Page 41 - Modern physical chemistry

30 Structure in Molecules and Atoms

When the two atoms are the same, the scattering factors are equal,
Al = A2 = Ao,

and we obtain

2.5 Electron Diffraction Molecular Parameters
When a monoenergetic beam of electrons is diffracted by randomly oriented mole-
cules, a diffraction pattern in which the intensity varies only with deflection angle () is
produced. For a given screen position, maxima and minima in the pattern can be located
and the corresponding ()'s calculated. The wavevector k can be determined from the accel-
erating potential. Then the interatomic distances r jk can be varied consistent with the
molecule's geometry until the Wier! equation fits the data.
As an approximation, one may consider scattering factor Aj to be proportional to the
number af electrons Zj in the jth atom. Hydrogen atoms may be ignored because of their
small scattering power.
Each independent bond distance is a separate parameter. The bond a.'1gles are related
to these by geometric considerations. Good results are obtained only for the simpler mol-
ecules, those with only a few independent parameters.
Representative results appear in table 2.1.

2.6 Intensity in a Beam
Properties of molecules and atoms can be induced from absorption measurements,
from how the intensity of a beam diminishes as it passes through the material under
study. See figure 2.4. But what is intensity and how can it be measured?
Intensity I may be defined as ( a) the number of particles with the chosen properties
passing by a point per unit cross section per unit time, or (b) the kinetic energy of the
pertinent kind of radiation passing by a point per unit cross section per unit time, or
(c) a number proportional to either of these.
A traveling particle with a rest mass will interact with electrons, ions, or molecules
along its path. A homogeneous beam of such particles will produce excitations propor-
tional to the intensity and to the time of exposure.
With electromagnetic radiation, each frequency v propagates independently. Fur-
thermore, this component interacts with matter as if it were composed of particles
(photons) with the energy
E = hv = tim. [2.35]

TABLE 2.1 Equilibrium Electron Diffraction Parameters

Molecule Interatomic Distances, A Bond Angles

CO 2 C-O 1.16 O-C-O 180.00°
S02 8-0 1.43 O-S-O 119.3°
CC14 C-Cl 2.89 CI-C-Cl 109.47°
SiCl4 Si-Cl 2.00 Cl-Si-Cl 109.47°
C6H6 C-C 1.39 C-C-C 120.00°
P4 P-P 2.21 P-P-P 60.0°