Application of Quantum Theory to Chemical Reactions. 27 



of bimolecular reactions, the attempt was made to work out 

 an expression for the velocity constant of a unimolecular 

 reaction, based on the quantum theory. It should be observed 

 that there is a fundamental difference between a unimolecular 

 and a multimolecular reaction, in that a unimolecular 

 reaction represents a spontaneous process independent of 

 collisions with other molecules. The rate at which such a 

 process occurs must in fact be determined wholly by the 

 rate at which radiation of the absorbable type can be absorbed. 

 Let us consider a simple case, namely, the dissociation of 

 the gas AB into A and B. By the term unimolecular velocity 

 constant is meant the proportionality factor which occurs in 

 the expression : 



dC/dt = kC, 



7 X 1 °0 



/^log-, 



where is the concentration of the gas, its initial con- 

 centration, and t is time expressed in seconds. 



On applying the radiation hypothesis to such a process, it 

 follows that the velocity constant k (which stands for the 

 amount of material decomposed per second, expressed as a 

 fraction of the concentration unit, when the material is 

 itself at unit concentration) should be obtained by dividing 

 the rate of absorption of radiation of frequency v by the 

 quantity hv, the latter being the amount of energy required 

 to decompose the molecule of AB. 



From the standpoint of the physicist the chief interest of 

 the problem lies in the fact that quite different results are 

 obtained, according as we assume the radiation absorption to 

 be continuous (Planck) or discontinuous (Einstein). 



First of all let us assume that the absorption is continuous. 

 On this basis Planck has shown that the amount of energy 

 absorbed by a single oscillator or molecule per second is 



ire 2 

 dm 



where e and m are the charge and mass of an electron, and 



u v is given by 



lirfaiV 



The simple exponential form is justifiable, as the wave- 

 lengths which are known to be responsible for chemical 

 changes are sufficiently short, c is the velocity of light in 



