from 4.11 into Y3 and plot the function with respect to the stability function.
| 4.14 Using the intersect feature of the calculator, calculate the point of intersection of the Kr-92 decay function with the stability function. This point represents the nuclear composition for the theoretical terminal nuclide in Kr-92's decay series. |
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4.15 What is the formula (element and mass) for the stable element from Kr-92's beta decay chain? Write a decay series showing all of the daughter nuclides as Kr-92 decays to a stabile isotope? Is this trend similar for all of the fission daughters? Explain.
4.16 What conclusions can you draw about spent fuel radioactive waste from fission reactions?
By federal law, reactor waste must be stored on site of production, usually in nuclear waste storage tanks. Final disposal of radioactive waste is the responsibility of the U.S. government and we currently do not have any permanent disposal sites.
Consider yourself a policy maker in a community split between proponents for using nuclear energy and those against. Many feel that nuclear waste generated from fission reactions represents "Pandora's Box".
