Ch1b2010_week2_c

Ch1b2010_week2_c - 1 Molecular Vibrational Spectroscopy H...

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Unformatted text preview: 1 Molecular Vibrational Spectroscopy H vib = E vib Li F The molecule is modeled as two atoms connected together by a spring Potential energy term from Hookes Law (remember high school physics) Kinetic E + Potential E Pot E r (bond length) r e f(x) = potential energy = kx 2 2 New Parameter: The vibrational quantum #: v h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant v = 0,1,2,3, e or e = vibrational frequency (tricky!!) 3 New Parameter: The vibrational quantum #: v h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant v = 0,1,2,3, e or e = vibrational frequency (tricky!!) E( e or e ) = h e ( v +1/2) Vibrational Energy Levels: 4 h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant E( e or e ) = h e ( v +1/2) Vibrational Energy Levels: e = 1/2 (k/ ) 1/2 The vibrational frequency, or energy of vibration, is: k = bond force constant (spring constant from Hookes Law) = reduced mass 5 Molecular Vibrational Spectroscopy H vib = E vib = 1,2,3 e (the vibrational frequency) is determined by the stiffness of the spring 6 Molecular Vibrational Spectroscopy = 1,2,3 Note that v =0 is NOT at the bottom of the potential energy well 7 11 12 14 15 8 Li-F +- - Li - F +- - = dipole moment = charge x distance Molecular Vibrational Spectroscopy Li-F +- - E time Molecules can absorb or emit light at their frequencies of vibration What if molecular vibration doesnt change dipole moment? 1 9 Some Vibrations that we might or might not be able to see using absorption or emission spectroscopy S =C= O S = C = O Symmetric stretch O=C= O O = C = O Symmetric stretch 10 Some Vibrations that we might or might not be able to see using absorption or emission spectroscopy S =C = O S = C= O As ymmetric stretch O =C = O O = C= O As ymmetric stretch 11 Hooke's Law says that the restoring force due to a spring is proportional to the length that the spring is stretched, and acts in the opposite direction. F =-kx , where F is the force, k is the spring constant, and x is the amount of particle displacement. The model for molecular vibrations: Hookes Law Integrate Hookes force Law to get the potential energy 12 Molecular Vibrational Spectroscopy H vib = E vib Li F The molecule is modeled as two atoms connected together by a spring Potential energy term from Hookes Law (remember high school physics) Kinetic E + Potential E Pot E r (bond length) r e f(x) = potential energy = kx 2 13 New Parameter: The vibrational quantum #: v h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant v = 0,1,2,3, e or e = vibrational frequency (tricky!!) 14 New Parameter: The vibrational quantum #: v h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant v = 0,1,2,3, e or e = vibrational frequency (tricky!!) E( e or e ) = h e ( v +1/2) Vibrational Energy Levels: 15 h = 6.626E-34 J s (kg m 2 s-1 ) = Plancks constant E( e or e ) = h e...
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This note was uploaded on 10/27/2010 for the course CH 1b taught by Professor Natelewis during the Winter '09 term at Caltech.

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Ch1b2010_week2_c - 1 Molecular Vibrational Spectroscopy H...

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