0000000Timothy F. Jamison

0000000Timothy F. Jamison - 5.33 Lecture Notes: A Classical...

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Unformatted text preview: 5.33 Lecture Notes: A Classical Description of Absorption Why is there light absorption? What is your picture? Quantum mechanical? This quantum mechanical picture may satisfy conservation of energy (when you quantize light and molecular energies), but it has lots of problems and doesnt tell you much. We can learn a lot from classical models of light absorption Classically, light interacts with charges: Molecules are composed of charges particles. Light (an electromagnetic field) exerts a force on these charges. The force exerted on the molecules depends on the strength of the field, the magnitude of the charges, and how far the charges move. (more on this later). A classical model of absorption: We need to describe three things: (1) Light: An oscillating electric (and magnetic) field (2) Matter: Treat as a harmonic oscillator (3) Interactions: Oscillating external force field driving harmonic oscillator Molecule in ground state BEFORE h Molecule in excited state AFTER (No more photon) 1) Light An oscillating electromagnetic field, which oscillates in time and space. E r,t r E cos t k r Polarization vector ( ) = ( ) o ( ) Wavevector defines direction of propagation Amplitude Frequency (rad/sec) To simplify: (1) Propagate along x ; (2) = 0 (for the time being we will drop the polarization) E x,t ( ) = E t ) o cos ( kx 2 = x E E 0 k oscillations in space 1 2 : time = oscillations in time propagating at c Now, we will drop wave vector ( k 0 , since >>x and we consider molecules at x=0) 2 E t ( ) = E cos t I = c E o o 4 2 k = = c c 2.998 10 m /s = 5.33 Lecture Notes: A Classical Model for Spectroscopy Page 2 8 (2) Molecules treat as harmonic oscillator Why should we be able to call molecules harmonic oscillators? i.e., a mass on a spring? Molecules feel a restoring force when pushed from equilibrium. The covalent bond can be thought of as a spring. The equilibrium length is a balance between attractive and repulsive forces. If we push/pull on this bond, there is a restoring force that pushes the system back to equilibrium....
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0000000Timothy F. Jamison - 5.33 Lecture Notes: A Classical...

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