TAMU CHEM 327 - PPt5x-327 (41 pages)

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PPt5x-327



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PPt5x-327

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Pages:
41
School:
Texas A&M University
Course:
Chem 327 - Physical Chem I
Physical Chem I Documents

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Chapter 5 MOLECULAR SPECTROSCOPY The Schr dinger equation for H2 r r e r r T H R r E R r R 2 nuc el When the Born Oppenheimer approximation is applied the electronic motion can be separated from the nuclear motion e r r H R R r E R R r 2 el where el el 1 1 h r H r e 2m r r 2 2 el 2 e Ae Be Once el and E R have been determined as a function of R the nuclear motion may be treated r r T E R R E R nuc nuc nuc Transitions in molecules 1 c 1 wavenumber 1 cm 1 Electronic E 5 eV 250 nm 40 000 cm 1 UV visible Vibrational E 0 2 eV 6 2 m 1600 cm 1 Infra red Rotational E 4x10 4 eV 3 mm 3 cm 1 Microwave Schematic diagram showing the relative ordering of electronic vibrational and rotational energy levels v 2 rotational energy levels J 11 10 9 1 v 1 vibrational energy levels v 0 excited electronic energy level v 2 rotational energy levels J 11 10 9 1 v 1 v 0 ground state electronic energy level vibrational energy levels The electromagnetic spectrum 103 wavelength m 10 6 10 3 1 radiowaves microwaves infrared 10 9 ultraviolet x rays visible 12 14 16 18 20 22 24 26 wavenumber 103 cm 1 ROY G BIV Transition rates and selection rules Three general types of transitions stimulated absorption stimulated emission spontaneous emission Radiation field required Stimulated transitions E t r r E t E cos2 t 0 The time dependent potential energy acting on a molecule Is primarily associated with its dipole moment r r r r V r t E r t where is the dipole moment r r e r i i For a transition from state m to state n the transition rate is n m 2 3h 2 mn 2 mn Where mn is the time averaged energy density at the transition frequency and r d mn n m transition dipole moment integral Total transition rates and Einstein coefficients n m The total rate of transition m n is Rmn mnNm NmBmn mn stimulated absorption where B mn 2 3h 2 2 mn The total rate of transition n m is Rnm nmNn NnBnm nm stimulated emission plus the rate of spontaneous emission from m n R nm NnAnm At equilibrium Rmn Rnm R mn which results in



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