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Absorption/Emission

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Absorption/Emission

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  1. Some of this weeks seminars:Dynamical Studies of the Photodissociation of Ozone: From the Near IR to the VUVFebruary 12 | 4-5 p.m. |  Pitzer Auditorium, 120 Latimer Hall Dr. Reinhard Schinke, Max-Planck-Institut fuer Dynamik und Selbstorganisation, Goettingen, GermanyEngineering Organic-to-Semiconductor HeterojunctionsFebruary 13 | 4-5 p.m. |  Pitzer Auditorium, 120 Latimer Hall Professor Thomas F. Kuech, Dept. of Chemical & Biological Engineering, University of Wisconsin - MadisonUsing Supported Lipid Bilayers as a Separation MatrixFebruary 15 | 4-5 p.m. | 775A Tan HallProfessor Paul Cremer, Dept. of Chemistry, Texas A & M University

  2. Absorption/Emission

  3. Connections between the rates of stimulated and spontaneous emission: Case a) Thermal equilibrium in a cavity W(w), the energy density and A,B the Einstein A and B coefficients which are the rate constants (per molecule), excepting the energy density for the transition probability, Wif. Also N large so we need not consider statistics. E2,N2,g2 A21 B12W(w) B21W(w) E1,N1,g1 At equilibrium dN1/dt = -dN2/dt = 0 = N2A21-N1B12W(w)+N2B21W(w)

  4. Connect A and B to Golden Rule

  5. The two expressions are equal at all T only if: Comparing again to Planck’s Law at l=50mm, 6THz, 200 cm-1 T=300K Longer wavelengths stimulated exceeds spontaneous rate Shorter stimulated emission is slow compared to spontaneous rate

  6. Case b) A light source, Now W is not thermal energy density but the energy density of the light source (assumed to be large enough that we can neglect the thermal field). At the stimulated and spontaneous rates are equal. Consider visible light of frequency 5x1014 Hz, 3x10-19J Intensity obtained by ,multiplying by c is 3x10-6 dw W/m2 dw for an ordinary spectroscopic light source is ~1011 Hz The intensity required to equalize spontaneous and stimulated emission rates is ~105W/m2

  7. Some light sources Footnote: Derivation of relations between A, B, assumed thermal radiation. The relations hold so long as either the radiation field or the molecules are randomly oriented in space—not necessarily for solids interacting with lasers.

  8. E2,N2,g2 N2+N1=N absorption negligible A21 B12W(w) B21W(w) E1,N1,g1 dN1/dt = -dN2/dt = N2A21+ (N2-N1)B12W(w)

  9. Expanding the exponential as 1-(A+2BW)t

  10. Why this behavior? N2/N time

  11. Steady state value N2/N What is the limiting ratio? BW/A 1 4

  12. How does this connect to Beer’s Law? Recall I=I0e-Nsl=I02.30310-eCl g(n) a normalized lineshape function n index of refraction

  13. The square of the transition dipole can be expressed as an integral (over all frequencies) of the absorption cross-section (or molar absorptivity).

  14. What happens when we increase [ ] vs. I? (Discussion)

  15. Breakdown of Beer’s Law. BW/A>>1 Intensity falls off linearly with distance in absorber not exponentially and is independent of I0

  16. Oscillator Strength (CH4.4.3) fif=1; 1 electron allowed transition >1 multiple transitions =0.001-0.01; forbidden transitions

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