Unformatted text preview: 7-6 Radiation Interactions Chap. 7 A small homogeneous ample of mass m (g) with atomic mass A is irradiated s uniformly by a constant flux density </Jcm-2 S-1). If the total atomic cross ( section for the sample material with the irradiating particles is denoted by at (cm2), derive an expressionfor the fraction of the atoms in the sample that interact during a I-h irradiation. State any assumptionsmade. Solution: The number of interactions that occur, during a time interval ~t, in the sample with atom density N, a volume ~ V, a mass density p, and an atomic weight A is Nint = iit~V~t = JLtc/J~V~t (Nut)c/J(m/p)~t = The number of atoms in the sample, Natorns= (mNa}/A. Hence the fraction of atoms in the sample that experience an interaction is Fraction reacting = no. interactions no. atoms = Nint = O"tljJ~t. Natorns 10. A 1-mCi sourceof 60Cois placed in the center of a cylindrical water-filled tank with an inside diameter of 20 cm and depth of 100 cm. The tank is make of iron with a wall thickness of 1 cm. What is the uncollided flux density at the outer surface of the tank nearestthe source? Solution:
From Ap. D or Fig. 5.12, we see that 60Coemits a 1.17 MeV and a 1.33 MeV gamma ray, each with a frequencyof almost 100% per decay. For simplicity, we will assume that each decay of 60Co emits 2 photons each with an average energy of 1.25 MeV. Thus, the source emits Sp = 2 X (10-3 Ci)(3.7 X 1010decays/Ci) = 7.4 x 107 'r/s each with an energy of 1.25 MeV. To reach the outside of the tank nearestthe source, an uncollided photon must pass through t1 = 10 cm of water and t2 = 1 cm of iron. From Eq. (7.27) the maximum uncollided flux density outside the tank is (P7.2)
From Ap. C we find for 1.25-MeV photons, Ji,H20= 0.0632 cm-l and Ji,Fe0.4191 cm-l. Then substitution into Eq. (P7.2) gives July 24, 2002 9. ...
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This note was uploaded on 02/01/2010 for the course ECE 4130 taught by Professor Cady during the Spring '06 term at Cornell.
- Spring '06