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Unformatted text preview: Frequency- and Time-Domain Spectroscopy We just showed that you could characterize a system by taking an absorption spectrum. We select a frequency component using a grating or prism, irradiate the sample, and measure how much gets absorbed we just change frequency and repeat. (1) Absorption Spectrum ↔ Frequency domain Vary frequency of driving field. P av ( ω ) Disperse color → measure power absorbed γ ω 0 ω The variables ω and γ characterize the time-dependent behavior of our H.O. So we could also measure these variables if we applied a short driving force and watched the coordinate directly. (2) Watch coordinate ↔ Time domain Q e A −γ t short driving force → watch relaxation/oscillation −γ t F ext = F 0 δ( t ) → Q t ( ) = F e sin Ω t 2 π m Ω This is the basis for time-resolved spectroscopy using short pulses of light to exert an impulse reponse on the system and watch chemical processes happen. Also, all modern NMR instruments work this way, applying a burst of RF radiation to sample in field and watch relax. The information content is essentially the same in either domain. Why use time? 1) All data collected in single observation—faster than collecting one frequency point at a time! 2) Resolving power between peaks is often better. In practice, different methods work better for different spectroscopic or different types of measurements/information. Fourier Transform Relations In fact, there is a formal relationship between the time domain and frequency domain → Fourier transform : Joseph Fourier showed that any periodic function can be expressed as an expansion in cosines + sines....
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.
- Spring '07