Biochemistry - Chemical Reactions in Living Cells, Volume 3 - D. Metzler 1980

Light in Biology
Light Absorption by Matter
Quantitative Aspects of Light Absorption

Light absorption is the foundation of all Photochemistry and the core principle behind absorption spectroscopy [5–10]. Absorption is inherently quantum-mechanical in nature, meaning it occurs exclusively when the energy of a photon, $h\nu$, matches the exact energy difference between two quantum states of the absorbing molecule:

Class="center">E₂ - E₁ = hv. (13-4)

Thus, understanding how light absorption takes place requires a clear grasp of molecular energy levels. A vital condition for absorption is not only that the photon energy equals E₂ — E₁, but also that the molecule's dipole moment changes during the transition between these energy levels. Only under this condition can the electric field of the light wave interact with the molecule. Another constraint governing light absorption relates to the Symmetry of the wavefunctions associated with each energy level. Quantum-mechanical analysis reveals that transitions between certain energy levels are allowed, whereas others are forbidden. Although a detailed Structure/133.html">Discussion of these concepts is beyond The Scope of this book, the reader should appreciate that the underlying quantum-mechanical Selection rules ultimately dictate the Absorption of Light by Matter.

An absorption spectrum is a plot showing how absorption intensity, expressed in various units, varies with wavelength or wavenumber. Sample transmittance is defined as The ratio of the transmitted light intensity (I) to the incident light intensity (I0). Transmittance is typically measured at a single wavelength using monochromatic light. According to the Beer-Lambert law, absorbance (or optical density) is given by

A = lg(I₀/I) = εcl.      (13-5)

Here, l is the optical path length (in cm), c is the concentration (in mol∙l^-1), and ε is the molar extinction coefficient (in l ∙ mol^-1∙ cm^-1). The reader can readily derive equation (13-5) by assuming that the number of photons absorbed within a thin layer of substance of thickness dx is proportional to the number of absorbing molecules in that layer. Integrating with respect to x from 0 to I yields the Beer-Lambert law. Equation (13-5) generally holds exceptionally well for solutions containing a single ionic or molecular species; however, it is strictly valid only for monochromatic light.