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

5.4 Advanced collision theory 128
I
Figure 5.21: Collision energy along line-of-centers
Functional expression for ( ):
(1) We assume that a reaction can occur only if ≥ 0 . Thus, we first determine
(see Fig. 5.21):
y
= cos (5.179)
2 = 2 cos 2 (5.180)
= ¡ 2 1 − sin 2 ¢ (5.181)
µ
= 2 1 − 2
(5.182)
2
=
µ
1 − 2
2
(5.183)
(2) We see from this expression that decreases with increasing . Thus, for a
given ,wehaveamaximalvalueof (i.e., a value max ), for which ≥ 0 .
We determine max from the condition that
µ
= 1 − 2
≥
2 0 (5.184)
y
y
2 ≤ 2 µ
1 − 0
= 2 max (5.185)
( )= 2 max = 2 µ
1 − 0
(5.186)