Page 40 - Modern physical chemistry

2.4 Diffraction by Randomly Oriented Molecules 29

for angle 0), and I the intensity measured at angle O. A plot of the scaled intensity against
product sr appears in figure 2.3.
For a polyatomic molecule exhibiting scattering factors A j , Ak from the jth and kth
atoms a distance r jk apart, the resulting intensity is
1(0) = LLAjAk sinsrjk [2.33]
i k Srjk
with
s = 2ksin!0. [2.34]
2

Formula (2.33) is called the Wierl equation.

ExampJe2.2
Show that for a homonuclear diatomic molecule, equation (2.34) reduces to (2.31).
For a diatomic molecule, equation (2.34) becomes
1(0)= AlAI sinsrll +AIA2 sinsrl2 +A2 A I sinsr21 +A2A2 sinsr22
srll srl2 sr21 sr22
But

and
lim
1
sin a
lim --= cosa=.
a--+O a a--+O
Also

So the equation for a diatomic molecule reduces to
sinsr
-()
22
I 0 = Al +A2 +2AIA2 --.
sr

FIGURE 2.3 Variation of the
scaled intensity with a function
sr = 2kr sinl/2 (J of the scattering angle.