Problem 5.16 The density of copper is 8.96 gm/cm, and its atomic weight is 63.5 gm/mole. (a) Calculate the Fermi energy för copper (Equation 5.43). Assume q = 1, and give your answer in electron volts. (b) What is the corresponding electron velocity? Hint: Set EF = (1/2)mv². Is it safe to assume the electrons in copper are nonrelativistic? (c) At what temperature would the characteristic thermal energy (kB T, where kB is the Boltzmann constant and T is the Kelvin temperature) equal the Fermi energy, for copper? Comment: This is called the Fermi temperature. As long as the actual temperature is substantially below the Fermi temperature, the material can be regarded as "cold," with most of the clectrons in the lowest accessible state. Since the melting point. of copper is 1356 K, solid copper is always cold. (d) Calculate the degeneracy pressure (Equation 5.46) of copper, in the electron gas model.

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Problem 5.16 The density of copper is 8.96 gm/cm', and its atomic weight is
63.5 gm/mole.
(a) Calculate the Fermi energy för copper (Equation 5.43). Assume q = 1, and
give your answer in electron volts.
(b) What is the corresponding electron velocity? Hint: Set Er = (1/2)mv². Is
it safe to assume the électrons in copper are nonrelativistic?
(c) At what temperature would the characteristic thermal energy (kBT, where kB
is. the Boltzmann constant and T is the Kelvin temperature) equal the Fermi
energy, for copper? Comment: This is called the Fermi temperature. As
long as the actual temperature is substantially below the Fermi temperature,
the material can be regarded as "cold," with most of the electrons in the
lowest accessible state. Since the melting point of copper is 1356 K, solid
copper is always cold.
(d) Calculate the degeneracy pressure (Equation 5.46) of copper, in the electron
gas model.
Transcribed Image Text:Problem 5.16 The density of copper is 8.96 gm/cm', and its atomic weight is 63.5 gm/mole. (a) Calculate the Fermi energy för copper (Equation 5.43). Assume q = 1, and give your answer in electron volts. (b) What is the corresponding electron velocity? Hint: Set Er = (1/2)mv². Is it safe to assume the électrons in copper are nonrelativistic? (c) At what temperature would the characteristic thermal energy (kBT, where kB is. the Boltzmann constant and T is the Kelvin temperature) equal the Fermi energy, for copper? Comment: This is called the Fermi temperature. As long as the actual temperature is substantially below the Fermi temperature, the material can be regarded as "cold," with most of the electrons in the lowest accessible state. Since the melting point of copper is 1356 K, solid copper is always cold. (d) Calculate the degeneracy pressure (Equation 5.46) of copper, in the electron gas model.
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