Page 42 - Modern physical chemistry

Z.7 The Cross Section Concept 31
Intensity '0 Intensity ,
\ I
/
!
Incident I) \ \

Beam Transmitted
Beam
lI-
X
M
FIGURE 2.4 Passage of a beam of radiation through a medium with
reduction of its intensity from 10 to 1 in distance x.

Here h is Planck's constant, Ii equals h/21r, and tv is the angular frequency 2Jrv. Thus,
absorption occurs in steps. In each of these, the radiation loses a photon; the energy
(2.35) is transferred to the absorbing electron, ion, or molecule, exciting it.
Both energetic particles and photons can be detected plwtographically. The active layer
on photographic film consists of an emulsion of very small grains. These contain some pho-
tosensitive substance(s) such as silver bromide. An incident ray excites grains along its
path. The resulting latent image is developed, fixed, and measured with a densitometer.
High energy particles and photons can be detected by the ionization they produce.
The active agent may be a gas enclosed between two electrodes. Applying a potential
difference then causes the electrons to move rapidly to the anode, the positive ions to
move slowly to the cathode. The effect can be multiplied by increasing the potential
applied until the mobile electrons produce further ionization before they reach the pos-
itive electrode. An external electric circuit serves to count the resulting pulses.
Alternatively, the active agent may be a momentarily superheated or supersaturated
phase. The ionized molecules and electrons then serve as nuclei for evaporation or con-
densation. The resulting tracks can be illuminated and recorded with a camera.
In various materials, the excitation produced by a ray may be relieved by emission
of one or more photons-a scintiUation. This may be observed directly or multiplied in
a photomultiplier tube.
The photovoltaic detector involves a p-n junction in silicon or some other semicon-
ductor. The p material is produced by adding a small amount of impurity that combines
with conduction electrons; the n material by adding impurity that supplies additional
conduction electrons. Associated with the junction at equilibrium is an electric field.
When an incident ray excites an electron, producing an electron-hole pair, these move
to alter the field. A change in voltage across the junction results. This is measured.

2.7 The Cross Section Concept
The atoms in an absorbing material act to reduce the intensity of a beam by either
deflecting or absorbing particles or photons. Insofar as the beam is concerned, it is as if
each atom removes all incident particles falling on a fraction of the cross sectional area
that it occupies, while it lets all others through. See figure 2.5.
The hypothetical shading area that an atom or molecule presents is called its cross
section (J'. This varies with the nature of both reactants, the absorbing atom or molecule,
the projectile particle, and with the particle's kinetic energy.
When a beam traverses distance /j,x of the sample, it sweeps over volume /j,x per unit
cross sectional area. If the number density of the absorbing atoms or molecules is n, the