Chemistry, Third edition

20 · LIGHT AND SPECTROSCOPY

In ‘whole body NMR imaging systems’, the patient lies inside a tube with the main

magnetic field lying along the longitudinal axis of the body, with the radio field acting

upwards. Smaller magnetic fields are used to select a ‘slice’ of body for examination.

Such instruments are able to produce ‘pictures’ of the chemical compositions of slices

of human tissue, (including organs), with different chemical compositions being

highlighted in different shades or colours. The patient is not harmed by the scan.

Changes in the composition of tissue are often valuable clinical indicators of a medical

condition, and scanners are therefore used in the diagnosis of a range of illnesses.

Beer–Lambert law

Beer–Lambert equation

The relationship between the absorbanceof a sample at a wavelength , symbolized

A, and the concentration of absorber c, is known as the Beer–Lambert law and is

summarized by the equation

A=!cb

where!(read as ‘epilson at wavelength lambda’) is a constant for the absorbing

substance known as the molar absorption coefficientof the substance at wavelength

, and bis the thickness of the sample (the cell pathlength).

This equation applies at any particular wavelength, and (practical considerations

aside) works just as well with ultraviolet, visible or infrared light.

The Beer–Lambert equation shows that if the concentration of absorberdoubles,

theabsorbanceof the solution also doubles. The fact that the absorbance is also pro-

portional to cell pathlength can be useful. If the absorbance of a solution or gas is low

because the concentration of absorber is low, this may be compensated for by an

increase in the cell pathlength. For example, the analysis of trace gases in car exhausts

by infrared spectroscopy is often accomplished using a cell with a pathlength of 10 m,

giving 100 times the absorbance of a standard 10 cm gas cell.

More about!

●If the units of care mol m–3and the units of bare metres then the units of !are

mol–1m^2.

●Perhaps the easiest way to look upon is to think of it as simply the absorbance of

the sample when the concentration of the absorber is 1 mol m–3and when the

pathlength is 1 m. The bigger the value of !, the more intenseis the absorption of

the compound at that wavelength.

●If an absorbing compound chemically reacts in any way (e.g. it dissociates or asso-

ciates by forming hydrogen bonds) !changes too. Even changes of solvent may

alter!.

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