spectroscopy-4-Fundamentals of Molecular & Spectroscopy-Banwell
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1 The rotational spectra of diatomic molecules
Transcript of spectroscopy-4-Fundamentals of Molecular & Spectroscopy-Banwell
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The rotational spectra of diatomic molecules
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Key concepts in rotational spectroscopy
Rigid and non-rigid models of molecules Center of mass Moment of inertia Discrete rotational energy levels Spectral lines and their intensities Applications of rotational spectroscopy:
isotope effect and bond length measurement
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Molecular models: simplifying reality
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Type of rotors
• Rigid rotor • Non-rigid rotor
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Center of mass: static view
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Center of mass: dynamic view
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Center of mass of a diatomic molecule: mathematical view
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Moment of inertia
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Moment of inertia of a diatomic molecule: mathematical view
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Rotational energy levels of a rigid rotor from quantum mechanics
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Emission and absorption of electromagnetic waves by a rigid
rotor
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Energy diagram of a rigid rotor
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The rotational spectra of a rigid rotor: selection rules
• Only a molecule with a permanent electric dipole moment may interact with electromagnetic waves
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The microwave spectrum of CO: general features of rotational spectra
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Intensity of spectral lines: the role of temperature on population
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Intensity of spectral lines: the role of quantum degeneracy
• What is degeneracy? • When degeneracy emerges?
Degeneracy emerges when a physical quantity of a system may be changed without affecting the energy of system
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Angular momentum in classical and quantum mechanics
• Classic version • Quantum version
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Quantum degeneracy associated to angular momentum
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Degenerate energy levels of rigid rotor
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Intensity of spectral lines: The final outcome
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Isotope effect: The role of atomic masses
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Non-rigid rotor
• The bond length is not completely constant
• When J grows the bond length also increases
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Energy levels and their spacing in non-rigid rotor
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Comparison of rigid and non-rigid rotors
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What one learns from rotational spectra
• Precise measurement of bond length
• The ratio of isotopes masses
• The amount of non-rigidity of a bond
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Let’s Consider the rotational spectra of
polyatomic molecules in next session
