problem 1: Illustrate co-ordination number? Find out the number of nearest neighbors and the nearest neighbor distance for monoatomic sc, bcc and fcc structures. Illustrate that the atomic packing factors for fcc and hcp metals are similar.

problem 2:

a) Derive Bragg’s Law for X-ray diffraction in crystals. describe the principle of Laue’s diffraction method and describe the origin of Laue spots.

b) describe the powder method for X-ray diffraction

problem 3: Describe with appropriate illustrations the ionic, covalent, metallic and molecular binding in solids.

problem 4: Derive the dispersion relation for the frequency of lattice vibrations for linear monoatomic chain. Describe the long wavelength limit.

problem 5: describe the Einstein model of lattice heat capacity. Describe the successes and failures of this model.

problem 6:

a) Describe in detail the free electron model in three dimensions.

b) Describe the Fermi function and sketch Fermi distribution function for various temperatures.

problem 7: Show that the product of electron and hole concentrations in a semi-conductor is constant at a given temperature. How is the energy gap determined from the measurement of electrical conductivity of a semiconductor?

problem 8: prepare note on any two of the given:

a) Structure of diamond and co-ordinates of the atoms in the structure.
b) Experimental determination of elastic constants of solids.
c) Motion of electrons in a periodic potential well.
d) Injection Laser.