BSc Mathematics SEM VI 2016 17 2016-17 Real & Complex Analysis Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2). Figures to the right indicate full marks

1. Q1 Attempt any three of the following:
   • (A) Derive an expression for wave of P-branch and R-branch lines in a vibrational 5 rotational spectrum of a diatomic molecule
   • (B) The equilibrium internuclear distance in the molecule of HBr is 142.0 pm. Calculate 5 the frequency separation between successive lines in pure rotational spectrum in
   • (C) Calculate the number of modes of vibration in the molecule of CO, using appropriate 5 expression, draw them. Giving reason, predict which modes are IR active and which one/s are Raman active
   • (D) The vibrational frequency of CO molecule is 2.51x10" Assuming vibrations 5 to be harmonic, Calculate (i) vibrational frequency for the molecule in (ii) the force constant of the bond
   • (E) Derive the expression for moment of inertia of a diatomic molecule with m, and m, separated by internuclear distance 'r' @) Answer the following:
   • (a) Define dipole moment. 1
   • (b) molecules have zero dipole moment where as others the geometry of BF, and NH, on basis of dipole moment. 2 The overvoltage of hy
   • (D) Answer the
   • (p) Heisenberg's uncertainty Differentiate between matter waves and lect The velocity of an electron in mot is
   • (ii) The wavelength of the matter wé
   • (F) State the expression for time independent of mass 'm' moving in three and he t
2. Q3 Answer any three of the following:
   • (A) Describe with the help of neat labelled diagram, the fast reactions. Give two examples of fast reactions ? (B) Explain the method of electrolysis of water to produc e hy
   • (C) Explain the low resolution NMR spectrum of thanol ar de
   • (D) (a) State the expression for collision frequency of a bi and identify the terms
   • (b) any three drawbacks of collision theor, y of react
   • (E) Explain the principle, construction and working of s licon sol
   • (F) Answer the with respect to NMR
   • (b) What is meant by spin-lattice relaxation?
3. Q4 Answer any three of the following:
   • (A) What are tracers? Explain the use of tracer in studying help of a suitable example
   • (B) What is meant by nuclear transmutation and artificial radioactivit y? Dif fer between the two
   • (C) Explain the use of moderator, coolant, reflector, fuel and control rods in a nu
   • (D) Explain the use of phosphors and 5 used to detect and me Working of photomultiplier tube in scintillation ‘he half-life of ig 7 Tadioactivity, - 5 life 24.75 hour. Find the wei its daughter element is with half Find the Q Value and thr ght of in equilibrium with one 5 eshold energy of the following reaction
   • (A) State True False for the following statements Rule of mutual exclusion is applicable to linear molecule with centre of symmetry ne energy difference between any two successive vibrational energy levels is constant Dipole moment is a scalar quantity (d} In-plane bending vibrations are classified as rocking and. wagging
   • (A) Choose the correct answer:
   • (p) For stokes line in Raman spectra (i) (ii) A,
   • (q) For pure rotational spectra
   • (i) 2 (ii) Ay =B
   • (r) The vibrational degree of freedom for non-linear molecule of H,0
   • (s) Rotational spectra is observed
   • (B) State true or false for the following statements
   • (a) The phenomenon like Black body radiation is explained by taking into account the wave nature of light
   • (b) The mathematical expression of Tafel's equation is N= a - b
   • (c) The de Broglie relation shows that the wavelength is directly proportional to the momentum of a particle Electroplating reduces corrosion of metal Choose the correct erator Hamiltonian operator is
   • (q) If the operator operates ont
   • (r) The deposition potential is given by
   • (s) Hydrogen overvoltage is also State true of false for the following statements. 43
   • (a) According to collision theory of reaction rates, the rate of reaction is prope to the total number of collisions per cm? per second
   • (b) A fuel cell is a device that combines hydrogen and carbon-di-oxide to electricity and water
   • (c) In NMR spectroscopy, resonance refers to equal magnitude of ‘absorbed and
   • (d) FeS, is used as a cathode in lithium - ion
   • (C) Choose the correct answer
   • (p) The most likely alternative to fossil fuel for clean energy in future
   • (q) The nuclear spin of
   • (i) zero (iii)
   • (r) At low pressure many reactions are
   • (s) A semiconductor with excess holes is called
   • (ii) n-type
   • (D) State true or false for the following statements Threshold energy for nuclear reactions is calculated for exoergic reactions,
   • (b) Energised projectiles are used to induce artificial radioactivity
   • (D) Choose the correct OR
   • (p) The examples of f Gi). material is i
   • (q) (i) ayy by
   • (iii) and pressure Ty s time as compared to chemical equilibrium

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