Servomex NanoTrace DF-760E, Instruction Manual

Page: 147 / 182

Theory of Operation DF-760E 143
10.2.2 Absorption Spectroscopy
The relationship that defines absorption spectroscopy is known as Beer’s Law. Beer’s
Law equates, in rigorous terms, the concentration of any absorbing molecule based on
absorbed light intensity at a particular wavelength, given knowledge of the molecule’s
absorption strength and the “path length” of the sample medium.
Many are familiar with Beer’s Law as it is conventionally used in analytical laboratories:
C b I I T A
     
   

303 . 2 ) / log( ) / 1 log(
0
A 

Absorbance at wavelength

T

Transmittance
I
0

Reference Intensity of Light
I

Measured Intensity of Light after Absorption



Molar Absorptivity at wavelength

b

Path length
C

Molar concentration
In this embodiment, a solution with a broad absorbance band is dialed to a wavelength
within the band, where a substances molar absorptivity is known, and the concentration of
that substance is determined. The substance is usually a liquid solution, placed in a 1 cm
cuvette, and the concentration is expressed in moles/liter.
This same Law can have units reassigned to determine absolute numbers of molecules per
cubic centimeter, useful in gaseous measurements:
N b I I A
   
  

) / ln(
0



Molecular Cross Section (cm
2
/molecule) at wavelength

N

Molecular Density (molecules/cm
3
)
The values

and

are related primarily by Avogadro’s Number. If the molecular density
of an absorbing substance in gas, such as moisture, is known, it can be compared to the
number of molecules in an ideal gas, resulting in a report of parts per billion (PPB). In
gases, this concentration is also known more specifically as parts per billion in volume
PPB
v
.