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L3 - Biophysical Chemistry Chemistry 24a Winter Term...

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Biophysical Chemistry Chemistry 24a Winter Term 2009-10 Instructor: Sunney I. Chan Lecture 3 January 8, 2010 The Need for Quantum Mechanics in Molecular Spectroscopy Interaction of Light with Matter What have we learned from classical physics so far? (1) There must be an interaction between the charges in a molecule and the light. A charge or a set of charges that interact with the E-field of the light wave: Force Σ q i |e| E Energy of interaction - Σ q i |e| (r i · E ) = - μ e · E where μ e is the electric dipole moment of the system. dot product] Interaction of Light with Matter (2) Exchange of energy between the molecule and the light wave (absorption and emission of light) can only occur when the frequency of the light wave is equal to the resonance frequency of the interacting charge or charges: ω = ω o (radians/sec) where or ω = 2 πν and ν is the frequency of the light wave in Hz; ω o = 2 πν o is the resonance frequency of the interacting charge(s). In principle, there could be many resonances, corresponding to electrons with different force or “spring” constants (k) in the classical picture. Interaction of Light with Matter Note that ω = ω o (radians/sec) ω = 2 πν , and ν is the frequency of the light wave in Hz; ω o = 2 πν o , and ν o is the resonance frequency of the absorbing molecule. Frequency and wavelength ( λ ) are related by the relationship v λ = c, where c is the speed of light. Speed of light in vacuum = 2.99792 × 10 8 m/s or 3 × 10 10 cm/s Speed of light in a medium of refractive index n = c/ n

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Interaction of Light with Matter (3) Intrinsic dispersion or scattering of the light could occur at any frequency ω , except at resonance ( ω = ω o ) (radians/sec). absorption Dispersion (scattering) Interaction of Light with Matter Since light is an electromagnetic wave , there is also a time-dependent magnetic field associated with the light wave: H(t) = H o * cos ω t at each point in space where there is an E field associated with the light ( E(t) = E o * sin ω t ). The magnetic and electric components H(t ) and E(t) are orthogonal and out of phase. In light of this, it follows then that there can be spectroscopy arising from interaction between a magnetic dipole in a molecule with the H field of light. Torque: μ m x H (t) [ x cross product] Energy of interaction: - μ m · H (t) Example of this kind of spectroscopy: NMR and EPR. Next question : What are the resonances in the absorption or emission of light by a molecule ?
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L3 - Biophysical Chemistry Chemistry 24a Winter Term...

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