150 RADIATION BIOLOGY 



length of maximum emittance X^ shifts to shorter wave lengths in accord- 

 ance with the Wien displacement law, 



\^T = b, (3-15) 



where X^ is in millimicrons, T is in degrees Kelvin, and 6 is a constant, 

 2.896 X 10". At a temperature of 2896°K, X^ is 1000 m^. At 5782°K, 

 about the value of the surface temperature of the sun, X^ is 500 m^. 



Planck was the first to develop a radiation law that precisely described 

 all the experimental facts regarding the spectral energy distribution of 

 complete radiators. In deriving his law, Planck broke away from classi- 

 cal concepts of energy as a continuum and introduced the concept that 

 radiant energy is emitted and absorbed discontinuously in discrete units 

 that are proportional to the frequency: E — hv. The spectral radiant 

 emittance of a complete radiator for small intervals of wave length is 

 given by Planck's formula, 



Wx = CiX-^e'^^''^^ - 1)-' (3-16) 



where W\ = spectral radiant emittance, w cm"^ per micron of wave- 

 length interval, 

 e = Napierian logarithm base, 2.718, 

 A = area of the source, cm-, 

 C\ — first radiation constant, 37,350, 

 C2 = second radiation constant, 14,380, 

 X = wave length, ix, and 

 T = temperature, °K. 

 The Planck formula is difficult to calculate, and for most practical 

 purposes more simplified approximate formulas are used. Tables giving 

 the radiant power per unit wave length have been computed by various 

 authors (Fowle, 1929; Frehafer and Snow, 1925; Holladay, 1928; Moon, 

 1937; Skogland, 1929). 



Selective Radiator. The Planckian radiation laws may be applied to 

 non-Planckian, or selective, radiators by employing the emissivity factor 

 e. The Stefan-Boltzmann law is then modified as follows: 



W = €,aT\ (3-17) 



where ej is the total emissivity. It is 1 for a complete radiator and less 

 than 1 for all actual substances. The absorptivity a from Kirchhoif 's law 

 and total emissivity can be shown to be equal; therefore the total emis- 

 sivity of any radiator is equal to its absorptivity for the flux emitted by 

 a complete radiator operating at the same temperature (Forsythe, 1937). 

 The total emissivity is a function of the composition of the radiator and 

 its temperature. The spectral emissivity ex is a variable that is a func- 

 tion of composition, temperature, and wave length. 



Since the complete radiator is a highly reproducible source whose radi- 



