Answer the following problems

problem 1) Derive Braggs Law for X-ray diffraction in crystals. describe the principle of laueís diffraction method and describe the origin of Laue spots.

problem 2) describe the powder methos for X-rax diffraction.

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

problem 4) Derive the dispersion relation for the frequency of lattice vibrations for linear monoatomec 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) Describe in detail the free electron model in three dimensions.

problem 7) Describe the Fermi function and sketch Fermi distribution function for different temperatures.

problem 8) describe the basic principles of Hall effect in semiconductors. describe an experimental set-up for the measurement of Hall voltage.

problem 9) Show that product of electron and hole concentrations in a semiconductor is constant at a given temperature. How is the energy gap find out from the measurement of electrical conductivity of a semiconductor?

problem 10) prepare detail note on the following:

(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