Beer's Law
When light shines on matter, it may be transmitted (as with a glass of water), refracted and scattered (as with dust particles in the air at sunset), reflected (as with the chrome trim of an automobile), or absorbed (as with exposed skin at the beach).
The light which we can see, known as visible light, is made up of a continuum of different wavelengths of electromagnetic radiation. Each wavelength in this range of wavelengths, or spectrum, which makes up visible light, has its own associated color, ranging from red to violet. Also, the visible spectrum of light is only one part of a larger continuum of electromagnetic radiation. These wavelengths that are not visible to the human eye range from radio waves at one extreme to x rays at the other.
The nature of visible light and its properties, including how light interacts with matter, has remained the subject of study and speculation by scientists from the very early stages of the development of scientific thought into the twentieth century. The works of Plato (427-347B.C.) and Aristotle (384-322B.C.) formed the basis for much of the speculation which preceded the Scientific Revolution (c.1550-1700). Isaac Newton (1642-1727) laid the groundwork for the modern scientific consideration of the properties of light, and Albert Einstein applied quantum ideas to the properties of electromagnetic radiation.
Among the phenomena that scientists sought to explain was the fact that the intensity of light was diminished as it passed through substances, including chemical solutions. In 1729, P. Bouguer (1698-1758), was the first to state the law of absorption: the fraction of light absorbed by a particular material (i.e., the decrease in the intensity of the light beam as it passes through the material) is directly proportional to the thickness of the material. The proportionality constant is called the absorption coefficient or the extinction coefficient. For instance, if the intensity of light is 1/4 as strong after passing through a 5-inch thickness of an aqueous solution of a dye, it will be diminished to 1/2 its original intensity upon passing through a 10-inch sample. The absorption coefficient in this case is 0.05.
As sometimes happens in the history of science, Bouguer's discovery did not make a significant impact and was forgotten. Sometime later, a better known scientist, J. H. Lambert (1728-1777), independently rediscovered and published this law of absorption. Although Bouguer had priority in the discovery, confusion remains, and the law is known both as the Bouguer Law and the Lambert Law.
As additional observations and more accurate measurements were made, it was noticed that the amount of light absorbed by solutions also depends on other factors. In 1852, J. Beer announced a more complete law of absorption which is known variously as Beers law, the Lambert-Beer law, and the Bouguer-Beer law. Given the history of the discoveries and the rules of scientific priority, the law should carry the name Bouguer-Beer.
Beer observed that, in addition to the effect of the thickness of the sample, the amount of radiation absorbed by a solution is proportional to the concentration of the dissolved substance which is absorbing the radiation. Written mathematically, the Bouguer-Beer law (Beer's law) is: log (P0/P)=ebc, where P0 is the power of the incoming radiation, P is the power of the radiation after passing through the sample, e is the extinction coefficient (or absorption coefficient), b is the length of the radiation path through the solution, and c is the concentration of the absorbing material in solution.
This law has formed the basis for the development of quantitative spectroscopy, particularly as applied to analytical chemistry, where it provides, for instance, a method of determining concentrations without having to destroy a portion of the sample.
In addition to thickness and concentration, the amount of radiation absorbed by a sample depends on the chemical identity of the sample and on the wavelength of the radiation. The determination of the wavelengths absorbed by a particular molecule and the relationship to the energy levels in atoms and molecules is the basis of the field of spectroscopy, on which much of the understanding of the nature of atoms and molecules and their interactions is based. Spectroscopy owes much of its basic quantitative framework to the pioneering work of Bouguer, Lambert, and Beer.
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