PopDistributionsDiatMolLect18ME501F2011

PopDistributionsDiatMolLect18ME501F2011 - Purdue University...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 18: Population Distributions for Diatomic Molecules Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana [email protected] , 765-494-5623 (Phone) October 17, 2011
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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • The nuclear partition function. • Rotational distributions for heteronuclear molecules. • Vibrational distributions. • Electronic distributions. • Rotational distributions for homonuclear molecules.
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Patterned Border Template 3 Purdue University School of Mechanical Engineering The Nuclear Partition Function • Let I A and I B be the spins of the ground states of nuclei A and B (don't have to consider excited nuclear states very often):  ,, 21 oA A oB B nuc o A o B A B gI Zg g I I   • The nuclear partition function is often grouped with the rotational partition function because of the strong influence of nuclear spin on the relative intensities of even and odd J lines for homonuclear molecules, 1 rot nuc A B rot ZZ I I     
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Patterned Border Template 4 Purdue University School of Mechanical Engineering Rotational Distribution for a Heteronuclear Molecule • Boltzmann distribution law is applied separately to each mode: for the translational mode this leads to the Maxwell velocity distribution that will be discussed in detail later. • Rotational distribution: Assume that T >> rot , heteronuclear molecule, electronic level with electronic degeneracy =1. Then:        v v 21 e x p 1 / exp / / rot JJ B lJ lr o t r o t J T gk T N NZ T   • Note that the level population is proportional to (2 J +1). • Determination of the rotational level with the maximum population. Assume that J varies continuously: v max 1 0 22 rot dN T for J dJ 
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Patterned Border Template 5 Purdue University School of Mechanical Engineering Rotational Distribution for the OH Molecule • For OH in the ground electronic state, B e = 18.911 cm -1 , rot = 27.2 K.
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This note was uploaded on 12/26/2011 for the course ME 501 taught by Professor Na during the Fall '10 term at Purdue.

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PopDistributionsDiatMolLect18ME501F2011 - Purdue University...

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