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External and Internal Dose Calculation

External and Internal Dose Calculation. Center For Applied Physical Sciences Research Institute King Fahd University of Petroleum and Minerals. External Dose Calculation Variation of dose as a function of Time Distance Shielding Estimation of Dose rate for Gamma sources Beta Sources

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External and Internal Dose Calculation

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  1. External and Internal Dose Calculation Center For Applied Physical Sciences Research Institute King Fahd University of Petroleum and Minerals

  2. External Dose Calculation Variation of dose as a function of Time Distance Shielding Estimation of Dose rate for Gamma sources Beta Sources Alpha sources Neutrons Internal Dose Calculation Physical Half life Biological Half life Effective Half life Effective clearance Annual Limit of Intake Derived Air Concentration Outline

  3. Dose Limits Occupational • Annual Dose limit = 20 mSv/y • Weekly Dose limit = 20/50 = 0.4 mSv/w • Daily Dose limit = 0.4/5 = 0.08 mSv/d = 80 µSv/d • Hourly Dose limit = 80/ 8 = 10 µSv/h

  4. Radiation Protection Principles The methods of reducing external radiation Dose • Decrease time of exposure • Increase distance from the source • Increase the amount of shielding present

  5. Variation of Dose as a Function of Time Dose received is a linear function of the exposure time Where • is the radiation dose • is the radiation dose rate • t is the exposure time

  6. Example Question: • Estimate the time required for a radiation worker working in a 2.5 mSv/h. so that the worker should not exceed the daily limit? Answer: • Daily limit = 20/(50 x 5) = 0.08 mSv • Time required to receive the daily limit = / • 0.08 (mSv) / 2.5 (mSv/h) = 0.032 h = 1.92 min.

  7. Variation of Dose as a Function of Distance Point Source Of Activity A Sphere Surface Area = 4r2

  8. Variation of Dose as aFunction of Distance Radiation dose decreases as the square of the distance from the source of radiation (Inverse-square law) Where • D1 dose rate at distance 1 • D2 dose rate at distance 2 • S1 is distance 1 • S2 is distance 2 D2 S22 = D1 S12

  9. Example The dose rate at 2 meters away from a gamma source measures 100 mSv/h. What is the dose rate at 4 meters? D2 S22 = D1 S12 • Answer: • D2 = D1 x (S12/S22) = 100 x (22/42) = 25 mSv/h

  10. Variation of Dose as a Function of Shielding (Narrow Beam Geometry) • I is the radiation intensity after traversing a thickness x • Io is the original radiation intensity • µ is the linear attenuation coefficient (cm-1) • x is the thickness of attenuating material (cm) I = Io e (- µ x) Io x

  11. Variation of Dose as a Function of Shielding • The attenuation of gamma radiation by an absorbing material is described by: • where • D is the dose rate after traversing a thickness x • Do is the original radiation dose rate • µ is the linear attenuation coefficient (cm-1) • x is the thickness of attenuating material (cm) D = Do e (- µ x)

  12. Dose Variation Time Activity Shielding e (- µ x) A t D  d2 Distance

  13. Dose Rate Variation Activity Shielding e (- µ x) A  d2 Distance

  14. Estimation of Dose Ratefrom Gamma Sources • The equivalent dose rate from a gamma source is calculated by: • where • is the equivalent dose rate in µSv/h • is the gamma factor (dose rate constant) in µSv-m2/(MBq-h) • A is the activity of the source in MBq • d is the distance in meters from the source

  15. Specific Gamma DoseRate Constant • Is the equivalent dose rate in µSv/h at 1 meter from 1 MBq of the radionuclides in µSv-m2/(MBq-h) Isotope factor Co-60 Cs-137 Ir-192 0.351 0.086 0.13

  16. Estimation of Dose Ratefrom Gamma Sources • If  is not known for a a certain gamma source, the equivalent dose rate is estimated by: • where • is the equivalent dose rate in µSv/h • A is the activity of the source in MBq • E is the gamma ray energy in MeV • d is the distance in meters from the source

