Napierian absorption coefficient

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 ... 

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... 

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. 

The physical meaning of the quantities a(A) and K X) can be stated thus the reciprocal of the Napierian coefficient of absorption a(A) corresponds to the thickness of the medium for which the incident intensity is divided by the base of the Napierian logarithm (i.e., e = 2.718281828...), while the reciprocal of the Bunsen-Roscoe coefficient of absorption K X) corresponds to the thickness of the medium for which the incident intensity is divided by ten. In most practical applications the decadic absorption coefficient is used, but the Napierian absorption coefficient is introduced more naturally in theoretical equations. 

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. 

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