Fluid Mechanics

Homework 5 Solution
Question 14.6 Define the following quantities pertaining to the flow of electrons in a metal conductor: (a) drift velocity; (b) relaxation time; (c) electron mobility. Answer 14.6 (a) The drift velocity vd, is the average velocity achieved by an electron in the presence of a uniform electric field, E. An average value is used since the electron’s motion varies periodically, in a sawtooth manner, as the particle accelerates, collides with positive-ion cores, and reaccelerates. (b) The relaxation time τ, is the average time between collisions of a conduction electron with the positive-ion cores of the metal lattice. (c) The electron mobility, µ, is the proportionality constant relating to the drift velocity to the applied electric field as vd = µ*E. The SI units for µ are m2/(V*s). Question 14.8 What structural defects contribute to the residual component of the electrical resistivity of a pure metal? Answer 14.8 Dislocations, vacancies, grain boundaries and impurity atoms are common structural defects that contribute to the small residual component of a pure metal’s electrical resistivity. Question 14.13 What explanation is given for the good electrical conductivity of magnesium and aluminum even though these metals have filled outer 3s energy bands? Answer 14.13 Although the outer 3s energy bands in magnesium and aluminum are filled, these metals have good electrical conductivity because their 3s bands overlap their 3p bands. In the case of magnesium, the empty 3p band combines with the 3s band to form a partially filled 3sp band. Similarly, in aluminum, the 3p band, which contains one electron, overlaps the full 3s band. Question 14.14 How does the energy-band model explain the poor electrical conductivity of an insulator such as pure diamond? Answer 14.14 In an insulator, such as pure diamond, the electrons are tightly bound in covalent or ionic bonds. The energy-band model theorizes that these bound electrons fill a lower valence band which...