Sec. 16.5] INTERNAL DOSIMETRY 425 



where v = fraction of disintegrations in which the particular isomeric 

 transition occurs 

 / = conversion coefficient (defined by N e /{N y + N e ), where N e , N y 

 are numbers of conversion electrons and gamma rays per transition 

 The value of A for annihilation follows in a similar way 



A an = 2 X 3.7 X 10% 



where v p is the fraction of disintegrations in which a positron is emitted. 

 Each positron on annihilation produces two gamma rays, each of 0.511 mev 

 (m c 2 ). Nuclei that undergo K capture in a fraction v% of disintegrations 

 cause the emission of K x-radiation. The number of such x-rays is 



A K = 3.7 X 10 V 



The estimation of x-rays associated with internal conversion is often less 

 certain. If only one gamma ray is strongly converted, the value of Ai. c . for all 

 x-rays (K, L, . . . ) is ,4 i.e. = 3.7 X 10 4 j/i. t ./, where vi. r . is the fraction of 

 disintegrations in which the isomeric transition occurs. If several gamma 

 ray are converted, A = SA», summed over all isomeric transitions. 



The values of the constants v and / are given when known in the decay 

 schemes for various isotopes. Unfortunately, accurate values of these 

 quantities are known for only a few isotopes of biological and clinical interest. 



The factor /, as used in the formulas above, is the dose in roentgens 

 received at the surface of a sphere of unit radius due to a single gamma 

 quantum of energy E y emitted from the center. For the purpose of its 

 evaluation, consider a single unstable atom placed at the center of a spherical 

 shell of medium with a radius of 1 cm. When the single gamma ray is 

 emitted, the gamma energy converted to kinetic energy of secondary elec- 

 trons per gram of medium at any point on the unit sphere is 



EjU£. = T [Ey(T m "J" a<Tm) + (Ey ~ 2m o C 2 )li m ] 

 47T 



where E y = gamma ray energy, ev 



T m , a cr m , K m = photoelectric, scattering, and pair production mass-absorption 



coefficients 

 Dividing E k .e. by the energy absorbed per gram of the medium exposed to 

 1 r, the constant / is obtained as 



T Ek.E. i 



I = —^tt- r/7 ray at cm 



nW 



where n = number of ion pairs formed per gm medium per 1 r exposure 



W = average energy absorbed to form one ion pair by a secondary 

 electron 

 If the medium chosen is air, n = 1.62 X 10 12 ion pairs per gram air per 



