DiatomicMoleculesIILect10&11ME501F2011

DiatomicMoleculesIILect10&11ME501F2011 - Purdue...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 12 and 13: Energy Level Structure of Diatomic Molecules Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana Lucht@purdue.edu , 765-494-5623 (Phone) September 19 and 21, 2009
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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics Further consideration of rotational and vibrational energy levels: beyond the rigid rotor and harmonic oscillator. Effects of vibrational anharmonicity. Centrifugal stretching and vibration-rotation coupling. Electronic states in diatomic molecules. Coupling of the rotational angular momentum and the angular momentum of the electrons.
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Patterned Border Template 3 Purdue University School of Mechanical Engineering Further Consideration of Rotational and Vibrational Energy Levels From our previous consideration of the SWE we found that the vibrational and rotational energy levels of a diatomic molecule are given by:    2 2 22 1 2 1 0, 1, 2, 3,. .... 2 1 8 rot J e rot e JJ gJ J r h FJ B B hc c r   rotational constant 11 (v) v vib ee k G hc c     vibrational wavenumber These results were obtained for an idealized molecule: harmonic oscillator rigid rotor vibrational and rotational modes do not interact (couple)
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Patterned Border Template 4 Purdue University School of Mechanical Engineering Vibrational Anharmonicity: The Morse Potential Actually we must consider a number of effects to accurately calculate the energy level structure of diatomic molecules: Vibrational Anharmonicity: The potential function is approximately harmonic only for the lowest vibrational levels, and is more accurately described by a Morse potential: 2 2 e 11 (v) v v 22 4 D e ee e e e Gx x      where D e is the electronic dissociation energy (cm -1 ). From the SWE solution
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DiatomicMoleculesIILect10&11ME501F2011 - Purdue...

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