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Lect20[Compatibilit - Physics 344 Foundations of 21st Century Physics Relativity Quantum Mechanics and Their Applications Their Applications

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Notices: Locate your old copy of Matter & Interactions Volume II Exam I average was
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Particle Decays and Radioactivity When a sample of unstable matter initially containing N 0 active particles is observed over a period of time its activity (average number of particle decays per second) decreases exponentially with time. The rate at which the number of particles in the sample changes over time is, therefore, 0 t dN e dt λ ⎛⎞ = < ⎜⎟ ⎝⎠ 0 where λ , the decay constant, is a characteristic of the particular unstable particle involved and is simply related to the particle’s half-life as we showed last time. This implies that the number of particles present in the sample at time t is ) tt t t N d t N e d t + =+ ( ) 00 0 () 1 1 t t t Nt e NN e t ∫∫ 0 λλ
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Since ( ) 00 11 lim ( ) 1 0 t tt dN Nt N e N dt λ λλ →∞ →∞ ⎛⎞ =+ = ⎜⎟ ⎝⎠ we conclude that 0 0 1 N =− o, we can express N(t) in the simpler form So, e ca e p ess () es pe o ( ) 0 1 N N e Ne = N d N e N t = Because the average rate at which unstable particles in a sample of matter decay is proportional to the number of unstable particles in the sample, we can say that the probability of any one of the unstable particles decaying during a time interval Δ t is decay probability during (number of decays during )/ N t ΔΔ = =
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Quantum mechanics predicts such probabilities and only such probabilities. It
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University-West Lafayette.

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Lect20[Compatibilit - Physics 344 Foundations of 21st Century Physics Relativity Quantum Mechanics and Their Applications Their Applications

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