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1. 1. Radiation Shielding Chapter 7 Section 2 Shielding
2. 2. Radiation Shielding Objectives Understand How radiation is emitted from a source The difference between fluence and flux How to calculate flux (& fluence) at a known distance from a point source Calculate dose at a point in space using a dose conversion factor
3. 3. Nature of Radiation Emissions When a radionuclide decays, the radiation goes out from the source in any direction This is called isotropic emission We measure the strength of the radiations (intensity) at some distance from the source
4. 4. Radiation Intensity The fluence (Φ) is the number of photons moving through a target area (γ/cm2) The flux (φ) is the number of photons moving through an area per time (γ/cm2s)
5. 5. Why Calculate Flux? Fluence and flux tell you: Photons per area, and Photons per area & time If you know: Energy per photon Then, you can calculate Energy deposited per area and, ultimately, dose
6. 6. Calculating Flux Need to answer two questions: What is the source strength S0 (in photons/s) or the total number of disintegrations (D)? What is the distance, r, from the source (at point P) where you want to calculate the flux? r P
7. 7. Calculating Flux, continued Consider each photon as it leaves the source It moves further away from others that have been emitted Therefore, the flux (γ/cm2s) decreases
8. 8. Another Way to Look at It If a source emits 4 photons/s, what is the flux at 1 cm, 10 cm, and 1m? Consider the surface area of the sphere(s) the photons are passing through:
9. 9. Surface Area of a Sphere S . A. = 4 π r 2 S.A.1 cm = 12.57 cm2 1 cm 10 cm 100 cm S.A.10 cm = 1257 cm2 S.A.100 cm = 125,664 cm2
10. 10. Calculating Fluence and Flux, continued D Φ= 4π r 2 S0 φ= 4π r 2 Φ = Fluence γ/cm2 φ = Flux γ/cm2s D = total number of photons emitted S0 = source strength (photons/s) R = distance from source (1, 10, 100 cm)
11. 11. Calculating Fluence and Flux, continued If source emits 4 photons/s, S0 = 4, The φ (flux) is then calculated: At 1 cm = 4 γ /12.57cm2s φ = 0.318 γ/cm2s At 10 cm φ = 4 γ /1257 cm2s φ = 3.18 x 10-3 γ/cm2s φ At 100 cm =4 γ /125,664 cm2s φ = 3.18 x 10-5 γ/cm2s φ
12. 12. Calculating Fluence and Flux, continued For this same problem, what is the photon fluence? Can we calculate it at all? Why? Why not?
13. 13. Calculating Flux At any point from the source, the photon intensity (flux) can also be estimated as: S0 φ= 2 4π r But, what happens if we put some photon absorbing material between the source and our measurement point?
14. 14. Attenuation Occurs Remember the “universal” equation (or one form of it): −µ x 0 I ( x) = I e This describes how a beam of photons is Reduced in intensity by absorbing material Absorber of thickness x is in the photon path The source can be said to be “shielded”
15. 15. Source Strength From Shielded Source The two equations can be combined to yield: φ ( x) shielded = φ unshielded e So −µ x = e 2 4π r −µ x The term 1/(4πr2) is called the geometeric attenuation factor
16. 16. Converting to a Dose Rate S0 P Photon intensity can be converted to dose rate Called an “uncollided” dose rate Use tables of “dose conversion factors”: φ ( x) shielded x r So −µ x = e 2 4π r  = k ( E ) E So e−µ x Du 2 4π r
17. 17. Previous Example, continued Assume S0 = 4 photons/s Photon energy is 0.8 MeV Shielding material is 0.5 cm Uranium (U) Calculate the exposure rate at 1, 10, and 100 cm.
