Isotope Effects
5
molecule is described in terms of the electronic energy plus the translation, rotation, and vibration energies of the molecules. The energies
associated with the mutual interactions of these motions must also be
included. For isotopes of the same element the electronic, translation,
and rotation energies are more or less equal. This leaves molecular
vibrations as the origin of "isotope effects".
Figure 3 shows schematically the energy of a diatomic molecule as a
function of the distance between two atoms. According to the quantum
theory, the molecule cannot assume any energy on the continuous curve
shown in Fig.3, but is restricted to certain discrete energy levels. The
>~
CIJ
C
CIJ
c
CIJ
~
I sotope effect
associated with
zero - poi nt energy
Interatomic distance
Fig. 3. Schematic potential-energy curve for the interaction of two atoms in a stable
molecule or between two molecules in a liquid or solid. (After BIGELEISEN, 1965)
lowest level is not at the minimum of the energy curve, but above it by an
amount of liz hv, where h is Planck's constant and v is the frequency with
which the atoms in the molecule vibrate with respect to one another. The
vibrational frequency of a molecule depends inversely on the masses of
the atoms in the molecule. Therefore, different isotopic species will have
different zero-point energies in molecules with the same chemical formula: The molecule of the heavy isotope will have a lower zero-point
energy than the molecule of the light isotope. This is shown schematically in Fig. 3, where the upper horizontal line (EL) represents the zeropoint energy of the light molecule and the lower line (EH ), that of the
heavy one.
This means that bonds formed by the light isotope are more readily
broken than bonds involving the heavy isotope. Thus, during a chemical
reaction, molecules bearing the light isotope will in general react slightly
more readily than those with the heavy isotope.
5
molecule is described in terms of the electronic energy plus the translation, rotation, and vibration energies of the molecules. The energies
associated with the mutual interactions of these motions must also be
included. For isotopes of the same element the electronic, translation,
and rotation energies are more or less equal. This leaves molecular
vibrations as the origin of "isotope effects".
Figure 3 shows schematically the energy of a diatomic molecule as a
function of the distance between two atoms. According to the quantum
theory, the molecule cannot assume any energy on the continuous curve
shown in Fig.3, but is restricted to certain discrete energy levels. The
>~
CIJ
C
CIJ
c
CIJ
~
I sotope effect
associated with
zero - poi nt energy
Interatomic distance
Fig. 3. Schematic potential-energy curve for the interaction of two atoms in a stable
molecule or between two molecules in a liquid or solid. (After BIGELEISEN, 1965)
lowest level is not at the minimum of the energy curve, but above it by an
amount of liz hv, where h is Planck's constant and v is the frequency with
which the atoms in the molecule vibrate with respect to one another. The
vibrational frequency of a molecule depends inversely on the masses of
the atoms in the molecule. Therefore, different isotopic species will have
different zero-point energies in molecules with the same chemical formula: The molecule of the heavy isotope will have a lower zero-point
energy than the molecule of the light isotope. This is shown schematically in Fig. 3, where the upper horizontal line (EL) represents the zeropoint energy of the light molecule and the lower line (EH ), that of the
heavy one.
This means that bonds formed by the light isotope are more readily
broken than bonds involving the heavy isotope. Thus, during a chemical
reaction, molecules bearing the light isotope will in general react slightly
more readily than those with the heavy isotope.