Question

Q 4(a) [7 Marks] Explain the basic assumptions of the free electron model of solids. Explain also what is meant by the term 'density of states' when applied to the free electron model of a solid. Q 4(b) [8 Marks] Mention and briefly discuss two areas where the free electron model of solids is able to explain physical behaviours which the classical Drude model cannot, and also two areas where the free electron model fails to explain observed behaviour of solids. Q 4(c) [8 Marks] You are told that a certain metal has an atomic density of 2.3 x $10^{28}$ m$^{-3}$, and has a valence of 2. What are: (i) the Fermi wavevector (ii) the Fermi energy, (iii) the Fermi velocity (iv) the Fermi Temperature of this metal. Q 4(d) [4 Marks] What is the density of states of this metal at the Fermi surface for a 0.05 m$^3$ volume crystal? Estimate the size of a cube of this metal for which the spacing between energy states close to the Fermi surface is 0.025 eV. Q 4(e) [6 Marks] State Bloch's theorem and briefly explain the significance of Bloch's theorem for the structure of energy bands in crystalline solids.

          Q 4(a)
[7 Marks]
Explain the basic assumptions of the free electron model of solids. Explain also what
is meant by the term 'density of states' when applied to the free electron model of a
solid.
Q 4(b)
[8 Marks]
Mention and briefly discuss two areas where the free electron model of solids is able
to explain physical behaviours which the classical Drude model cannot, and also two
areas where the free electron model fails to explain observed behaviour of solids.
Q 4(c)
[8 Marks]
You are told that a certain metal has an atomic density of 2.3 x $10^{28}$ m$^{-3}$, and has a
valence of 2.
What are:
(i)  the Fermi wavevector
(ii) the Fermi energy,
(iii) the Fermi velocity
(iv) the Fermi Temperature of this metal.
Q 4(d)
[4 Marks]
What is the density of states of this metal at the Fermi surface for a 0.05 m$^3$ volume
crystal?
Estimate the size of a cube of this metal for which the spacing between energy
states close to the Fermi surface is 0.025 eV.
Q 4(e)
[6 Marks]
State Bloch's theorem and briefly explain the significance of Bloch's theorem for the
structure of energy bands in crystalline solids.

Q 4(a)
[7 Marks]
Explain the basic assumptions of the free electron model of solids. Explain also what
is meant by the term 'density of states' when applied to the free electron model of a
solid.
Q 4(b)
[8 Marks]
Mention and briefly discuss two areas where the free electron model of solids is able
to explain physical behaviours which the classical Drude model cannot, and also two
areas where the free electron model fails to explain observed behaviour of solids.
Q 4(c)
[8 Marks]
You are told that a certain metal has an atomic density of 2.3 x 10^28 m^-3, and has a
valence of 2.
What are:
(i) the Fermi wavevector
(ii) the Fermi energy,
(iii) the Fermi velocity
(iv) the Fermi Temperature of this metal.
Q 4(d)
[4 Marks]
What is the density of states of this metal at the Fermi surface for a 0.05 m^3 volume
crystal?
Estimate the size of a cube of this metal for which the spacing between energy
states close to the Fermi surface is 0.025 eV.
Q 4(e)
[6 Marks]
State Bloch's theorem and briefly explain the significance of Bloch's theorem for the
structure of energy bands in crystalline solids.

Added by John K.

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