Question

Q1// Do the electrons or phonons carry the greater part of the heat current in a metal? Explain that.

Q2//Explain the origin of the energy gap and find the magnitude of the energy Gap.

Q3// Give general remarks about Bloch^,s theorem.

Q4//    Complete the following statements :-

1. The energy of the topmost filled level in the ground state of the (N) electron System is called as------------------------.
2. The number of orbitals per unit energy range is called as----------------------.

     (3)The model answers almost all the qualitative questions about the behavior of electron in metals is --------------------------. (4) The electrical resistivity of most metals is dominated at liquid helium temperature by collisions of the conduction electrons with--------------------------- in the lattice.

(5) The crystals is called ---------------------- or semimetal if one or two bands are slightly filled or slightly empty.                                                          

(6)At temperatures much below both the Debye temperature and the Fermi temperature ,the heat capacity of metals may be written as --------------------.                        

(7) The number of orbitals with the same energy is called -----------------------.

(8) At absolute zero the chemical potential is equal to ---------------------------.

(9)The region which results from intraction of conduction electron waves with the ion cores of the crystals is called-------------------------.

Answer 1

Q1) Thermal conductivity of electrons Ke is atleast a magnitude greater than the thermal conductivity of phonon Kp.

Electrons carry greater part of heat current in metals.

Presence of electrons gives rise to additional mechanism for scattering of phonons. This scattering influences Kp and thermal conductivity of metal has greater part of from electron than from phonons i.e. Ke than Kp.

Q2) When large number or more than 1 identical atoms come together to form a crystal or molecule, according to Pauli exclusion principle, 2 electrons can't have the same quantum numbers hence the atomic orbitals split into molecular orbitals and overlap to form bands. The size of these bands is related to the degree of overlap of atomic orbitals. Some time the bands are not wide enough to cover the entire energy range and the left over range results in band gap.

Magnitude of Band gap is ~1eV for semiconductors and > 5eV for insulators.

Q3) Bloch's Theorem specifies the form of the wave functions (i.e. a plane wave) that characterize electron energy levels in a periodic crystal.

Hence according to Bloch's Theorem, the solution to shrodingers equation is the product of 2 terms, the plane wave and periodic potential of the crystal.

Q4) 1) The energy of the topmost filled level in the ground state of the (N) electron System is called as Fermi Energy.

2) The number of orbitals per unit energy range is called as Density of states.

3) The model answers almost all the qualitative questions about the behavior of electron in metals is Nearly Free Electron Mod

4) The electrical resistivity of most metals is dominated at liquid helium temperature by collisions of the conduction electrons impurity atoms and mechanical imperfections in the lattice.

5) The crystals is called semiconductor or semimetal if one or two bands are slightly filled or slightly empty.

6) At temperatures much below both the Debye temperature and the Fermi temperature ,the heat capacity of metals may be written as C = Cel + Cph = gamma*T + beta*T^3.

7) The number of orbitals with the same energy is called degenerate.

8) At absolute zero the chemical potential is equal to Fermi energy.

9) The region which results from intraction of conduction electron waves with the ion cores of the crystals is called Band Gap.

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