  17. Example • Calculate the equivalent dose rate at a distance of 5 m from an Ir-192 gamma source which has n activity of 400 MBq. • Answer • D = x A / d2 = 0.13 x 400 / 52 = 2.08 µSv/h

  18. Estimation of Dose Ratefrom Beta Sources • The equivalent dose rate from a beta source is calculated by: • where • is the equivalent dose rate in µSv/h • A is the activity of the source in MBq • E is the average energy = Emax/3 in MeV • d is the distance in meters from the source

  19. Example Calculate the equivalent dose rate at a distance of 20 cm from a thin unshielded P-32 beta source which has n activity of 20 mCi. • Answer: • Activity in MBq = 20x10-3 x 3.7x1010 x 10-6 = 740 MBq • Eavg = Emax/3 = 1.71 / 3 = 0.57 MeV • D = 5 x 740 x 0.57 / 0.22 = 52700 µSv/h

  20. Estimation of Dose Ratefrom Neutron Sources • The equivalent dose rate from an isotropic neutron source can be calculated as follows: • where • is the equivalent dose rate in µSv/h • N is the neutron fluence in neutrons/s • C is the neutron flux to equivalent dose rate conversion factor in (µSv/h)/(n/m2s) • d is the distance in meters from the source

  21. Equivalent Dose Rate Conversion Factor in (µSv/h)/(n/m2s) Neutron Energy Conversion factor 1 KeV 10 KeV 100 KeV 500 KeV 1 MeV 5 MeV 10 MeV 3.74 x 10-6 3.56 x 10-6 2.17 x 10-5 9.25 x 10-5 1.32 x 10-4 1.56 x 10-4 1.47 x 10-4

  22. Example Calculate the equivalent dose rate at 0.5 m from an Am-Be neutron source that emits 3x107 n/s, assuming the average energy of the neutron is 1 MeV. • Answer: • From table C for 1 MeV = 1.32 x 10-4 (µSv/h)/(n/m2s) • D = ( 0.08 x 1.32x10-4 x 3x107 ) / 0.52 • = 1.27x103µSv/h.

  23. Estimation of Dose Ratefrom Alpha Sources • Alpha particles do not present an external radiation hazard. • Range of 8 MeV Alpha is 0.07 mm of skin • External dose calculations are generally not required.

  24. Internal Dose Calculation • Physical Half life • Biological Half life • Effective Half life • Body burden • Effective clearance • Annual Limit of Intake

  25. Physical Half life • Clearance of internally deposited radioactivity depend on the loss of activity due to the physical decay of the radionuclides, according to lp=ln2/Tp Tp=ln2/ lp

  26. Biological Half life • Clearance of internally deposited radioactivity depend also on the biological removal caused by the action of normal body physiology, according to lb=ln2/Tb Tb=ln2/ lb

  27. Effective Half life • Overall clearance of the internally deposited radioactivity depends on the combined effect of both biological and physical clearance, as follows:

  28. Effective Half life leff=ln2/Teff

  29. Effective Half life

  30. Example • The physical half-life for I-131 is 8 days and its biological half-life in the thyroid is 180 days. Find its effective half-life and the effective decay constant? • Teff = (180 x 8) /(180+8) = 7.7 days • = 0.693/7.7 = 0.09 day-1

  31. Example A radioisotope is measured in a urine sample. It was calculated from the urine concentration that the subject has a body burden, At, of 666 KBq. This sample was submitted, t, 6 days after the accident. Calculate the max. Body Burden, Ao, for the his subject if leff=0.1 day-1? Ao = 666/e-(0.1x 6) = 666/ e-0.6 = 666/0.5488= 1214 KBq

  32. Annual Limit of Intake (ALI) • The intake of a given radionuclides in a year by reference man which result in a committed dose equal to the relevant annual dose limit of 20 mSv.

  33. Derived Air Concentration (DAC) • Limit of Radioisotope in Air of a given radionuclides in a year which result in a committed dose equal to the relevant annual dose limit of 20 mSv.

  34. THANK YOU

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