Absorption Napierian

Physicists usually prefer to use the Napierian absorption coefficient a(A)... 

Finally, the molecular absorption cross-section capture area of a molecule. Operationally, it can be calculated as the (Napierian) absorption coefficient divided by the number N of molecular entities contained in a unit volume of the absorbing medium along the light path ... 

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... 

First item in a series (for example, the first carbon linked to a carboxyl group). 2. Abbreviation for alpha particle. 3. Symbol for angle of optical rotation. 4. Symbol for degree of dissociation. 5. Symbol for electric polarizability of a molecule. 6. Often with a subscript number (i) the coefficient of [A] in the numerator of the generalized rate expression. 7. Symbol for is proportional to. 8. Symbol for Napierian absorption coefficient. 9. In brackets, symbol for specific optical rotation. 

The absorbance (or optical density) of the films were estimated from the transmittance T using the relation A = -log(T). Here we assumed that all the incident light is either transmitted or absorbed, reflection or scattering being negligible. The Napierian absorption coefficient of the sample was calculated using Lamberts... 

With a representing the absorption cross section in cm per molecule (for the conversion to Ex see Tab. 3-2). To avoid any misinterpretations it is very important to state the origin of the absorption coefficients Ex and ax with respect to their logarithmic base as decadic or as Napierian (for conversions see Tab. 3-2). Many useful conversion factors for changing absorption coefficients from one set of units to another have been summarized by Finlayson-Pitts and Pitts (1986). To get a feeling for the magnitude of these values, several absorption coefficients and absorption cross sections of some molecules of environmental importance are presented in Tab. 3-6. 

Absorption coefficient (decadic-a or Napierian-a) Absorbance divided by the optical pathlength, 1 ... 

Depth of penetration (of light) The inverse of the absorption coefficient. The SI unit is m. If the decadic absorption coefficient, a, is used, the depth of penetration (1/a) is the distance at which the spectral radiant power, Px decreases to one tenth of its incident value, P . If the Napierian absorption coefficient, a, is used, the depth of penetration (1/a = p in this case) is the distance at which the spectral radiant power decreases to 1 /e of its incident value. 

The macroscopic and molecular properties are related by the integral Napierian absorption coefficient... 

The integral Napierian absorption coefficient of the Alh normal vibration is given by... 

The proportionality constant b, which is characteristic of the absorbing medium, is known as the Napierian absorption coefficient, or the Napierian extinction coefficient. 

In this relationship k, is named the Napierian (natural) molar absorption coefficient [1 mol" cm ] of reactant Aj at wavelength of irradiation. In principle the derivation of the kinetic equations becomes easier if exponential functions and Napierian logarithms are involved. For this reason the Napierian units are used first. Division of the relationship above by the volume of the chosen volume element results in... 

In the course of this formal deduction of the amount of light absorbed, the Napierian molar absorption coefficient k is used. Later in the experimental section and during the practical examples using absorbance measurements, e symbolises the decadic (molar) absorption coefficients obtained in calibration experiments using UV/vis spectrometers. 

Derivation of photochemical equations can become easier using the Napierian molar absorption coefficient. This is discussed in detail in Section 5.1.2.2. The result is the photokinetic factor given by... 

Using eq. (1.39), relationships are obtained in the case of Napierian units for the absorption coefficients and the absorbance E at the wavelength of irradiation X. ... 

In formal kinetics the symbols A, B,... are used for the reactants. The symbol E is used to represent absorbance in this book. Napierian units are used in this chapter (see Section 1.4.3). In Chapters 4 and 5 decadic units are used for convenience and the decadic molar absorption coefficient is indicated by B as used in Section 1.4.4. 

In Chapter 3 Napierian units were used for absorption coefficients and absorbance. The reason was a simpler handling of the equations. Since instrumentation reads decadic units, they are used in most equations in this chapter. The decadic molar spectral absorption coefficient e of the compounds (i) varies with wavelength A. For this reason Bouguer-Lambert-Beer s law is restricted to monochromatic radiation. This restriction and the interactions between molecules in concentrated solutions cause two problems in applying the law to quantitative evaluation ... 

In this and the following example k and E describe the absorption coefficients and the absorbances at the wavelength of irradiation as derived in Chapter 3 (Napierian units). For any wavelength of measurement A one finds according to eqs. (3.56) and (3.62)(since = 0)... 

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