Absorbance Natural logarithm

The International Union of Pure and Applied Chemistry recommends that the definition should now be based on the ratio of the radiant power of incident radiation (Pq) to the radiant power of transmitted radiation (P). Thus, A = log(Po/P) = log T. In solution, Pq would refer to the radiant power of light transmitted through the reference sample. T is referred to as the transmittance. If natural logarithms are used, the quantity, symbolized by P, is referred to as the Napierian absorbance. Thus, B = ln(Po/P). The definition assumes that light reflection and light scattering are negligible. If not, the appropriate term for log(Po/P) is attenuance. See Beer-Lambert Law Absorption Coefficient Absorption Spectroscopy... 

Taking natural logarithms, the differential optical absorbance (D ) is given by... 

To quantify the measured spectra, a combination of linear and nonlinear least-squares fitting routines are used, in which the measured intensities are fit to those of scaled reference spectra while minimizing the residual absorbance. Taking the natural logarithm of Eq. (E), one obtains... 

Figure 4.12 Cell survival fractions SF(D) as a function of absorbed radiation dose D in Gy (top panel). The bottom panel is the so-called reactivity R(D) given by product of the reciprocal dose D-1 and the negative natural logarithm of SF(D), as the ordinate versus D as the abscissa. Experiment (symbols) the mean clonogenic surviving fractions SF(D) (top panel) and R(D) = — (1/D) ln(SF) (bottom panel) for the Chinese hamster cells grown in culture and irradiated by 50 kV X-ray [73]. Theories solid curve - PLQ (Pads Linear Quadratic) model and dotted curve - LQ model (the straight line a + /SD on the bottom panel).

The absorbed intensity Ia may be related to the incident intensity I0 by means of the well-known Beer-Lambert law. In applying this law, one can use either decadic or natural logarithms, as well as various concentration units and measurements of path length. However, the common usage, and the one we recommend here, is as follows ... 

Note that in analytical chemistry one customary uses the molar absorptivity s(m cm ) instead of the absorption cross-section a (cm ). Also, the absorbance A is often expressed in terms of the decadic rather than the natural logarithm (recall that In x = 2.303 log x). Exploiting the well-known relation between number densities and concentrations (moles/litre), and that a mole incorporates 6.023 x 10 particles (also known as the Avogadro number), one finds for the relation between a and a... 

The absorbance A(X) (formerly called the optical density) is defined as the common logarithm of the same ratio as in the second natural logarithm in Eq. (23.1-14b) ... 

Figure 203 Time-resolved Infrared difference spectra of photoexcited PYP (photoactive yellow protein) measured using a step-scan FT-IR spectrometer [141. Time is indicated on a common logarithmic scale after 50 ns from photoexcitation. AAbsorbance, absorbance difference a.u., absorbance unit. (Source Reprinted by permission from Macmillan Publishers Ltd Nature Structural and Molecular Biology [14]. Copyright 2001.)...

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