Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.4 Advanced collision theory 129
y
⎧
⎨
( )=
⎩
2 µ
1 − 0
0
(5.187)
0 0
( ) is shown as function of in Fig. 5.22. Crossed molecular beam experiments
have indeed shown similar dependencies for a number of reactions.
I
Figure 5.22: Reactive cross section for the line-of-centers model.
(3) Result for ( ) from Eq. 5.162:
y
µ 1
( )=
Z ∞ µ
× 2
0
=
µ 1
×
Z ∞
0
( )=
12 µ 2
32
1 −
0
12 µ 2
32
2 ( − 0 )exp
µ 8
µ
exp −
(5.188)
µ
−
(5.189)
12 µ
2 exp −
0
(5.190)
This result is identical to that of our primitive “hard sphere-fixedmeanrelative
speed” model from Section 5.1!