Lecture10

x 1 4 m 1 2 2 n x h n e n 2

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Unformatted text preview: !" 2( % 1 n 2 n! m" x ! H n (*)e + *2 /2 !E = !" Energies are quanDzed and equally spaced SoluDons m" != x ! 1/ 4 m" ' 1 $ + *2 /2 !n (x) = & H n (*)e ) n % #! ( 2 n! 1' $ En = & n + ) !" 2( % n=0 Note for n=0, there is a finite energy called the zero ­point energy. Corresponds to quantum fluctuaDons resulDng from uncertainty principle. n=1 n=50 SelecDon rules AbsorpDon of light dictated by “dipole transiDon matrix element” (we’ll show this later when we talk about Dme dependent Shrodinger) # $ "# !* x! m dx = 0 n unless n = m ± 1 V(x) ! 1$ & E 2 = #2 + &!' # # & 2& " % ! 1$ & E1 = #1 + &!' # # 2& & " % 1 E 0 = !! 2 x EsDmate of ΔEvib V(R) m m Z1Z 2 e2 V ( R) ! 4"!0 R Screened nuclei: Z’s ~ 1 d 2V 2 e2 k= 2 = dR 4"!0 R 3 What is k? … ΔE ΔE ΔE M red R ! 2 a0 k = 390 J/m^2 M1M 2 = M1 + M 2 != k M red k !E vib = !" = ! M red The larger the molecule, the lower the frequency of vibraDon. At room temperature, are the molecule...
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This document was uploaded on 02/04/2014.

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