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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] 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 The Decay of Unstable Quantum Systems The model of decays of radioactive nuclei that we began to develop last time also applies to other decay processes we’ve considered, including decays of unstable particles like muons and pions and to the decay of excited atoms to lower energy states in which photons are emitted. We must learn how to account for both the predictable average behavior and the uncertainty in the behavior of such quantum systems. Last time, we showed that we could explain the observed average behavior of a large sample of some kind of unstable system, specifically, the exponential decay of its activity if we assumed that the probability that any individual system will decay, p , is p = λ∆ t for sufficiently short time periods ∆ t . The number of decays we expect to occur in a large sample of N of the systems during ∆ t is then dN N pN N t N dt λ λ ∆ = = ∆ ⇒ =  which implies that over longer periods of time ( ) t t dN N t N e N e N dt λ λ λ λ = ⇒ =  =  with N the initial number of particles in the sample at t = 0. Q1. If you flip a coin N times, N >> 1, and count 1 each time heads comes up and 0 each time tails comes up, what do you expect the average “face value”, total count / N , to be? A) 0 B) 1/ N C) 1/3 D) 1/2 E) 1 * This is an example of a mean or expectation value. We’ll discuss how to compute them given more complicated probability distributions than the one for coin flips. Q2. If the probability of rolling a 3 on a fair die is 1/6, one chance in six, what is the probability of rolling anything but a 3? A) 0 B) 1/3 C) 1/2 D) 5/6 E)1 * The die is certain end up with one of its six faces facing up. The probability of that happening is 1, one chance in one. Each face is equally likely to come up. This is the reason p 3 = 1/6. The sum of the probabilities of all possible things must add up to 1 since one of the possibilities is certain to occur. So, the probability of rolling anything but a 3 must be 1 – p 3 = 5/6. The exponential decay of the activity of a macroscopic radioactive source is an example of the kind of predictable average behavior that can be exhibited by a system consisting of a very large number of identical subsystems each of which behaves in a fundamentally unpredictable way. In our model, the decay of a radioactive nucleus, or other unstable system, is characterized by a decay constant, λ , The limit means that the probability for any individual subsystem to decay during a sufficiently short time period ∆ t is proportional to ∆ t , p = λ∆ t . Beyond that we can say nothing more about what happens during...
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 Fall '08
 Garfinkel
 Physics, Normal Distribution, Probability, Variance, Probability theory, probability density function

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