Instant Notes: Analytical Chemistry

This has considerable importance in practice. For example:

● In infrared spectrometry, suppose a fundamental vibration occurs at a wave

number 3000 cm-^1 and has anovertone at around 6000 cm-^1. At room

temperature, approximately 300 K, NU/NL=5.55¥ 10 -^7 or about 1 in 2 million

molecules are in the upper level for the fundamental band, and for the first

overtone, NU/NL=3.09¥ 10 -^13 , which is very small. At 1000 K, the ratios are

0.0133 or 1 in 75 and 1.769¥ 10 -^4 , showing that transitions involving the over-

tone levels will be more probable at high temperature and are referred to as

‘hot bands’.

● In proton nuclear magnetic resonance spectrometry, the levels are separated

by about DE =6.6¥ 10 -^26 J. Therefore, at room temperature NU/NL=0.99998,

which indicates that the levels are very nearly equally populated. An NMR

spectrometer will need a very sensitive detection system, and precautions

must be taken to prevent the population of the upper level becoming greater

than that of the lower.

In emission spectrometry, the intensity of the spectral line is related to the

number of emitting species present in the emitting medium and to the proba-

bility of the transition. If there are Noatoms in the ground state, then the number

of excited atoms capable of emission, NE, is given by the Boltzmann distribution

law (see above).

Therefore, the emitted intensity, I,is given by an equation of the form:

I =A.No.exp(-DE/kT)

where A is a constant for a particular transition, incorporating the transition

probability, the degeneracies and any reduction due to other unwanted transi-

tions, such as ionization in atomic spectra.

Under constant temperature and other excitation conditions, this may be

written:

I =k’c

where k’ is a constant and c the concentration.

The constant, k’, may vary in a complex way as cvaries, and calibration, plus

the use of an internal standard (see Topic B4) must be used to obtain reliable

quantitative results.

For absorption spectrometrythe intensity of the incident (exciting) radiation is

reduced when it interacts with the atoms or molecules, raising them to higher

energy levels. In order to interact, the radiation must come into contact with the

species. The extent to which it does this will depend on the concentration of the

active species and on the path length through the sample, as shown in Figure 3.

As the radiation of a particular wavelength passes through the sample, the

intensity decreases exponentially, and Lambert showed that this depended on

the path length, l,while Beer showed that it depended on the concentration, c.

The two dependencies are combined to give the Beer–Lambert absorption

law:

It=Ioexp (-k’ c l)

where Io and Itare the incident and transmitted intensities, respectively.

Converting to the base 10 logarithmic equation:

Beer–Lambert
absorption law

Quantitative
spectrometry

E2 – Atomic and molecular spectrometry 197