intensityI 0 passes through a sample with appropriate transparency and the path length
(thickness)d, the intensityIdrops along the pathway in an exponential manner.
The characteristic absorption parameter for the sample is the extinction coefficienta,
yielding the correlationI=I 0 ead. The ratioT=I/I 0 is calledtransmission.
Biochemical samples usually comprise aqueous solutions, where the substance of
interest is present at a molar concentrationc. Algebraic transformation of the expo-
nential correlation into an expression based on the decadic logarithm yields thelaw of
Beer–Lambert:lgI^0
I¼lg^1
T¼ecd¼A ð 12 : 2 Þwhere [d]¼1cm,[c]¼1 mol dm^3 ,and[e]¼1dm^3 mol^1 cm^1 .eis themolar absorption
coefficient(alsomolar extinction coefficient)(a¼2.303ce).Ais theabsorbance
of the sample, which is displayed on the spectrophotometer.
The Beer–Lambert law is valid for low concentrations only. Higher concentrations
might lead to association of molecules and therefore cause deviations from the ideal
behaviour. Absorbance and extinction coefficients are additive parameters, which
complicates determination of concentrations in samples with more than one
absorbing species. Note that in dispersive samples or suspensions scattering effects
increase the absorbance, since the scattered light is not reaching the detector for read-
out. The absorbance recorded by the spectrophotometer is thus overestimated and
needs to be corrected (Fig. 12.5).Deviations from the Beer–Lambert law
According to the Beer–Lambert law, absorbance is linearly proportional to the concen-
tration of chromophores. This might not be the case any more in samples with high
absorbance. Every spectrophotometer has a certain amount of stray light, which is light
received at the detector but not anticipated inthe spectral band isolated by the mono-
chromator. In order to obtain reasonable signal-to-noise ratios, the intensity of light at the
chosen wavelength (Il) should be 10 times higher than the intensity of the stray light (Istray).
If the stray light gains in intensity, the effects measured at the detector have nothing or little
to do with chromophore concentration. Secondly, molecular events might lead to devi-
ations from the Beer–Lambert law. For instance, chromophores might dimerise at high
concentrations and, as a result, might possess different spectroscopic parameters.Absorption or light scattering – optical density
In some applications, for example measurement of turbidity of cell cultures (determin-
ation of biomass concentration), it is not the absorption but thescatteringof light (see
Section 12.6) that is actually measured with a spectrophotometer. Extremely turbid
samples like bacterial cultures do not absorb the incoming light. Instead, the light is
scattered and thus, the spectrometer will record anapparent absorbance(sometimes
also calledattenuance). In this case, the observed parameter is calledoptical density(OD).
Instruments specifically designed to measure turbid samples arenephelometersor Klett
meters; however, most biochemical laboratories use the general UV/Vis spectrometer
for determination of optical densities of cell cultures.486 Spectroscopic techniques: I Photometric techniques