Attempt to Separate the Isotopes oj Chlorine. 431 



CI35CI35, C1 3 5C1 37 , and Cl3 7 Cl 37 should be in the ratio 

 1 : 10 9 : 10 24 , provided that the molecules which absorb 

 energy react at a rate proportional to the energy which 

 they absorb and that the absorption bands do not overlap. 

 Under these conditions the hydrochloric acid which is 

 formed should consist almost entirely of HCI 37 , provided 

 that the reaction is allowed to proceed for a suitable period. 

 Under favourable circumstances the photochemical com- 

 bination of chlorine and hydrogen takes place more than 

 a million times as fast as would be expected on Einstein's 

 Theory of Photochemical Equivalence ; and if, as seems 

 probable from recent experiments (Nernst, Pliys. Zeit. 

 vol. xxi. p. 106, 1920), this is due to secondary reactions 

 set up by the primary photochemical reactions between 

 chlorine and hydrogen, in which large numbers of other 

 molecules participate, it is evident that the separation of 

 isotopes by this method would be impossible unless these 

 secondary reactions could be eliminated. 



It is also doubtful whether the difference in the spectra 

 would be sufficient to effect a separation, as the differences 

 which have hitherto been observed in the spectra of isotopes 

 relate to the spectra emitted by atoms : whereas in the 

 present case we are concerned with the absorption spectra 

 of molecules, and there is not the smallest experimental 

 or theoretical basis for predicting" the magnitude of the 

 difference. Account must also be taken of the widths of 

 the absorption lines, which cannot be less than a certain 

 inferior limit imposed by the translatory motions of the 

 absorbing molecules, operating in accordance with Doppler's 

 principle. Lord Rayleigh (Phil. Mag. vol. xxix. p. 274, 

 1915) has shown that on this basis the "half-width" hh, of 

 11 line of wave-length A may be found from the equation 



~=3'57xl0-V(T/M), where T is the absolute temp.- 



rature and M the mass of the radiating or absorbing atom 

 or molecule in terms of the hydrogen ;itom. In the case of 

 absorption this equation defines the " half-width " of the 

 absorbing power, the " half-width " SX denoting the distance 

 in wave-length from the maximum of absorption of a line 

 at which the absorbing power has fallen to one-half its value 

 at the maximum. Thus in the case of chlorine molecules 

 at 16°, for \=4000A we have S\ = i) 003 A. The relation 

 between the absorbing power and wave-length is of the 

 form A x = A e~ Kx2 , where A x is the absorbing power at a 

 difference of wave-length from the maximum of absorption 



