BSc Physics SEM V ATKT May 2018-19 ATKT PHYSICS ATOMIC & MOLECULAR PHYSICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 Attempt any two:
   • (a) For hydrogen atom, write down the differential equation for the radial part, 10 R(r), of the wave function = Using this, show that the magnitude of angular momentum is quantized
   • (b) State Pauli’s exclusion principle. Show that the system of electrons is 10 described by antisymmetric wave functions
   • (c) Discuss Stern-Gerlach experiment, which demonstrates the existence of 10 magnetic moment associated with electron spin 2 Attempt any two:
   • (a) Explain with neat diagram, L-S and J-J coupling, for two electron atoms. 10
   • (b) What is normal Zeeman effect? Discuss the quantum theory of normal 10 Zeeman effect and obtain an expression for Zeeman shift
   • (c) Write expression for average position of electron and explain allowed and forbidden transitions. State selection rules for allowed transitions and discuss whether following transitions are allowed or forbidden
   • (i) Y200 > Wioo Won Attempt any two:
   • (a) Write expression for vibration-rotation energy of a diatomic molecule. 10 Using appropriate selection rules, find the expression for the frequency of spectral lines in P and R branch of the spectrum. Draw energy level Prove that the vibrating diatomic molecule is equivalent to a single particle 10 executing linear harmonic motion. Write quantum expression for its vibrational energy and also draw energy level diagram
   • (c) Draw a labeled schematic diagram of a microwave spectrometer and 10 explain function of its various parts
2. Q4 Attempt any two:
   • (a) Explain pure rotational Raman spectra of a linear diatomic molecule. 10
   • (b) What is Raman effect? With the help of neat diagram, describe the 10 experimental set up of Raman effect
   • (c) Explain the principle of Electron Spin Resonance (ESR). Describe the 10 ESR spectrometer set up with the help of labeled diagram
3. Q5 Attempt any
   • (i) For a d-electron, draw space quantization diagram. Also calculate cosine of angle between each orientation of L and Z-axis Show that the solution Rio(r) = e of radial differential equation of hydrogen atom is normalized (iti) | Define Lande’s ‘g’ factor and find its value *P3/2 state. 05
   • (iv) A spectral line of 4000 A is subjected to 0.5 T of magnetic field. The 05 normal Zeeman shift is observed to be 0.03735 A. Determine the specific charge of an electron (e/m). Given : c = 3 x m/s
   • (v) rotational energy of J = 2 state ineV for HCl molecule having 05 bondlength 2.1 A. Given Reduced mass of HCl = 0.162 x
   • (vi) Calculate vibrational frequency of Hydrogen molecule if its force 05 constant is 480 n/m and mass of hydrogen atom is 1.67 x
   • (vii) of H2 1s 0.07417nm, what would be the position of the first 05 rotational Raman line in the spectrum?
   • (viii). The C NMR spectrum of a compound occurs at 10.705 MHz ina 05 magnetic field of 1 T. What is its resonance frequency if the applied field

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