Can you derive the expression for the total number of electrons (N) within the Fermi sphere with a radius k_F in the k-space, considering that the energy states inside the sphere in the free electron gas model for the electrical conductivity of metals are filled with electrons at T=0 Then: a) Calculate the expression for the radius of the Fermi sphere, its energy, the velocity of the electron at the Fermi surface and the Fermi temperature. b) Show that the electron density for electrons (fermions) is given by D(E)= dN/dE = 3N/2E.
Can you derive the expression for the total number of electrons (N) within the Fermi sphere with a radius k_F in the k-space, considering that the energy states inside the sphere in the free electron gas model for the electrical conductivity of metals are filled with electrons at T=0 Then: a) Calculate the expression for the radius of the Fermi sphere, its energy, the velocity of the electron at the Fermi surface and the Fermi temperature. b) Show that the electron density for electrons (fermions) is given by D(E)= dN/dE = 3N/2E.
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Transcribed Image Text:Can you derive the expression for
the total number of electrons (N)
within the Fermi sphere with a
radius k_F in the k-space,
considering that the energy states
inside the sphere in the free
electron gas model for the
electrical conductivity of metals
are filled with electrons at T=0
Then:
a) Calculate the expression for the
radius of the Fermi sphere, its
energy, the velocity of the
electron at the Fermi surface and
the Fermi temperature.
b) Show that the electron density
for electrons (fermions) is given by
D(E)= dN/dE = 3N/2E.
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