Page 325 - Instant notes

Practical aspects of spectroscopy 311

gaseous samples is often longer than for liquid samples because the concentration is
usually lower. Gaseous samples are essential for rotational (microwave) spectroscopy in
order that the molecules can rotate freely. For vibrational (infrared) spectroscopy, liquid
or solid samples are often ground to a paste with ‘Nujol’, a hydrocarbon oil, and held
between sodium chloride or potassium bromide windows which are transparent to
−1
−1
frequencies of 700 cm and 400 cm , respectively. The path length in any form of
absorption spectroscopy can be increased by reflecting the incident beam multiple times
through the sample using mirrors at each end of the sample cavity.

Intensity of spectral lines

Three principal factors influence the intensity of a spectral transition:
(i) The transition probability. This property is determined by the nature of the initial
and final quantum states of the molecule. Although detailed calculation of absolute
transition probabilities is often complex, it is usually possible to derive general
selection rules (see Topic I1) that distinguish whether a transition probability is zero
(forbidden) or non-zero (allowed). The magnitude of a transition probability may be
determined experimentally from absorption spectroscopy by application of the Beer-
Lambert law.
(ii) The concentration of the initial state. The greater the concentration of molecules in
the initial energy level of a transition, the more intense the spectral transition.
(iii) The path length of the sample. For absorption transitions, the more sample the beam
of radiation traverses, the more energy will be absorbed from it.

Beer-Lambert law

The Beer-Lambert law states that the intensity of radiation absorbed by a sample is
proportional to the intensity of the incident radiation, I 0, the concentration of the
absorbing species, [X], and the path length of the radiation through the sample, l.
Mathematically, the observation can be written in terms of the decrease in intensity, −dI,
that occurs for an increase in path length dx:
−dI=σI[X]dx

where σ is the constant of proportionality, which depends on the identity of the absorbing
species and the frequency of the incident radiation. Rearranging the expression and
integrating over the full path length (from 0 to l) along which absorbance occurs gives: