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CHEM 515 Spectroscopy

CHEM 515 Spectroscopy. Microwave Spectroscopy II. Moment of Inertia. Moment of inertia ( I ) , also called mass moment of inertia or the angular mass , is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass.

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CHEM 515 Spectroscopy

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  1. CHEM 515Spectroscopy Microwave Spectroscopy II

  2. Moment of Inertia • Moment of inertia (I), also called mass moment of inertia or the angular mass, is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass. • The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis.

  3. Moment of Inertia

  4. Moments of Inertia for a Water Molecule Given: r = 0.958 Å θ = 104.5° mH = 1.00 atomic mass unit (u) mO = 16.00 atomic mass unit (u) Results in: f = 0.7575 Å g = 0.5213 Å h = 0.0652 Å

  5. Classes of Rotating Molecules • Molecules can be classified into five main groups depending on their moments of inertia.

  6. Linear Molecules IC = IB , IA = 0 Linear molecules Other examples: • HCl • CO2 • H–C≡C–H • H–C≡C–C≡C–C≡C–H • LiF

  7. Spherical Top Molecules IC = IB = IA Spherical top Other examples: • CH4 • CCl4 • Generally, molecules with Oh, Td, or Ih point groups are considered spherical top molecules.

  8. Prolate Symmetric Top Molecules IC = IB > IA Prolate symmetric top

  9. Oblate Symmetric Top Molecules IC > IB = IA Oblate symmetric top

  10. Asymmetric Top Molecules IC > IB > IA Asymmetric top Most of the molecules are asymmetric top.

  11. Line Intensities in Rotational Spectra

  12. Line Intensities in Rotational Spectra

  13. Centrifugal Distortion

  14. Splitting Due to Stark Effect

  15. Nuclear Hyperfine Splitting • An atomic nucleus is a collection of protons and neutrons. • These particles are `spin-1/2' particles. They have a spin quantum number of 1/2. The nucleus itself has a total spin angular momentum formed by the coupling of the individual spin angular momenta of its constituent protons and nuclei (nucleons).

  16. Nuclear Hyperfine Splitting

  17. Nuclear Hyperfine Splitting

  18. Symmetric Top Molecules

  19. Energy Levels for Symmetric Top Molecules

  20. Energy Levels for Symmetric Top Molecules

  21. Selection Rules for Symmetric Top Molecules

  22. Rotational Spectra of Symmetric Top Molecules

  23. Rotational Spectra of Symmetric Top Molecules

  24. Asymmetric Rotor Rotational Levels

  25. Asymmetric Rotor Rotational Levels

  26. Asymmetric Rotor Rotational Levels

  27. Selection Rules for Asymmetric Rotor

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