262 BIOLOGICAL EFFECTS OF RADIATION 



posed by Planck, in 1906. Previous to this time formulas had been 

 developed on the basis of classical theories of light which expressed the 

 relationship between intensity of radiation emitted by a heated solid 

 and wave-length, both in the infra-red region of the spectrum and in the 

 ultra-violet region. There was no satisfactory way of expressing the dis- 

 tribution of energies throughout the whole spectrum as given in Fig. 5. 

 In attempting to find a satisfactory equation for the distribution of energy 

 from a black body, Planck was led to the assumption that the radiation is 

 emitted not continuously but discontinuously in small units of radiation 

 which he called quanta. On this assumption he obtained a compara- 

 tively simple formula which reproduced the experimental facts (shown 

 in Fig. 5) with extraordinary exactness throughout the whole spectrum. 

 The assumption of the discontinuity of radiation was so radical at that 

 time that Planck's quantum theory probably would not have been 

 accepted, except for the fact that the concept of quanta immediately 

 became of great importance in widely different fields. In the study of 

 photoelectric phenomena and specific heat, in the interpretation of the 

 data of spectroscopy, and in various other fields it became at once evi- 

 dent that the quantum theory provided the necessary means for correlat- 

 ing and explaining an enormous number of experimental facts. At the 

 present time the quantum theory seems to be fully established and 

 exceedingly useful. 



The fundamental equation of the quantum theory is 



6 = hv (7) 



according to which the energy of one photon, one quantum e, is directly 

 proportional to the frequency of the light v. The proportionality factor h 

 has the value 6.554 X lO^^^ erg-sec. This value has been checked by 

 careful experiments in many different fields and is a constant of universal 

 importance. It has been fully established that there are 6.06 X lO^^ 

 molecules in a gram molecule (or atoms in a gram atom) and this 

 number is known as the Avogadro number A^. If one takes 6.06 X lO^^ 

 photons one has the number of photons equal to the number of molecules 

 in a gram molecule and this quantity is useful in photochemistry. It has 

 been given the name "Einstein." One Einstein of radiation, then, 

 absorbed by a given system produces the activation of a gram molecule 

 of the material. Only in case secondary effects are absent will the Ein- 

 stein of radiation produce a gram equivalent of the chemical product. 

 According to equation (7) the energy required to produce a mole of 

 activated molecules is then equal to Nhv. 



It is clear that the greater the frequency of radiation the greater is 

 the energy contained in the radiation, and this fact is illustrated in 

 Table 1. It is frequently necessary to convert wave-lengths orJ"requen- 

 cies into energies. In so doing, it should be remembered that 1 Angstrom 

 unit (1 A) is one 100 milhonth of a centimeter, (IQ-^ cm.), and that 1 m/x 



