 Na is a monovalent metal (BCC) with a density of 0.9712 g cm^{3}. Its atomic mass is 22.99 g mol^{1}. The drift mobility of electrons in Na is 53 cm^{2}(Vs)^{1}. [solution available]
 Consider the collection of conduction electrons in the solid. If each Na atom donates one electron to the electron sea, estimate the mean separation between the electrons. (Note: If n is the concentration of particles, then the particles's mean separation d = 1/n^{1/3}.)
 Estimate the mean separation between an electron (e^{}) and a metal ion (Na^{+}), assuming that most of the time the electron prefers to be between two neighbouring Na^{+} ions. What is the approximate Coulombic interaction energy (in eV) between an electron and an Na^{+} ion?
 How does this electron/metalion interaction energy compare with the average thermal energy per particle, according to the kinetic molecular theory of matter? Do you expect the kinetic molecular theory to be applicable to the conduction electrons in Na? If the mean electron/metalion interaction energy is of the same order of magnitude as the mean KE of the electrons, what is the mean speed of electrons in Na? Why should the mean kinetic energy be comparable to the mean electron/metalion interaction energy?
 Calculate the electrical conductivity of Na and compare this with the experimental value of 2.1 x 10^{7} (ohmm)^{1} and comment on the difference.
 The resistivity of aluminum at 25^{o}C has been measured to be 2.72 x 10^{8} ohmm. The thermal coefficient of resistivity of aluminum at 0^{o}C is 4.29 x 10^{3} K^{1}. Aluminum has a valency of 3, a density of 2.70 g cm^{3}., and an atomic mass of 27. [solution available]
 Calculate the resistivity of aluminum at 40^{o}C.
 What is the thermal coefficient of resistivity at 40^{o}C?
 Estimate the mean free time between collisions for the conduction electrons in aluminum at 25^{o}C, and hence estimate their drift mobility.
 If the mean speed of the conduction electrons is about 2.0 x 10^{6} m/s, calculate the mean free path and compare this with the interatomic separation in Al (Al is FCC). What should be the thickness of an Al film that is deposited on an IC chip such that its resistivity is the same as that of bulk Al?
 What is the percentage change in the power loss due to Joule heating of the aluminum wire when the temperature drops from 25^{o}C to 40^{o}C?
 Electron drift mobility in indium has been measured to be 6 cm^{2}V^{1}s^{1}. The room temperature resistivity of In is 8.37 x 10^{8} ohmm, and its atomic mass and density are 114.82 amu and 7.31 g cm^{3}, respectively. [solution available]
 Based on the resistivity value, determine how many free electrons are donated by each In atom in the crystal. How does this compare with the position of In in the Periodic Table (Group IIIB)?
 If the mean speed of conduction electrons in In is 1.74 x 10^{8} cm/s, what is the mean free path?
 Calculate the thermal conductivity of In. How does this compare with the experimental value of 81.6 W (mK)^{1}?
 Consider a thin insulating disk made of mica to electrically insulate a semiconductor device from a conducting heat sink. Mica has thermal conductivity of 0.75 W (mK)^{1}. The disk thickness is 0.1 mm, and the diameter is 10 mm. What is the thermal resistance of the disk? What is the temperature drop across the disk if the heat current through it is 25 W? [solution available]
 Consider a coaxial cable that has a copper core conductor and polyethylene dielectric with the following properties: Core conductor resistivity of 19 nohm m, core radius of 4 mm, dielectric thickness of 3.5 mm, dielectric thermal conductivity of 0.3 W (mK)^{1}. The outside temperature is 25^{o}C. The cable is carrying a current of 500A. What is the temperature of the inner conductor? [solution available]
 Consider a rectangular sample, a metal or an ntype semiconductor, with a length L, width W, and thickness D. A current I is passed along L, perpendicular to the crosssectional area WD. The face W X L is exposed to a magnetic field intensity B. A voltmeter is connected across the width to read the Hall voltage V_{H}. [solution available]
 Show that the Hall voltage recorded by the voltmeter us V_{H} = IB/Den
 Consider a 1micronthick strip of gold layer on an insulating substrate that is a candidate for a Hall probe sensor. If the current through the film is maintained at constant 100 mA. What is the magnetic field that can be recorded per microvolt of Hall voltage?
 Consider Matthiessen's rule applied to a thin film. Show that, very approximately, the product of the thermal coefficient of resistivity (TCR) and the resistivity of the thin film is equivalent to the product of the bulk TCR and resistivity. [solution will be posted soon]


