Napierian units

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... 

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. 

Derivations assume that reactant A absorbs the radiation and starts the photoreaction. Napierian units are used. Intense stirring of the solution is required. The Bodenstein hypothesis is valid for all the photophysical intermediates. 

If the quantum yield does not depend on the intensity of irradiation, direct integration of eq. (3.35) is possible between the limits of concentration a,(f)and a,o = 0)using Napierian units and the symbol to mark the wavelength of irradiation ... 

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)... 

In eq. (5.155) Napierian units are used, although decadic units are given in the table. Seven cases are given. In each the absorbance at the wavelength of irradiation at the end of the reaction amounts to that at the beginning multiplied by some factor. 

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 ... 

NEPER (Np), A dimensionless unit for expressing the ratio of two voltages, two currents, or two power values in a logarithmic manner. The number of nepers is the natural (Napierian) logarithm of the square root of the ratio of the two values being compared. Thus, the neper uses the base of 2.71828 in contrast with the bel (or decibel) which uses the common-logarithm base of 10. One neper equals 8.686 decibels. 

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. 

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 term Bouguer-Lambert law is not familiar to many spectroscopists. The term Beer-Lambert law or merely Beer s law is frequently used in its place. Technically, Beer s law refers to the observation that the contribution of an absorber to the absorbance of a sample is proportional to the concentration of the absorber. The symbol k is referred to by some spectroscopists as the Beer-Lambert absorption coejficient. Because of the possibility of decadic or napierian absorbance and the various units by which concentration can be expressed, several different quantities are all Beer-Lambert absorption coefficients. The term absorptivity is commonly used in equations for decadic absorbance and can include concentration in any rmits. The term linear absorption coefficient is the usual name for the linear napierian absorption coefficient of a pure material. 

---