Chapt. 27Currents and Resistance2093. The probability of electron collision (with an ion, impurity, or defect) in a metal happening inthe time span from last collision to timetisP(t) = 1−e−t/τwhereτis thee-folding time for collisions.a) Take the derivative ofP(t) with respect to time.b) The derivative from part (a) is a probability densityρfor collisions:i.e.,ρdtis theprobability for a collision happening in the differential time intervaldt. The time intervalover which the density applies is from time 0 (immediately after the last collision) to timeinfinity.If you haveNelectron flights between collisions,Nρdtis the mean number ofthem that end indt. Say you have a quantityQassociated with the electron flights: ingeneralQdepends ont. The mean total value ofQfor flights that end indtisQNρ(t)dt.The mean total value for allNflights isNintegraldisplay∞0Qρdt.The average value ofQper flight (i.e.,(Q)) given by(Q)=integraldisplay∞0Qρdt.
This is the end of the preview.
access the rest of the document.