Chemistry Reference
In-Depth Information
The rate of energy flow per unit area (flux) is proportional to the vector prod-
uct of the electric and magnetic field vectors. Since the latter two are at right
angles to each other and are in phase and proportional to each other, the flux of
light energy depends on the square of the scalar magnitude of the electric vector.
Experimentally, we are primarily concerned with the time-average flux, which is
called the intensity,
I
, and which is proportional to the square of the amplitude of
the electric vector of the radiation.
When a light wave strikes a particle of matter that does not absorb any radia-
tion, the only effect of the incident field is a polarization of the particle.
(Quantum, Raman, and Doppler effects can be ignored in this application.) If the
scattering center moves relative to the light source, the frequency of the scattered
light is shifted from the incident frequency by an amount proportional to the
velocity component of the scatterer perpendicular to the direction of the light
beam. Such very small, time-dependent frequency changes are undetectable with
conventional light-scattering equipment and can be neglected in the present con-
text. They form the basis of quasi-elastic light scattering, which has applications
to polymer science that are outside the scope of this text.
According to classical theory, the electrons and nuclei in the particle oscillate
about their equilibrium positions in synchrony with the electric vector of the inci-
dent radiation. If the incident light wave is being transmitted along the
x
direction
and the electric field vector is in the
y
direction, then a fluctuating dipole will be
induced in the particle along the
y
direction. Each oscillating dipole is itself a
source of electromagnetic radiation. If the electron in the dipole were moving at
constant velocity, its motion would constitute an electric current and generate a
steady magnetic field. The fluctuating dipole is equivalent, however, to an accel-
erating charge and behaves like a miniature dipole transmission antenna. Since
the dipoles oscillate with the same frequency as the incident light, the “scattered”
light radiated by these dipoles also has this same frequency.
The net result of this interaction of light and a scattering particle is that some
of the energy which was associated with the incident ray will be radiated in direc-
tions away from the initial line of propagation. Thus, the intensity of light trans-
mitted through the particle along the incident beam direction is diminished by the
amount radiated in all other directions by the dipoles in the particle.
Classical electromagnetic theory shows that the intensity of light radiated by a
small isotropic scatterer is
I
0
θ
4
8
π
2
cos
2
I
0
5
4
r
2
α
ð
1
1
θÞ
(3-37)
λ
where
I
0
θ
is the light intensity a distance
r
from the scattering entity and
θ
is the
angle between the direction of the incident beam and the line between the scatter-
ing center and viewer.
In this equation
I
0
is the incident
light
intensity,
λ
(alpha), which is dis-
cussed below, is the excess polarizability of the particle over its surroundings.
Figure 3.3b
represents the scattering envelope for an isotropic scatterer with
(lambda) is the wavelength of the incident light, and
α
