Page 43 - Modern physical chemistry

32 Structure in Molecules and Atoms

FIGURE 2.5 Apparent cross sections presented
by the target atoms in thickness !xc of a material
-Mi- to a given beam.

number of atoms in this volume is n/).x. The corresponding shading area is an/).x. The
fraction of incident particles that strike this obstruction, per unit area, must be an/).x.
But intensity I is proportional to the number of projectile particles reaching this unit area
in unit time. So we have
M
-- = an/).x. [2.36]
I
We suppose that the cross sections in one atomic layer do not cast effective shadows
on those in successive atomic layers. We also suppose that the thickness of each of these
layers is relatively small so that the increments can be replaced by differentials. In this
continuum approximation, equation (2.36) becomes

_ dI =andx. [2.37]
I
Integrating (2.37) over the thickness x yields

I
In-=-anx. [2.38]
In
Here 10 is the intensity of the beam at x = 0 while I is its intensity after traveling distance
x through the absorbing medium.
A convenient unit for nuclear reactions is the barn, defined as 10- 28 m 2 (10- 24 cm 2 ).

Example 2.3
A beam ofthennal neutrons is reduced to 0.0100 percent of its initial intensity by 0.083
cm of cadmium. Calculate the cross section presented by a cadmium atom to the beam.
Solve equation (2.38) for the cross section:

nx