Silver melts at . At the melting point, what fraction of the conduction electrons is in states with energies greater than the Fermi energy of 5.5 eV? (See Problem 21)
The fraction of the conduction electrons with greater energies than the Fermi energy of silver is 0.03.
a) Melting point of silver,
b) Fermi energy of silver,
The electrons that are free to move within the walls of the substance and are not bound to any atom, are called conduction electrons or free electrons.
The fraction of electrons above Fermi level at the melting point are-
Using the given data in equation (i), we can get the value of the fraction of the conduction electrons of the copper material as follows:
Hence, the value of the fraction is 0.03.
(a) Show that the density of states at the Fermi energy is given by
in which n is the number density of conduction electrons.
(b) Calculate for copper, which is a monovalent metal with molar mass 63.54g/mol and density .
Verify your calculation with the curve of Fig. 41-6, recalling that = for copper.
A silicon sample is doped with atoms having donor states 0.110eV below the bottom of the conduction band. (The energy gap in silicon is 1.11eV ) If each of these donor states is occupied with a probability of at , (a) is the Fermi level above or below the top of the silicon valence band and (b) how far above or below? (c) What then is the probability that a state at the bottom of the silicon conduction band is occupied?
Calculate the number density (number per unit volume) for (a) molecules of oxygen gas at and 1.0 atm pressure and (b) conduction electrons in copper. (c) What is the ratio of the latter to the former? What is the average distance between (d) the oxygen molecules and (e) the conduction electrons, assuming this distance is the edge length of a cube with a volume equal to the available volume per particle (molecule or electron)?
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