02_NuclearChemistry_PostLab_Spr24 1

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Nuclear Chemistry Arianna Ballman 03-20-2024 TOTAL: 30 points

Arianna Ballman Estimating Half-Life Page 2 of 13 CHM 116 POST-LAB and LAB NOTEBOOK Nuclear Chemistry: Estimating Half Life of a “Radioactive” Element 1. Insert ONE picture of yourself in the appropriate lab attire and full PPE here ( include the Skittles® candy in your PPE picture ). **Remember to (1) show your full body so that we see you are wearing shoes; (2) wear your PPE (safety glasses, buttoned lab coat and gloves); (3) cover your lower legs and ankles (socks are required, even in Arizona); (4) tie back long hair in a ponytail or a bun; (5) remove jewelry. Note: Wearing full PPE may seem silly for tossing Skittles on a table, but we are establishing good lab protocol. If you have not received your lab kit (which contains your safety glasses), take the picture with what you have and include a note with your picture to explain why you are not wearing the complete PPE.

Arianna Ballman Estimating Half-Life Page 3 of 13 2. Enter the data that you collected during the experiment (from Tables 1 and 2 in the procedure) HERE. Remember to adjust the number of Rounds for each Trial to how many you completed . Table 1 (Trial 1) Table 2 (Trial 2) Round Skittles “ S ” Up (Parent Atoms) Skittles “S” Down (Daughter Atoms) Cumulative Daughter Atoms Round Skittles “ S ” Up (Parent Atoms) Skittles “S” Down (Daughter Atoms) Cumulative Daughter Atoms 0 58 0 0 0 60 0 0 1 31 27 27 1 28 32 32 2 17 14 41 2 17 11 43 3 13 4 45 3 7 10 53 4 2 11 56 4 3 4 57 5 1 1 57 5 1 2 59 6 0 1 58 6 0 1 60 3. Describe , in 2 - 3 sentences , what happens mathematically to the total number of candies in each round (the general trend)? How is this related to the concept of half-life in nuclear reactions ( or, what is each round simulating with regards to half-life )? 4. Are your two data sets exactly the same? If not, explain (in 1 – 2 sentences) using your experimental data. The amount of "S up"skittles reduces by roughly half each time which makes sense since the chance of getting a "S up" skittle is about 50%. In conclusion, the half-life of the parent Skittles continues to reduce by half until there are none left. No, the two sets of data were not the exact same. The data was very similar to each other but trail 1 started with 58 Skittles while trail 2 started with 60 skittles.

Arianna Ballman Estimating Half-Life Page 4 of 13 5. Use a graphing software to create the x-y scatter plot showing the Number of parent nuclei remaining vs. Round # (do not connect your points). Your ONE graph will show data points from BOTH trials of the experiment . On your graph, the x-axis should be Round Number , and the y-axis should be Parent Atoms Remaining ( NOT the daughter atoms or cumulative daughter atoms ) in that Round. In general, scientific graphs show the independent variable on the x-axis and the dependent variable on the y-axis. Do NOT connect your points; no trend line needed and m ake sure to: • Label the axes including the units in parentheses. • Include a figure legend (text below the graph) explaining the data in your graph. • Remove any default title, legend, and gridlines. • You should use two different symbols to represent the two data sets (i.e. a square for Trial 1 and a circle for Trial 2) You will not receive credit if you draw your graph by hand. Excel or Google Sheets are good choices that you can learn how to use quickly if you don’t already have a favorite graphing program. See other general tips for making graphs in the How to Make a Graph in Excel document located in the Introductory Materials for this lab.

Arianna Ballman Estimating Half-Life Page 5 of 13 6. Consider the trend shown in your graph in Question 5. Is it linear, exponential growth or exponential decay ? Is this trend consistent with your expectations for the kinetics of a nuclear reaction? Briefly explain why in 2 – 3 sentences. 7. Scientists like to use data to build physical models (or mathematical models to predict how data will look). Linear trends are easiest to work with; so we often look for ways to identify linear trends in a data set. Nuclear reactions all follow first order kinetics meaning the rate of a nuclear reaction is given by: ?𝒂?? = 𝒌[?𝒂?𝒊?𝒂??𝒊𝒗? 𝒊??????] in which k is a first order rate constant. As shown in the kinetics portion of this course, this relationship can be transformed to the following integrated rate law : 𝐥𝐧[?𝒂?𝒊?𝒂??𝒊𝒗? 𝒊??????] ? = −𝒌? + 𝐥𝐧[?𝒂?𝒊?𝒂??𝒊𝒗? 𝒊??????] ? Equation 1 in which ln is a natural logarithm, t is time (represented by the Round number in your experiment), [radioactive isotope] 0 is the concentration at time zero (the number of Skittles you start with in this experiment) and [radioactive isotope] t is the concentration of radioactive isotope at time t (number of remaining parent Skittles in this experiment). We need to adjust our data to create a graph which represents the above linear equation for first order kinetics. For each round in your experiment, calculate the natural log (ln) of the number of Parent atoms ( you are NOT using the above equation to find this value; just use the ln button on your calculator or create an equation in Excel ). Enter the Round number and number of Parent Atoms Remaining (from Tables 1 and 2 in Question #2), and ln(Parent Atoms) in Table 3 below: Table 3 : ln(Parent Atoms) vs. Round number Trial 1 Trial 2 Round Skittles “ S ” Up (Parent Atoms) ln (Parent Atoms) Round Skittles “ S ” Up (Parent Atoms) ln (Parent Atoms) 0 58 4.060 0 60 4.094 1 31 3.434 1 28 3.332 2 17 2.833 2 17 2.833 3 13 2.565 3 7 1.946 4 2 0.693 4 3 1.099 5 1 0 5 1 0 6 0 - 6 0 - It is exponential decay. This is because the expected half-life equation uses the natural log function which is the inverse of a exponential growth equation.

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