Light Absorption and Fluorescence. 25 



phase frequency and radiates 25 quanta at the infra-red 

 fundamental, since only one quantum at this fundamental is 

 required to activate it. If, now, these 25 quanta are com- 

 pletely radiated to their surroundings, then one quantum 

 is absorbed at the phase frequency for every molecule of 

 the hydrogen peroxide that reacts. Unless the conditions 

 are especially suited this will not occur, and the radiated 

 energy will be re-absorbed by fresh molecules of hydrogen 

 peroxide. If none of this energy escapes, then altogether 

 26 molecules of hydrogen peroxide will be rendered reactive 

 as the result of the absorption of one quantum at the phase 

 frequency. 



We may now consider the reaction itself , 2H 2 2 = 2H 2 + 2 . 

 The total amount of energy evolved in this reaction will 

 obviously be the sum of that absorbed in activating the 

 molecules and the observed heat of reaction. As for the 

 purposes of calculation we have assumed that 2(5 molecules 

 of hydrogen peroxide have been activated and are therefore 

 decomposed, the total energy evolved is 26 quanta at the 

 fundamental infra-red frequency plus the observed heat of 

 reaction for 26 molecules of hydrogen peroxide. The 

 observed heat of decomposition for one gram-molecule of 

 hydrogen peroxide is 23059 calories, which is 1*564 x 10 _1 " 

 erg per molecule. The observed energy evolved for 26 

 molecules is therefore 4*0664 x 10" 11 erg, which is almost 

 exactly equal to 130 quanta at the infra-red fundamental. 

 The total energy therefore evolved after the absorption of 

 one quantum at the phase frequency of hydrogen peroxide 

 (complete re-absorption being assumed) is equal to 156 

 quanta at the infra-red fundamental. If, again, this is 

 completely re-absorbed, 156 fresh molecules will be rendered 

 active, and so the reaction will proceed through the whole- 

 mass. 



Two extreme conditions are possible — one in which the 

 whole of the internally radiated energy escapes to the 

 surroundings without re-absorption, and the other in which 

 it is re-absorbed to the maximum possible extent by fresh 

 molecules of hydrogen peroxide. In the first, the Einstein 

 law will apparently hold — that is to say, whilst one quantum 

 will be absorbed for every molecule reacting, this quantum 

 is a multiple of the amount actually employed in making the 

 molecule react. In the second, when one quantum at the 

 phase frequency has been absorbed, an unlimited number of 

 molecules will react; for it is obvious that the reaction velocity 

 will rise to a critical limit, and in the extreme case will pass 

 as an explosion wave through the substance. 



