Converting the natural logarithm to base 10 logarithm gives:
(14.7)
where the proportionality constant ε, known as the molar absorption
coefficient, or extinction coefficient, is related to κby:
(14.8)
If we define the transmittance Tto be the ratio of the intensities then the
expression becomes:
(14.9)
The absorbance or optical density is defined as:
A=−logT (14.10)
yielding
A=εcl (14.11)
Measuring absorption
Notice that Tmust have a value between zero and one since the amount
of light going through the sample will generally be less than the amount
going through the reference. The absorbance A, therefore, will always be
a positive number. The reason for defining the absorbance in this fashion
is so that Ais directly proportional to the concentration of the molecule
in question. For proteins or nucleic acids, the absorbance provides an
easy method to determine the sample concentration accurately. For this
reason, perhaps the most common of all analytical tools in chemistry is
the ultraviolet–visible absorbance spectrophotometer (Figure 14.4). The
basic idea of the spectrophotometer is that a light source, usually either
an ultraviolet deuterium lamp or a visible tungsten or tungsten/halogen
lamp, is used to create two equal beams of light. A single wavelength of
the light is selected by passing the light through a monochromator, which
uses a dispersive element such as a grating or a prism to spatially separate
the colors of light, followed by a slit to select one of the colors. One of these
beams passes through the sample, while the second beam passes through
logTclT
I
I
=−ε =
0
ε
κ
ln
=
10
log
I
I
cl
0
=−ε
294 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY
