Question

Consider the conduction electrons in silver, which is monovalent (one free electron per atom), has a mass density 10.5 × 10³ kg m?³, and an atomic weight of 107. Show that the Fermi energy (at T = 0) is ?? = 5.6 eV, and the equivalent temperature—the so-called Fermi temperature—is TF = ?? / k = 65,000 K. Thus, if T ? TF (as is definitely the case at room temperature) then the conduction electrons are highly degenerate. Furthermore, show that at room temperature (T = 300 K), the contribution of the conduction electrons to the molar specific heat is only c?? / R = 2.2 × 10?².

          Consider the conduction electrons in silver, which is monovalent (one free electron per atom), has a mass density 10.5 × 10³ kg m?³, and an atomic weight of 107. Show that the Fermi energy (at T = 0) is
?? = 5.6 eV,
and the equivalent temperature—the so-called Fermi temperature—is
TF = ?? / k = 65,000 K.
Thus, if T ? TF (as is definitely the case at room temperature) then the conduction electrons are highly degenerate. Furthermore, show that at room temperature (T = 300 K), the contribution of the conduction electrons to the molar specific heat is only
c?? / R = 2.2 × 10?².

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Consider the conduction electrons in silver, which is monovalent (one free electron per atom), has a mass density 10.5 × 10³ kg m?³, and an atomic weight of 107. Show that the Fermi energy (at T = 0) is
?? = 5.6 eV,
and the equivalent temperature—the so-called Fermi temperature—is
TF = ?? / k = 65,000 K.
Thus, if T ? TF (as is definitely the case at room temperature) then the conduction electrons are highly degenerate. Furthermore, show that at room temperature (T = 300 K), the contribution of the conduction electrons to the molar specific heat is only
c?? / R = 2.2 × 10?².

Added by Isabel K.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

06/15/2022

Step 1

To find the number density (n) of conduction electrons, we first need to calculate the number of atoms per cubic meter in silver. Given that silver is monovalent, each atom contributes one free electron. The number density n can be calculated using the formula: \[ Show more…

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Consider the conduction electrons in silver, which is monovalent (one free electron per atom), has a mass density 10.5 !! 10 kg m, and an atomic weight of 107. Show that the Fermi energy (at T = 0) is ΙF = 5.6 eV, and the equivalent temperature—the so-called Fermi temperature—is TF = ΙF / k = 65,000 K. Thus, if T ≪ TF (as is definitely the case at room temperature) then the conduction electrons are highly degenerate. Furthermore, show that at room temperature (T = 300 K), the contribution of the conduction electrons to the molar specific heat is only cV(e) / R = 2.2 !! 10.

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