60 



r Q you have to take has to be gather small. For example, for a group of six 

 radicals it has to be about 10 A. 



It might be worthwhile to examine this situation in a rough way, since it will 

 not take long. The fraction of radicals which combine during the expansion is 



y , but all of these are not observed as taking part in the F reaction, 



1+ y 



since the combination of H and OH produces water again. The net fraction which 

 produces Hz and B2,O z is I N o - 1 v The fraction of radicals which 



N - 1 U y ' 



are observed as entering the F reaction is, therefore, given by 



I N o - 1 1 



2 



n - i i + y 



1 No - i y 



N - i i + y i + y 



If we take No = 6 and equate this quantity to 4, which is approximately the ob- 

 served ratio, we find y = 5/6. 



With relationships already introduced we can write 



3k N Q 9k 



2Trr \ u R Trr \ u R 



The quantity k is the reaction rate constand and we take for it 



1 2 



k z it 0- u R 



where a" is a collision radius for a radical pair. At this point one could object 

 violently to the use of the same 0- and u for both H and OH radicals. 



FANO: Doe what you are doing amount to something like an estimate of the 

 diffusion coefficient ? 



MAGEE: No, this is the reaction rate constant. I assume that the radicals 

 will react as often as they can find each other. The cross section is, tt cr 2 . 



FANO: u D is the thermal speed? 

 K 



MAGEE: Yes. 



FANO: I think any estimation of the diffusion coefficient based on this for- 

 mula will tend to give you something quite off in speed and -- 



MAGEE: The point is that in the quantity y you havespeed upstairs and you 

 have speed downstairs and the two cancel out and you don't put a number in for 

 speed. The reason I would not worry about the speed is because the motion, as 

 I visualize it, is like this: a radical is in first one position and then another. 

 It moves by jumping between pairs of positions. It does not jump with thermal 

 velocity, but it jiggles around in each position a certain number of times. You 

 don't know how long it jiggles around. Then it moves over and jiggles again, a 

 certain number of times, and so on. It has to wait until it gets thermal activa- 

 tion before it can change position. 



