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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.
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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
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Classes of Rotating Molecules
• Molecules can be classified into five main groups depending on their moments of inertia.
1. IC = IB , IA = 0 Linear molecules
2. IC = IB = IA Spherical top
3. IC = IB > IA Prolate symmetric top
4. IC > IB = IA Oblate symmetric top
5. IC > IB > IA Asymmetric top
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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
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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.
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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).