286 Vibrations set up in Molecules by Collisions. 



estimating numerically. The gas assumes an approximately 

 steady state *, given by d¥/dt = 0, or 



^~e-(/>(E) ^^^^^ 



Here e — <^(E) must be positive for physical reasons, and 

 f {Fi) has been seen to be very small. The whole question 

 at this point fits on to the theory which I have attempted to 

 develop in earlier papers, especially in that just referred to. 



Collision of a Molecule with a Free Ion. 



§ 12. I£ the body B is not a molecule but a free ion, two 

 changes must be made. 



Firstly, since the ion is of less mass than a molecule, its 

 probable velocity will be greater. There are about 700 ions 

 in the hydrogen atom, and therefore about 1400 in the mole- 

 cule, so that the most probable value for the velocity of an 

 ion at normal temperatures will be about >y/ 1400 times that 

 for the hydrogen molecule, and therefore about 7 x 10^ cms. 

 per sec. This kinetic theory velocity is of course quite dis- 

 tinct from the " velocity of diffusion " under an electric force 

 which is capable of direct measurement : it is probably more 

 analogous to the velocity of the Becquerel rays. 



Secondly, as the ion moves with greater velocity than the 

 molecule, it will approach to within a shorter distance of the 

 molecule A. Instead of 10~^ cm., the value found from 

 kinetic theory experiments for the closest approach of two 

 molecules, ^ve must use 10 ~^ cm., the value found by Townsend, 

 Rutherford and others from ionization experiments for the 

 closest approach of ions and molecules. 



The ratio of these two quantities — 7 X 10^ cms. per sec. and 

 10"'^ cm. — gives (7 x lO'^'^)"^ second as the appropriate unit 

 of time when discussing collisions between ions and mole- 

 cules. In these units the frequency of vibration of the 

 molecules is comparable with unity, so that appreciable 

 vibrations wdll be set up by collisions with ions, and these 

 vibrations may occur in all parts of the spectrum. The 

 actual number 7 x 10^'^ might suggest that violet light would 

 predominate, but the calculation is too rough for any stress 

 io be laid on this result. 



§ 13. To sum up briefly, we may say that the '^ elasticity'^ 

 of molecules has been found to be amply sufficient to resist 

 the slow attacks of other molecules, but not sufficient to 

 resist the faster attacks of free ions. 



* " The DistrilDution of Molecular Energ-y," Pliil. Trans, cxcvi. p. 397. 



