Lecture10

must consider pauli eects of uncertainty principle

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Unformatted text preview: s in the air vibra8ng beyond zero point mo8on? Energy Molecular rotaDons M M Erot n=1 n=0 r L2 ! 2 "(" + 1) = = 2I 2I 2 I ! M red R0 l=4 l=3 l=2 l =1 l=0 R0 ! 2 a0 ! 2 "( " + 1) E rot = 2 8M red a 0 But what happens when the parDcles are idenDcal (diatomics (H2, N2, etc.): Must consider Pauli Effects of uncertainty principle Assume a state with orbital angular momentum maximally aligned to z ­axis z " Recall that Lz = !i! "# Lz! ( R, " ) = Lz! ( R )e i!" M = "!! ( R, " ) ! Exchange of two nuclei means ! " ! + # x ei! (!+" ) = ei!! ei!" For fermions must be asymmetric: e For bosons must be symmetric: i!! = "1 ! must be ODD ei!! = +1 ! must be EVEN M y SelecDon rule for a transiDon ∆l = ±1 not allowed for “idenDcal” diatomics MulD ­atom molecules Symmetrical stretch Scissoring AnD ­symmetrical stretch Wagging Scissoring TwisDng For animaDons go to: hqp://en.wikipedia.org/wiki/Infrared_spectroscopy ApplicaDons of spect...
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This document was uploaded on 02/04/2014.

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