Extinction spectrum, normalized

The normalized light extinction spectrum is identical to the photoacoustic spectrum shown in Figure 1. At 600.Onm the extinction of the laser radiation was 2% for the 9.5cm spectrophone cavity optical path. Thus, from the Beer-Lambert Law,... 

Thus, E is defined as the product of the energy transfer rate constant, ku and the fluorescence lifetime, xDA, of the donor experiencing quenching by the acceptor. The other quantities in Eq. (12.1) are the DA separation, rDA the DA overlap integral, / the refractive index of the transfer medium, n the orientation factor, k2 the normalized (to unit area) donor emission spectrum, (2) the acceptor extinction coefficient, eA(k) and the unperturbed donor quantum yield, QD. 

It is difficult to measure the oscillator strengths of molecules embedded in a matrix. Despite this, good values of can be determined as a function of the temperature. A procedure we have used to extract the information from excitation spectra was to set the maximum of the excitation spectrum measured at room temperature equal to the extinction coefficient at the absorption maximum in solution. The integrals of the excitation spectra were then normalized to the integral of the corresponding spectmm at room temperature, which is reasonable because the oscillator strength / of a transition n <— m does not depend on the temperature. 

The spectra Fo(v) and Ca(v) are represented on the wavenumber scale and the fluorescence spectrum (F(v)) of the donor is normalized on this scale n is the refractive index, e iv) is the molar decadic extinction coefficient of the acceptor and To is the radiative lifetime (s) and R(nm) is the D-A center to center distant. For very strong coupling the rate is given by... 

Gaussian curves (normal distribution functions) can sometimes be used to describe the shape of the overall envelope of the many vibrationally induced subbands that make up one electronic absorption band, e.g., for the absorption spectrum of the copper-containing blue protein of Pseudomonas (Fig. 23-8) Gaussian bands are appropriate. They permit resolution of the spectrum into components representing individual electronic transitions. Each transition is described by a peak position, height (molar extinction coefficient), and width (as measured at the halfheight, in cm-1). However, most absorption bands of organic compounds are not symmetric but are skewed... 

The theoretical light curve is shown in Pig. 1a together with the observed one (van Genderen A.M., The P.S., 1985, Space Sci. Rev., 39, 313). The theoretical curve properly reproduces the dimming timescale and the depth of the observed curve. Theoretical spectrum shown in Pig. 1b displays discrepancies with observations in short waves. The deficit of optical radiation can be explained only by non-uniformity of the dust envelope which increases the contribution of scattering. The slope of far infrared spectrum is due to the adopted extinction tables. Angular distribution of monochromatic brightness (normalized, in arbitrary units) is shown in Pig. 1d. 

The ir ir transition in the UV spectrum of trans-stilbene (frans-C6H5CH=CHC6H5) appears at 295 nm compared with 283 nm for the cis stereoisomer. The extinction coefficient emax is approximately twice as great for trans-stilbene as for c/.s-stilbene. Both facts are normally interpreted in terms of more effective conjugation of the it electron system in trans-stilbene. Construct a molecular model of each stereoisomer, and identify the reason for the decreased effectiveness of conjugation in cw-stilbene. 

Figure 3-21 Comparison of TCNQ - electronic absorption spectrum and resonance Raman excitation profiles, (a) Electronic absorption spectrum from 15,000 to 17,850 cm-1. The extinction coefficient, e, scale is normalized with respect to e at 663.0nm (15,083cm-1) = 3.0 x 103M-Icm-1. (b) Superposition of the v2 (2,192cm-1). v4 (1,389cm-1), v5 (1,195cm-1) and V9 (336 cm-1) excitation profiles. The relative intensity scale has been scaled to 0.00 to lO.Ofor all four spectra. (Reproduced with permission from Ref. 76. Copyright 1976 American Chemical Society.)...

Since the senses are sharpened by prior expectation, we could detect by eye a slight reddish-yellow coloration in concentrated solutions of the enzyme. On spectrophotometric examination a gradually ascending, unstructured spectrum was seen which rose from the red into the ultraviolet region where interference from the normal protein spectrum of the concentrated enzyme became serious. The molar extinction coefficient at 400 nm for lipoxygenase-1 is approximately 300 and varies with the age and quality of the preparation. 

For most materials the reflected energy is only 5-10%, but in regions of strong absorptions the reflected intensity is greater. The data obtained appear different from normal tra(nsmission spectra, as derivative-iike bands result from the superposition of the normal extinction coefficient spectrum with the refractive index dispersion (based upon the Fresnel relationships from physics). However, the reflectance spectrum can be corrected by using the Kramers-Kronig (K-K) transformation. The corrected spectrum appears similar to the familiar transmission spectrum. 

Steady-State Spectral Convolution. The steady state absorption and emission spectra of dilute dye samples can be measured using standard spectroscopic techniques. Once the extinction coefficient, e( ), and the normalized luminescence spectrum, f(v), are known for a particular dye, the self—absorption probability r over a pathlength L in the sample containing the dye at a concentration C is given by... 

A neutron soure is used to begin the first stage or cycle of any calculation in normal use, the source neutrons are chosen at random from the fission spectrum. In other applications, a source of specified spectrum and angular distribution may be used to start every stage or in some cases the first stage or any stage which becomes extinct. 

The Forster radius is calculated via Eq. (6.2), where is a parameter that depends on the relative orientation of the dipoles and gains a value between 0 and 4 (for two randomly oriented dipoles the value of is 2/3). corresponds to the luminescence quantum yield of the donor fluorophore, n is the refractive index of the medium, and J(k) represents the overlap integral that provides a quantitative meastue for the donor-acceptor spectral overlap (Figure 6.1). The overlap integral is calculated by Eq. (6.3), where Ea(X) is the extinction coefficient of the acceptor and Fd(X) is the normalized emission spectrum. 

Fa(X) is dimensionless. If Ex(X)is expressed in units of cm and X is in nanometerf, then y(X) is in units of cm nIn If X is in centimeters, then2(X) is in units of ilf cm. In calculating 2(X), one should use the corrected emission spectrum with its area normalized to unity (Eq. [13.3], mi e) or normalize the calculated value of 7(X) by the area (. [13.3], tight). The overlap integral has been defined in several ways, each with different units. In our experience, we find that it is easy to get confused so we recommend the units of nanometers or centimeters for the wavelength and units of JIT cm for the extinction coefficient. 

Here v is the wave number, e (v) the molar decadic extinction coefficient of the acceptor and (v) the spectrum of the donor emission (fluorescence or phosphorescence) measured in quanta per wave-number interval and normalized to unity on the same scale. N is the number of molecules per millimole, n the refractive index of the surrounding medium and the intrinsic life time of the excited donor state, k is a numerical factor representing the orientation dependence of dipole-dipole interaction. Its average is /2/3 = 0.816 for fast Brownian rotation of both molecules and 0.690 for random but rigid orientations . 

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