Consider the . According to investigations of thermal conductivity, the free electrons in an alkali metal must have very high velocities that are relatively independent of the temperature, up to a thousand degrees centigrade or so. These electrons can be treated as composing a "gas", since they are kinetic particles confined in a definite volume by the atomic lattice of the metal. However, electrons differ from molecules, such as those of hydrogen and helium, in many important respects. Modern statistics gives a representation of the distribution of electrons with respect to energy such as that shown in fig.8.9. The line S indicates the "energy surface" of the electrons at room temperature. The vertical dotted line represents the energy surface at absolute zero. The area is shaded in order to indicate that the energy space indicated is : there is no room for more electrons at the lower energies.
. The sphere drawn in the figure represents the "surface of the maximum
energy" at absolute zero. As the temperature increases, this surface becomes
increasingly "fuzzy".
It has been calculated, using modern theory, that the electrons in a
metallic conductor will not make their full (ideal gas) contribution the
specific heat before a temperature of 30,000° K is reached, before which, of
course, the metal will have completely vaporized.
Review this account of the electron gas in the light of what you have
learnt and the items on the RESPONSE ARRAY. Choose items which indicate concepts you
would use in order to understand what has been said about the electron
gas.