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Beer-Lambert-Law

If a medium is irradiated three major processes may occur: i) absorption, ii) reflection and iii) scattering. Absorption is the transfer of energy from an electromagnetic field to a material or a molecular entity. Reflection describes the change of direction of the electromagnetic radiation caused by a changing refractive index at an interface between two different media. Scattering also causes a change of the direction of the radiation but is caused by localized non-uniformities in a medium (e.g. an atom, particle, drop, etc.). The transmittance T, which is the fraction of radiation received/detected after a particular medium, can be expressed as:beerlamberteq1with f(λ,l) being the absorption factor, which is the fraction of radiation absorbed by the system, ρ(λ,l) being the reflectance, which is the fraction of radiation reflected by the system, and σ(λ,l) being the fraction of light scattered by the system. All these terms of the sum depend on the wavelength and the length/thickness of the irradiated system.

Irradiating a homogeneous medium perpendicular to the surface normal of the medium or vessel (e.g. a cuvette or reactor) leads to the situation, that the terms describing reflection and scattering do not contribute to the transmittance. Hence, the fraction of radiation passing through the medium just depends on the absorption. The absorption process can be described by the BEER-LAMBERT law:

                                         beerlamberteq2 The absorbance A(λ), being the logarithmic fraction of the incident P0 to the transmitted spectral radiant power Pλ, is equal to the product of the molar (decadic) absorption coefficient ε(λ), the concentration of the absorbing species c and the optical path length l. A commonly used unit of ε(λ) is dm mol−3 cm−1 (M−1 cm−1). This correlation holds true for diluted solutions, where interactions between the absorbing species are negligible. This is typically the case if the concentration is kept below approximately c = 0.01 M.

 


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