**EXERCISES**

**1.**Elucidate the difference between the classical free electron theory and quantum free electron theory.**2.**State the main assumption of Sommerfeld’s free electron theory of metals.**3.**Define Fermi energy and Fermi factor. Discuss about the variation of Fermi energy with temperature and energy.**4.**Give an account of Fermi factor and define the same.**5.**What is Fermi factor? Give the theory of calculation of Fermi energy is 0K.**6.**What is physical basis for concept of Fermi energy? What is the assumptions made for Fermi energy at T>0^{0}K? Justify the same.**7.**Discuss the dependence of Fermi factor on temperature.**8.**Discuss the probability of occupation of various energy states by electron at T=0K and T>0, on the basis of Fermi factor.**9.**Give the concept of discrete energy levels for the atomic state and account for the formation of energy bands in the solid state.**10.**Explain band theory of solids.**11.**Describe the concept of energy bands in solids.**12.**What are the essential features of Band theory of solids?**13.**Describe the periodic potential of solid for which Bloch’s theorem is applied.**14.**Explain the motion of free electrons in periodic lattice.**15.**Explain the classification of solids on the basis of energy band theory.**16.**Discuss the motion of electrons in a region of periodic potential. How can one understand electrical conductivity in a solid?**17.**Discuss the essential features of electron energy band structures of solid on the basis of Kronig-Penney model.**18.**Discuss Kronig-Penney model. Using the model show the energy spectrum of electron consisting of a number of allowed energy bands separated by forbidden bands.**19.**Distinguish between conductor, semiconductor and insulator on the basis of band theory of solids.**20.**Obtain an expression for carrier concentration of holes in intrinsic semiconductor.**21.**Obtain an expression for carrier concentration in an N-type semiconductor.**22.**Obtain an expression for carrier concentration of charges in P-type semiconductor.**23.**What are traps? Discuss simple model to show the effect of traps on the photoconductivity. Calculate the gain factor.**24.**What is photoconductivity? State the principle of photoconductive cell. Describe construction, working and use. Show the illumination characteristic and spectral response.**25.**What is photovoltaics? Discuss the energy conversion process in a photovoltaic cell/solar cell.**26.**What is superconductivity? What are the basic aspects of it?**27.**Describe Meissner’s effect. Distinguish between Type I and Type II superconductors. Write various applications of superconductors.**28.**Explain in detail the BCS theory of superconductivity.**29.**Describe and explain following:- Meissner’s effect
- Isotope effect
- BCS Theory
**30.**Prove the Meissner effect contradicts the Maxwell’s equation.

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