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Unformatted text preview: 9-6 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 h-1). 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 10-11C(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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- Spring '06