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Rotational Spectroscopy

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Published in: Chemistry | Physics
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Rotational Spectroscopy

Akhilesh K / Lucknow

4 years of teaching experience

Qualification: M.Sc (NIT Rourkela - 2019)

Teaches: All Subjects, English, Mathematics, Science, Chemistry, Physics, Algebra, IIT JEE Mains, AIPMT, NEET

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  1. Esp Stationary 3p Upward transition 3s he Emission 38 Bright line Translation z x Rotation z Vibration Dark line Interaction with matter x Rotational Spectroscopy microwave level 5 level 4 level 3 level 2 electrone Energy levels Spectroscopy Electronic Transitions level I Absorption Spectroscopy Degrees of Freedom Vibrational Spectroscopy infrared level 5 level 4 level 3 level 2 level I Emission Spectroscopy
  2. Rotational Spectroscopy
  3. ' The sun produces a full spectrum of electromagnetic radiation Gamma Rays Gamma Rays X-Rays Visible \-.............................................4 k...............................................l Wavelength (cm) Microwaye Radio http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html Visible Infrared X-Rays Ultraviolet Radio, TV Microwaves mw ovens 10 •16 10-14 10 -12 10-10 10 •8 104 (1 cm) 100 (1 meter) 10 2 Electromagnetic Wavelength (meters) http://kr.blog.yahoo.com/bmw26z/2188
  4. Components of Electro Magnetic Radiation
  5. Two Components of EM Radiation ' Electrical field (E): varies in magnitude in a direction perpendicular to the direction of propagation ' Magnetic field (M): at right angle to the electrical field, is propagated in phase with the electrical field Wavelength (X), distance from one wave crest to another Frequency (v), No. of crests passing a fixed point/ given time Amplitude, height of each peak (watts/sq. meter The speed of EM energy c 300,000km/second, c = vi where X and v are inversely related
  6. Interaction of radiation with matter X-rays X-ray Ionization Ionization energy Large number Of available energy states, strongly absorbed. Small number of available states, almost transparent. Photoionization Ultraviolet Visible Infrared X-ray ionization Compton Scattering Longer wavelength X-ray Electron level changes. Molecular vibration Molecular Microwaves rotation and torsion Wavelength ' If there are no available quantized energy levels matching the quantum energy of the incident radiation, then the material will be transparent to that radiation
  7. Fate of molecule? Non-radiative transition: + M M + heat Spontaneous emission: M* M + hv (very fast for large AE) Stimulated emission (opposite to stimulated absorption) These factors contribute to linewidth & to lifetime of excited state.
  8. Molecular Motion and Spectroscopy Study of Interaction of Matter and Light (Photon) Molecular Spectroscopy -5 Information about molecules such as geometry and energy levels are obtained by the interaction of molecules and photons ' Molecular motions: Translation, Rotation, Vibration -5 determines the energy levels for the absorption or emission of photons
  9. Electronic, Vibrational, and Rotational Energy Levels of a Diatomic Molecule Excited electronic state Rotational states Vibrational states Ground electronic state Exercise: Indicate the molecular state in which it is electronically in the ground state, vibrationally in the first excited state, and rotationally in the ground state.
  10. ROTATIONAL SPECTROSCOPY
  11. Microwave interactions Small number of available states, almost transparent. Microwaves rotate molecules Molecular Microwaves rotation and torsion ' Quantum energy of microwave photons (0.00001-0.001 eV) matches the ranges of energies separating quantum states of molecular rotations and torsion ' Note that rotational motion of molecules is quantized, like electronic and vibrational transitions D associated absorption/emission lines ' Absorption of microwave radiation causes heating due to increased molecular rotational activity The electric field of an electromagnetic wave exerts a torque an an electric dipole,
  12. Molecular rotations Potential vibrational levels Vibrational transition (in infrared} curve representing the ground electronic state, Rotational transitions (in microwave} Internuclear separation
  13. Types of Rigid Rotors 'A schematic illustration of the classification of rigid rotors. Linear Spherica Symmetrt rotor Asymmetrt rotor
