Geoscience Reference
In-Depth Information
3. Vibrational energy. Because they are subjected to combined attractive and repulsive
forces, the individual atoms of a diatomic molecule, such as H and Cl in HCl, vibrate
around their position at rest. The energy of this movement is the most important
cause of isotopic fractionation. Acoustic waves in solids provide a collective form of
vibrational energy. Vibrating charge pairs can be seen as little antennas. The energy
that these antenna can emit or receive is proportional to the electric dipole of the
pairs.
4. Electronic energy. Electrons in atoms and molecules can rise to energy levels above
their ground state, normally from low-energy to high-energy orbitals by absorption of
light. This phenomenon is, however, of very short duration and involves energies too
large to be of concern in this chapter.
The total energy of a system is the sum of these four components. Vibrational and rota-
tional energy are gained or lost by absorption or emission of photons, i.e. by interaction
of matter with electromagnetic radiation, such as infrared, visible, or ultraviolet light.
In much the same way as “kicks” (shocks) redistribute translational energy among gas
molecules, the electromagnetic field carried by photons kicks the electronic dipole and
magnetic moments. We are going to see that all these kicks must carry discrete amounts of
energy.
Quantum mechanics states that energy is measured by quanta, that we can see as
“grains,” which means that it is distributed over discrete energy levels. These quanta
characterize the spacing between successive energy levels. For the conditions of temper-
ature of interest to us, the translation quanta are much smaller than the rotational quanta,
which themselves are much smaller than vibrational quanta (
Fig. 3.1
). The “classical” ther-
mal energy
RT
(or
kT
for an isolated molecule with
k
being the Boltzmann constant)
represents the equivalent of an enormous number of translational and rotational quanta,
which indicates that the corresponding levels are well populated and can be treated as a
continuum via the methods of classical physics. For reasons that will appear later, they
do not produce temperature-dependent effects. At temperatures of geological interest, both
translational and rotational energies are therefore unimportant for isotope fractionation in
solids and liquids, with rare exceptions such as the CO
3
spinner of carbonate minerals. In
contrast, the more energetic vibrational levels are more scantily populated, which is the
reason for the temperature dependence of isotopic effects, and they therefore will need
special attention.
When two atoms come close to one another, their orbitals can interact with one another to
form a single molecular orbital. The energy of a chemical bond, e.g. O-H for the hydroxyl
does not describe the situation as accurately as true molecular orbitals, one can see the opti-
mum position as resulting from a trade-off between the repulsion of the positively charged
nuclei and the attraction between each nucleus and the orbiting electrons. Energetically,
the most favorable position of the electrons is between the nuclei, which leads to a mutual
attraction between the O and H atoms. These competing effects tend to confine the two
atoms to an optimum distance at the lowest point of a potential “well.” Any movement
changing the length of the bond will be opposed by a counteracting force, which leaves
the system in a perpetual state of vibration. We can represent such a system with two balls
