Instant Notes: Analytical Chemistry

In a vacuum, this wave travels at a fundamental constant speed, co

co=2.997 925¥ 108 m s-^1

The wave is characterized in three ways, as shown in Figure 1.

The wavelength, l, is the distance between equivalent points on the wave

train, for example, between two consecutive positive crests, or two points where

the wave increases through the zero value. The wavelength has been expressed

in a variety of units, but these should now all be related to the metre, as shown

in Table 1.

190 Section E – Spectrometric techniques

Table 1. Wavelength units

Name Units

femtometer (fermi) 10 -^15 m=1 fm

micrometer (micron) 10 -^6 m = 1 mm

nanometer 10 -^9 m =1 nm

Older units such as the Ångstrom (Å) are used in earlier work.

1 Å = 10 -^10 m.

The frequency, n, is the number of cycles of radiation passing a point in space

per second. It is expressed as s-^1 , or hertz (Hz).

The above definitions show that the relation between these quantities is:

n=co/l

Sometimes the wavenumber, n

_

, is used where

n

_

=1/l

The wavenumber is frequently given in cm-^1 , especially in infrared spectro-

metry, and it should be noted that 100 m-^1 =1 cm-^1. (Note that if there are 100

per meter, there is 1 every centimeter.)

The energy, e, of the radiation is most important, since it defines the molec-

ular or atomic processes which are involved. For a single photon,

e=hn=hco/l=hcon

_

where h is the Planck constant, 6.62608¥ 10 -^34 J s-^1.

Occasionally, the electron-volt is used as a unit for energy, where

1 eV =1.602¥ 10 -^19 J

Thus, a wavelength of about 5.00 mm is equivalent to a frequency of 5.996¥

1013 Hz, a wavenumber of 2000 cm-^1 , and energy 3.973¥ 10 -^20 J. This corresponds

to molecular vibrational energy. It is sometimes an advantage to consider

1 mole of photons. For the above example the molar energy will be:

NAe=6.022¥ 1023 ¥ 3.973¥ 10 -^20 =23.9 kJ mol-^1

Table 2shows the very wide range of wavelengths and energies that relate to

spectrometric techniques (see Topic A3) and Figure 2relates this to the electro-

magnetic spectrum.

When electromagnetic radiation is directed at an atom or molecule, the atom

or molecule can absorb photons whose energy corresponds exactly to the differ-

ence between two energy levels of the atom or molecule. This gives rise to an