13s_562ln08

13s_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.62 Lecture #13 Supplement: Nuclear Spin and Symmetry Number P 12 Ψ = ± Ψ is required for all pairs of identical particles. + for boson, – for fermion. (Identical means same nucleus, not same chemical environment.) (P 12 ) 2 Ψ = Ψ means that there are only two classes of symmetry functions for each group of identical nuclei. e.g. benzene 6H I i = 1/2 I = 3,1 para: degeneracy 7 + 3 = 10 4, 2, 0 ortho: degeneracy 9 + 5 + 1 = 15 6C I i = 0 only I tot = 0 To construct Ψ with legal permutation symmetry with respect to ψ rot , we need to consider superpositions of bonded networks. e.g. the C 2 symmetry operation permutes pairs of C’s and pairs of H’s. Yet the permutation must be even with respect to C’s. How many bonded networks are there? 6!6! 2·6 We divide by 12 because this is the overcounting due to rotationally related identical
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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13s_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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