  14. RIGID ROTOR A diatomic molecule can rotate around a vertical axis. The rotational energy is quantized. 1112 Copyright@ 2008 Pearson Education, Inc.
  15. THE RIGID ROTOR A diatomic molecule may be thought of as two atoms held together with a massless, rigid rod (rigid rotator model). Consider a diatomic molecule with different atoms of mass ml and 1112, whose distance from the center of mass are rl and respectively 1 1.1 2 The moment of inertia of the system about the center of mass is: 2 I = 1711 VI +
  16. The Definition of Moment of Inertia ' In this molecule ' three identical atoms attached to the B atom ' three different but mutually identical atoms attached to the C atom. ' Centre of mass lies on the C 3 axis ' Perpendicular distances are measured from the axis passing through the B and C atoms. 3mArA ma + 3morD
  17. Rotational levels The classical expression for energy of rotation is :ln the harmonic oscillator model, the energy was all potential energy. In the rigid rotor, it' s all kinetic energy: 10 2 h — where L= angularmomentum 21 2 ' where J is the rotational quantum number 2 21 2m h the rotational constant 8 IT2c I
  18. Quantization of Rotational Energy + V(x, y, z)Q/J E Q/' 2 öy2 öz2 87 m Ox cyclic boundary condition: IV(21T + 9) = 1+(9) By solving Schrodinger equation for rotational motion the rotational energy levels are h2j(j + 1) e. 8721 Rotational energy levels in wavenumber (cm-I) —nj(j + 1) Bj(j + 1) 87 cl (B h 81T2cI
  19. Spacing between adjacent rotational levels J and Ae 2B 56B 12B 6B 2B Aej,j-l 14B 6B 2Bj
  20. The Gross Selection Rule for Rotations A rotating polar molecule looks like an oscillating dipole which can stir the electromagnetic field into oscillation. Classical origin of the gross selection rule for rotational transitions.
  21. Rotational Spectroscopy (1) Bohr postulate As = hv = hc/ Selection Rule (2) Rotational energy levels Aj = +1 (absorption) AE = 613/2 Aj = —1 (emission) Aej,j-l AE=2Bh 2Bj Spectrum 2B 8B Energy 30131, 20131, 1213/2 6131, 2131, 10B
  22. Vibrationa/ Motion: Molecular Calisthenics Harmonic oscillator F = -k(r-re) (a) (b) T vib - evib Center of mass (c) vib A molecule vibrates æ50 times during a molecular day (one rotation)
  23. Quantization of Vibrational Energy By solving Schrodinger equation for vibrational motion, Vibrational energy level — hv(v + i)' where v is a vibrational quantum number Zero point energy = ähv, Spacing between adjacent vibrational sates Aev = hv for any v
  24. Parabola (harmonic oscillator) Realistic
  25. 1.0 o.o @ 2003 Thomson-Brooks/Cole 3 a(R-Re) 4 max 5
  26. Selection Rule: Apart from Specific rule- AJ= ±1, Gross rule- the molecule should have a permanent electric dipole moment, g . Thus, homonuclear diatomic molecules do not have a pure rotational spectrum. Heteronuclear diatomic molecules do have rotational spectra Aj — +1 (absorption) ROTATIONAL SPECTRUM AE = 1013/2 AE = 813/2 AE=2Bh 5 4 Rotational energy levels 3 2 1 0 Energy 3013/2 2013/2 1213/2 6131, 2131, o Aj = —1 (emission) Spectrum @ 2003 Thomson-Brooks/Cole 2B 4B 6B 8B 10B
  27. Appearance of rotational spectrum We can calculate the energy corresponding to rotational transitions A E:EJ -EJ Or generally: for final Initial - BJ(J+I) V 2B(J+1) cm I Microwave absorption lines-should appear at : 4B cm 1 Note that the selection rule is AJ : ±1, where + applies to absorption and - to emission.
  28. Relative Intensities of rotation spectral I ines Now we understand the locations (positions) of lines in the microwave spectrum, we can see which lines are strongest. Intensity depen BJ(J+I) s upon two factors:
  29. Intensity depends upon two factors: 1,Greater initial state population gives stronger spectral lines. This population depends upon temperature, T. NJ exp hcv) k: Bj*nann's con 658 x 10 3 J We conclude that the population is smaller for higher J states. 1.52034V hc -1.52034 cmK
  30. 2. Intensity also depends on degeneracy of initial state. (degeneracy = existence of 2 or more energy states having exactly the same energy) Each level J is (2J+1) degenerate population is greater for higher J states. To summarize: Total relative population at energy EJ (2J+1) exp (-EJ / kT) & maximum population occurs at nearest integral J value to • Look at the values of NJ/No in the figure,
  31. max. pop. B = 10cm Plot of population of rotational energy levels versus value of J.

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