# NAT Sci 102 Breakout Activity. Radioactivity and Age Determinations. Due Date: April 22

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3 Elapsed Time in sec Raw Counts Background Net Counts (Raw minus Background) Uncertainty (Square Root of Raw) 0.00 Random Processes and Counting Statistics Randomness plays a large role in what can be observed and learned about nature. This stems from several causes including the fact that some things come in indivisible units -- photons and electrons are examples where you cannot have a third of a photon or 80% of an electron. Either you have one or you don't. Another way in which randomness enters is in the fundamental laws of physics. The branch of physics called quantum physics shows that all knowledge of locations and velocities of objects can only be described by probabilities. This behavior becomes very noticeable when studying small objects like atoms but mostly indistinguishable from behavior you would predict using Newton's Laws on scales like 3

5 occurred most often the most frequently occurring number of heads is the "maximum". Compute the value of the maximum divided by 2. The range of most likely values begins at the lowest number of heads that occurred at least half of the maximum number of times up to the highest number of heads that occurred at least half of the maximum number of times. What is your range? Compare your range to : The uncertainty in an experiment is approximately half the range computed in this manner. Figure 1: How to measure the range of values. The range in this figure is 90 to

6 What you have just illustrated is the principle that in an experiment where you count items, there is an uncertainty proportional to the square root of the counts. These means that if you expect to count 100 α - particles, your counts will most probably lie in the range from to 100+, 90 to 110. It is still possible for an experiment to result in counts outside this range but with lower probability. Completion of Measuring the Half Life of Pa 234 Below, we give the results of two independent counting experiments like the one that was run for you in class. Use these numbers to carry out the items below. Determine the background counts from the Geiger counter reading long after the radioactivity has decayed. There is a separate table with these numbers. Average the five entries to get a best value. Although of the values has an error of the square root of the number, because we have averaged five of them we can ignore this type of error in the best value. Enter this value in the background columns in the tables for runs 1 and 2. Compute the net counts by subtracting the background counts from each of the counts that was observed during the decay of the protactinium. Then put in the uncertainties for each reading. Prepare a graph where the horizontal axis represents elapsed time and the vertical axis represents net counts. A very convenient way to make a graph is to put all the numbers into a spreadsheet such as Excel provides. The number of decays will change with time as the quantity of protactinium changes. Use your graph to estimate the half life of protactinium and write it here: Do you see any deviations from a smooth decay with time? Give an explanation for these deviations (how do they compare with your estimates of the uncertainties in the counts): 6

7 Run 1 Elapsed Time In sec Raw Counts Background Net Counts (Raw minus Background) Uncertainty (Square Root of Raw) Background counts (use for both runs) Elapsed Time Background Counts In sec

8 Run 2 Elapsed Time In sec Raw Counts Background Net Counts (Raw minus Background) Uncertainty (Square Root of Raw)

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