Lecture21

Lecture21 - Physics 344 Foundations of 21st Century...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Fan Chen Office: PHYS 222 chen926@purdue.edu Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: nd edition or rd edition
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Recitation Recap: We were finally able to use our model of radioactive decay as a random process and the ideas about probability we’ve been discussing to analyze some experimental data. The number of alpha particles emitted by a source containing 10 14 radioactive nuclei was counted during 5 second periods. The counts for 50 of these periods were The point of the exercise was to see that our model accounts consistently for the average number of counts and for the uncertainty we observed in the counts, that is, the way in which the count fluctuates about the average value from one period to the next. I emphasize that such uncertainty is a consequence of fundamental quantum randomness. We will, therefore, be dealing routinely with analogous uncertainty in the measured properties of any state of a quantum system as we continue our study of such systems. Radioactivity simply provides a first example of how this is done.
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n 0 1 p Recall that the expected decay count during Δ t is simply N 0 times the expectation value computed from the probability distribution for the decay of a single radioactive nucleus during Δ t , 2 1 5 0 1 0(1 ) 1 k k s k N n p p p p C pN = < = = - + = = Our interpretation of the decay-count data was based on our model of the probability distribution for the decay of a single radioactive nucleus during a time interval Δ t that is short compared to its half life. For our data, Δ t = 5 seconds so our model predicts an expected number of decays per period of pN 0 = 10 14 p . One glance at the data shows that only 10 or so of the 10 14 nuclei initially present decay during each period, so, 5 seconds << T 1/2 as required. We also use variance of the probability distribution for single-nucleus decay to understand the uncertainty of our counts per 5 second period, ( 29 2 2 2 2 2 2 2 1 1 1 (1 ) (1 ) k k k n N p p p p p p p p σ = = - < = - + - = - 1-p
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For “large enough” N 0 the CLT and our decay model predict that the estimate of the probability p obtained by dividing the decay count for a single 5 second period by the number of nuclei in the radioactive source,
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Lecture21 - Physics 344 Foundations of 21st Century...

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