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Physics 1 Problem Solutions 213

Physics 1 Problem Solutions 213 - Chapt 27 Currents and...

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Chapt. 27 Currents and Resistance 209 3. The probability of electron collision (with an ion, impurity, or defect) in a metal happening in the time span from last collision to time t is P ( t ) = 1 e t/τ where τ is the e -folding time for collisions. a) Take the derivative of P ( t ) with respect to time. b) The derivative from part (a) is a probability density ρ for collisions: i.e., ρdt is the probability for a collision happening in the differential time interval dt . The time interval over which the density applies is from time 0 (immediately after the last collision) to time infinity. If you have N electron flights between collisions, Nρdt is the mean number of them that end in dt . Say you have a quantity Q associated with the electron flights: in general Q depends on t . The mean total value of Q for flights that end in dt is QNρ ( t ) dt . The mean total value for all N flights is N integraldisplay 0 Qρdt. The average value of Q per flight (i.e., ( Q ) ) given by ( Q ) = integraldisplay 0 Qρdt.
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