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Pune University - Sem - III : Solid State Physics, April 2010

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Total No. of Questions : 7] P888 [Total No. of Pages : 2 [3722]-301 M. Sc. PHYSICS PHY UTN - 701 : Solid State Physics (New Course) (Sem. - III) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory. Attempt 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 tables and pocket calculator is allowed. Given : Rest mass of electron Charge of electron Planck s constant Boltzmann constant Avogadro s number Bohr Magneton Permeability of free space Permittivity of free space = = = = = = = = 9.109 10 31 kg. 1.6021 10 19 C. 6.626 10 34 J-S. 1.3805 10 23 JK 1. 6.0225 1026 (Kilomole) 1. 9.27 10 24 A-m2. 4 10 7 Henry/m. 2 8.85 10 12 C /N-m2. Q1) Attempt any four of the following : [16] a) Show that for Kronig-Penny model with P<<1, the energy of the lowest !2 p . ma2 Electrical resistivity of Cu at R.T. is 1.6 10 8 m. If WiedemannFranz law applies to this material, find the electronic contribution of thermal conductivity of Cu at 27 C. For a simple square lattice, calculate K.E. of free electron at the corner and at the mid point of the side face of the 1st Brillouin zone. How are these two values related? A superconducting material has a critical temperature of 3.7 K in zero magnetic field and a critical field of 0.0306 Tesla at zero K. Find the critical field. A paramagnetic material has 1028 atoms/m3. The magnetic moment of each atom is 1.8 10 23 A-m2. Calculate the paramagnetic susceptibility at 300 K. band at K = 0 is E = b) c) d) e) P.T.O. f) The magnetic field strength in Cu is 106A/m. If the magnetic susceptibility of Cu is (0.8 10 5), calculate magnetization and flux density. Q2) a) Derive an expression for energy of free electron in 1-dimensional linear solid of length L. Define Fermi energy. [8] b) Q3) a) b) Q4) a) b) Q5) a) b) Q6) a) b) c) State Bloch function k(x) and prove it for degenerate k(x). [8] With the help of diagrams explain the concept of reduced, extended and periodic zone schemes used for the representation of energy bands. [8] For an atom placed at general lattice site, derive an expression for local electric field Elocal. Explain each term in the expression. [8] Give an account of Weiss theory of ferromagnetism and show from the plot of Langevin s function, spontaneous magnetization exists below the Curie temperature and vanishes above the Curie temperature. [8] Derive London equation for superconducting state and obtain an expression for the penetration depth. [8] Explain Antiferromagnetism with reference to the Neel temperature and [8] susceptibility. Hence describe ferrimagnetism. Describe the assumptions of BCS theory of superconductivity. [8] Discuss the origin of diamagnetism in a free atom. Obtain Langevin s diamagnetism equation for the diamagnetic susceptibility. [8] Describe Josephson superconducting tunneling. Distinguish between type - I and type - II superconductors. [4] [4] Q7) a) b) Explain the concept of hole based on band structure of solid. [4] Write a note on Fermi-Dirac statistics. Explain it s temperature dependence with the help of neat diagram. [4] c) Calculate the critical current which can flow through a long thin superconducting wire of Al of diameter 1 mm. The critical magnetic field for Al is 8 103A/m. [4] d) Describe the term Bloch wall with reference to magnetism. rrrr [3722]-301 -2- [4]

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Additional Info : M.Sc. PHYSICS, PHY UTN -701 : Solid State Physics (New Course) (2008 Pattern) (Semister - III), Pune University
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