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Unformatted text preview: 96 Radiation Doses and Hazards Chap.9 6. A rule of thumb for exposure from point sourcesof photons in air at distances over which exponential attenuation is negligible is as follows: x= " 6CEN 2' r where C is the source strength (Ci), E is the photon energy (MeV), N is the number of photons per disintegration, r is the distance in feet from the source, and X is the exposure rate (R h1). 1. Reexpressthis rule in units of Bq for the source strength and meters for the distance. 2. Over what rangesof energiesis this rule accurate within 20%? Solution: (a) The approximate formula can be transformed thusly: ( Xapprox R/ h)
= 6C(Ci)E(MeV)N [r(ft)]2 C(Bq) ~ = 6(3.7 x lOlO(BQ/Ci))(O:3~7"ft)) / 2 1.507 x 1011C(Bq)E(MeV)N (r(m)]2
(b) Now calculate the exact exposure rate. The uncollided flux density of photons a distance r(ft) from a source of activity C(Ci) emitting N photons/decay of energy E(MeV) is
0 2 1 3.7 x lO10(BqjCi) C(Ci) N ct>(cm h ) = 47r[30.48(cmjft)]2[r(ft)]2 x 3600(sjh). The exact exposure rate is given by Eq. (9.9) Substitute for cPon this expressionand combine the constants to obtain i . E(MeV)N . Xexact(R/h) = [ 209.36(JLen/)air (cm2 /g) ] C(Ci)[r(ft)] 2 p
The ratio of the approximate to exact exposure rates is thus Xapprox/Xexact= 6 [209.36(JLen/p)air(cm2/g)]1 Evaluating and plotting this ratio versus energy gives the results and plot on the next page. From this plot we find that Xapproxis within :1::25%f o Xexact for photon energiesbetween 0.05 and 2 MeV.
July 24, 2002 ...
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