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Pune University - Sem - III : Solid State Physics, April 2010 (Old Course)

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Total No. of Questions : 7] P878 [Total No. of Pages : 2 [3722]-31 M. Sc. PHYSICS PHY UT - 701 : Solid State Physics (Old Course) (Sem. - III) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory and solve any four questions from the remaining. 2) Draw neat labelled diagrams wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic table and pocket calculator is allowed. Given : Rest mass of the electron = 9.109 10 31 kg. Charge on the electron = 1.602 10 19 coulomb. Planck s constant = 6.026 10 34 J-s. Boltzmann constant = 1.3805 10 23 J.K 1. Avogadro s number = 6.0225 1026 (kilo mole) 1. Bohr magneton = 9.27 10 24 A-m2. Permeability of free space = 4 10 7 Henry/m. 2 Permittivity of free space = 8.85 10 12 C /N-m2. Q1) Attempt any four of the following : [16] a) Find the energies of the six lowest energy levels of a particle in a cubical box which of the levels are degenerate? b) Draw neat diagrams showing construction of the first two Brillouin sones in a two dimensional square lattice. c) If all the molecular dipoles in a 1.0 cm. radius water drop are pointed in the same direction, calculate the intensity of polarization. Dipole moment of the water molecule is 6 10 30 c-m. d) Calculate the critical current which can flow through a long thin superconducting wire of aluminium of diameter 10 3 m. The critical magnetic field for aluminium is 7.9 103 amp./m. e) A paramagnetic substance has 1028 atoms/m3. The magnetic moment of each atom is 1.8 10 23 amp.m2. Calculate the paramagnetic susceptibility at 300K. f) State Larmor s theorem. P.T.O. Q2) a) Distinguish between reduced zone, extended zone and periodic zone schemes of representing energy bands. [8] b) Define dielectric function of the free electron gas and derive an expression for plasma frequency. [8] Q3) a) State and prove Bloch theorem for the function K for a general potential at general value of K. [8] b) Write a note on ferroelectricity and ferroelectric crystals with reference to Batioz. [8] Q4) a) Derive London equation for superconducting state and obtain an expression for penetration depth. [8] b) Explain the quantum theory of paramagnetism and obtain curie law. Discuss the behaviour of rare earth ions. [8] Q5) a) Describe the assumptions of BCS theory of superconductivity. [8] b) Describe the Weiss molecular theory of ferromagnetism with reference to Curie point. Hence derive Curie-Weiss law. [8] Q6) a) Explain the origin of dimagnetism in a free atom. Derive Langevin s theory and derive an expression for diamagnetic susceptibility. [8] b) Discuss the term Anisotropy energy with reference to magnetisation.[4] c) What is meant by hystersis in magnetic materials? Q7) a) [4] An insulator must have an even number of valence electrons per atom. Comment. [4] b) Explain Meissner effect in superconductivity. [4] c) Discuss the domain structure in ferromagnetic materials. [4] d) Explain how Fermi surface can be constructed in two dimensions. [4] rrrr [3722]-31 -2-

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Additional Info : M.Sc. PHYSICS, PHY UT - 701 : Solid State Physics (Old Course) (Semister - III), Pune University
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