18. 18. Photon Energy Flux to Exposure Doserate Conversion Factors Energy of photon being evaluated Energy (E) in MeV Conversion Factor, k(E), R/hr per MeV/cm2 s 0.5 1.96 E-06 0.6 1.94 E-06 0.7 1.92 E-06 0.8 1.90 E-06 0.9 1.87 E-06 1.0 1.84 E-06 1.2 1.78 E-06 1.4 1.73 E-06 1.6 1.67 E-06 1.8 1.62 E-06 2.0 1.56 E-06 Scientific notation commonly used, should be read as: 1.96 x 10-6 These are “look up” values
19. 19. Total Linear Attenuation Coefficient Factors, µ (cm-1) Energy (E) in MeV Al (2.70)* Fe (7.86) Sn (7.31) W (19.3) Pb (11.34) U (18.7) 0.5 0.227 0.652 0.666 2.490 1.746 3.459 0.6 0.210 0.599 0.578 1.988 1.361 2.618 0.7 0.196 0.557 0.523 1.705 1.136 2.144 0.8 0.184 0.523 0.479 1.492 0.971 1.803 0.9 0.174 0.493 0.445 1.349 0.866 1.584 1.0 0.166 0.468 0.417 1.233 0.782 1.410 1.2 0.151 0.4285 0.382 1.114 0.699 1.245 1.4 0.140 0.397 0.354 1.022 0.635 1.121 1.6 0.131 0.372 0.332 0.949 0.585 1.023 1.8 0.123 0.352 0.314 0.889 0.544 0.944 2.0 0.117 0.334 0.298 0.838 0.510 0.879 * Normal density (ρ) in g/cm3 µ
20. 20. Total Linear Attenuation Coefficient Factors, µ (cm-1), continued Energy (E) in MeV Ordinary Concrete (2.35)* Barytes Concrete (3.50) Magnetite Concrete (3.55) Ferrophos. Concrete (4.68) Water (1.0) Air (0.001205)** 0.5 0.204 0.317 0.303 0.395 0.0967 1.048E-4 0.6 0.188 0.286 0.278 0.363 0.0895 9.70E-5 0.7 0.175 0.262 0.259 0.337 0.0835 9.05E-5 0.8 0.165 0.243 0.243 0.317 0.0786 8.52E-5 0.9 0.156 0.227 0.230 0.299 0.0743 8.05E-5 1.0 0.149 0.214 0.219 0.285 0.0707 7.66E-5 1.2 0.136 0.196 0.200 0.260 0.0643 6.97E-5 1.4 0.126 0.181 0.185 0.241 0.0594 6.44E-5 1.6 0.118 0.170 0.173 0.226 0.0554 6.01E-5 1.8 0.111 0.160 0.163 0.213 0.0522 5.66E-5 2.0 0.105 0.152 0.155 0.202 0.0494 5.36E-5 Normal density (ρ) in g/cm3 ** Air at 200C, 760 mm Hg *
21. 21.  Du = k ( E ) E So 4π r 2 e −µ x Calculating Exposure The uncollided flux previously calculated is: At 1 cm, φ = 0.318 γ/cm2s At 10 cm, φ = 3.18 x 10-3 γ/cm2s At 100 cm, φ = 3.18 x 10-5 γ/cm2s k(E) = 1.9 x 10-6 R/hr per MeV/cm2 s E= 0.8 MeV e-µx is e-1.803*0.5 = 0.41 So, the exposure rate is: 1.98 x 10-7 R/hr at 1 cm; 1.98 x 10-9 R/hr at 10 cm; 1.98 x 10-11 R/hr at 100 cm
22. 22. Calculating Flux From Complex Geometries Point Kernel method Source broken into many small kernels Contribution from each kernel evaluated for a common point Contributions are summed P
23. 23. Rule of Thumb #1 Some equations to memorize For estimating dose rate from a gamma point source where the distance is in feet, and the source strength is in Ci, and the energy of the gamma is expressed in MeV, then: 6.0 Eγ Ci rad  = Dγ ≈ 2 hr ft
24. 24. Rule of Thumb #2 For beta radiation, the equation is similar, where the maximum energy of the beta radiation is used. 2 E max Ci rad  = Dβ ≈ 2 hr ft
25. 25. Rules of Thumb, continued It is important to note that if a nuclide decays by multiple emissions (betas or gammas) that they have to be accounted for in the calculation. You can estimate the dose from each separately and sum the total.