132 RADIATION BIOLOGY 



(dsts, whereas the millimicron is preferred by biologists and chemists 

 where three significant figures are adequate. 



Interference and diffraction methods of characterizing radiant energy 

 yield data that are proportional to wave length, and most absorption 

 spectra in the visible and ultraviolet are plotted as a function of some 

 wave-length unit. However, as related to molecular structure, a fre- 

 quency unit is a more logical basis of specification, because the energy 

 of the quantum is proportional to frequency, and visible and infrared 

 absorption spectra display maxima that occur at simple multiples of 

 fundamental frequency units. Frequency may be expressed directly as 

 waves per second v or the fresnel /, which is 10'- waves per second. 

 However, the most commonly used unit, proportional to frequency, is 

 the wave number v', which is the number of waves per centimeter path 

 in a vacuum and is expressed in reciprocal centimeters, cm"', such that 



,' = 1/X = v/c. (3-2) 



X^' = 10^ when X is in millimicrons and v is in reciprocal centimeters. 

 Comparison of the various spectral units at 50-mM intervals of wave 

 length is presented in Table 3-3. 



QUANTUM ENERGY 



In addition to wave length and frequency, radiant energy may be 

 characterized by the energy of its smallest element, the quantum, or 

 photon. According to the quantum theory, the energy of the photon e 

 in ergs is equal to the product of Planck's constant h, which has a value of 

 6.624 X 10-^^ joule-sec, and the frequency v in reciprocal seconds, as 



follows : 



e = hp = hv'c = hc/\. (3-3) 



The quantum, or photon, energy is proportional to frequency and 

 inversely proportional to wave length. Since the individual molecule is 

 too small a unit for experimental treatment, the einstein, or mole of 

 quanta, is used: E = Nhv, where N is Avogadro's number, 6.02 X lO-'' 

 molecules per gram-molecule. Thus for 1 gram-molecule of substance 

 photochemically reacted in the primary process, 1 einstein of photons is 



required. 



Whereas the chemist usually expresses energy in gram-calories per 

 gram-molecule, the physicist and the theoretical chemist are inclined to 

 use the electron volt. • The magnitude of the electron volt is derived from 

 the kinetic energy the electron receives in dropping through an electro- 

 static field of 1 v; thus j^^mv'^ = eV. 



The energy that an electron, having a charge of 1.602 X lO"'^ coulomb, 

 acquires when it interacts with a photon and absorbs the whole quantum 

 of energy can be equated to the equivalent potential through which the 



