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Third Edition ( 2005 McGraw-Hill)
2.1 Electrical conduction 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 cm2 V-1 s-1.
a. 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’ mean separation d = 1/n1/3.)
b. 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 neighboring Na+ ions. What is the approximate
Coulombic interaction energy (in eV) between an electron and an Na+ ion?
c. How does this electron/metal-ion 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/metal-ion
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/metal-ion interaction energy?
d. Calculate the electrical conductivity of Na and compare this with the experimental value of 2.1
107 Ω-1 m-1 and comment on the difference.
a. If D is the density, Mat is the atomic mass and NA is Avogadro's number, then the atomic
concentration nat is
which is also the electron concentration, given that each Na atom contributes 1 conduction electron.
If d is the mean separation be