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Radiation Units and Dose Calcula

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					RADIATION UNITS AND DOSE CALCULATIONS:

    Three concepts are used in measuring ionizing radiation:

    1. Measurement of the electronic charge by an ionizing particle or
      ray.

    2. Measurement of the energy imparted to matter by the ionizing
      particle or ray.

    3. Assessment of the biological damage caused by radiation
      interaction.

    Each concept has unique units and some use in radiation protection.
    Terms which are related to measuring ionizing radiation are:

    • exposure

    • absorbed dose

    • biological dose equivalent

    • quality factor

    • activity




                                   1
EXPOSURE:

    Exposure is defined as a measure of the charge produced in air by
gamma and x-rays. The roentgen, R, is the unit of exposure. Here:


                   1esu
            1R                    @STP Dry Air
                   cm 3

            where esu = electrostatic unit

       The roentgen is applicable to the measurement of charge in air from
gamma and x-rays. The charge produced per unit time is the exposure rate
(R/hr.)


       Example: A radiation worker has worked for two hours in a radiation
field where the exposure rate is 25 mR/hr. Calculate the total gamma and x-
ray exposure received by the worker.

                    mR 
            Exp.   25       2hr 
                       hr 
                           
             50mR




                                       2
ABSORBED DOSE:

       Absorbed does is the energy imparted per unit mass of matter by
ionization and excitation caused by ionizing radiation. The unit of absorbed
due is the RAD (Radiation Absorbed Dose.)

      RAD = any ionizing radiation that imparts 100 ergs/g
           to any form of matter. For example, the RAD
           applies to air, biological system, etc.

      The unit useful for particles that have limited ranges (alpha and beta)

      Absorbed Dose Rate= energy imparted to matter/unit time.
                    (RAD/hr)

      Example: an alpha source delivers 100 RAD/hr to the air surrounding
the source. Determines the absorbed dose, D, in m RAD imparted to the air
in one hour.

               RAD         1, 000mRAD
      D   100      1hr 
                hr              RAD
       100, 000mRAD




                                      3
RELATIVE BIOLOGICAL EFFECTIVENESS:


      Biological effects depend not only on the total energy deposited per
gram (or per volume) but also on the way in which the energy is distributed
along the path of radiation.

       In particular the biological effect of any radiation increases with
linear energy transfer (LET) of the radiation. For example, given the same
absorbed dose, the biological effect damage due to alpha particles which
produce dense tracks of ionization is much greater than the damage from
gamma rays, which are less heavily ionized.


      RBE = 1     200 kev x-rays for a given tissue organ


      RBE depends upon the tissue, the biological effect under
consideration, the dose and dose rate.




                                    4
QUALITY FACTOR:

       The quality factor is a dimensionless factor that accounts for the
difference in biological damage to humans, caused by radiation of different
types and energies.

This factor, QF, is based on the concept of linear energy transfer. A LET is
measured for various energies and types of radiation using a sphere of water
  that approximates the size of a human body and the constituents of soft
                       tissue. A QF is then assigned.

                 Table 3.2 Linear Energy Transfer (LET)
                    Quality Factor (QF) Relationship



      Linear Energy Transfer (keV / 10-6 inch)           Quality Factor

            3.5 or less                                        1

            3.5 - 7.0                                          1-2

            7.0 - 23.0                                         2-5

            23.0 - 53.0                                        5 - 10

            53.0 - 175.0                                       10 - 20




                                    5
DOSE EQUIVALENT:

      The term Dose Equivalent (D) is used to denote the damage done to
the human body by ionizing radiation.

                   the unit = REM

                            = Roetgen Equivalent Man

                   D = R x QF

                     = RAD x QF

      Dose equivalent rate (DR) is provided in rem/hr or millirem/hr.

       If radioactive material is deposited within the body then distribution
of the material must be known.

                   D = R x QF x Distribution Factor

                     = RAD x QF x Distribution Factor

                         Beyond the scope of study




                                     6
                    Table 3.3 Radiation Quality Factors

                               NCRP-39
Type of Radiation              ICRP-9                     10CFR20

x-rays                           1                            1
Gamma Rays                       1                            1
Beta Particles                                                1
       E>0.03MeV                 1
       E<0.03 MeV                1.7
Neutrons                                                      10
       Thermal - 1 keV           2
       10 keV                    2.5
       100 keV                   7.5
       500 keV                   11
       1 MeV                     11
       2.5 MeV                   9
       5 MeV                     8
       7 MeV                     7
       10 MeV                    6.5
       14 MeV                    7.5
       20 MeV                    8
Protons                                                       10
Alpha Particles                  10                           20
Heavy Recoil Nuclei              20                           20




                                      7
     For most purposes, external radiation hazards may be considered as
     having a quality factor of one.

           1 rem = 1 RAD

     Exposure to external radiation is measured by dosimeter of some
     type.

     Neutron Flux (N/cm2/sec)

     Dose  1 x109 thermal N/cm2

           = 2.5x107 fast N/cm2

           =1 rem


           Table 3.4 Neutron Flux Dose Equivalents

Neutron Energy                         Neutrons/cm2 Equivalent To 1 rem
                                                  (N/cm2)


     Thermal                                970x106
     100 eV                                 720x106
     5 keV                                  820x106
     20 keV                                 400x106
     100 keV                                120x106
     500 keV                                43x106
     1 MeV                                  25x106
     2.5 MeV                                29x106
     5 MeV                                  26x106
     7.5 MeV                                24x106
     10 MeV                                 24x106
     >10 MeV                                14x106




                                   8
PROBLEM:

    A worker receives an absorbed dose of :

                                              2 RAD alpha
                                              3 RAD Nts.
                                              4 RAD's gamma

    Calculate the dose equivalent.




SOLUTION:


          D  2QF a  3QF    N
                                  4QF   

           2(20)  3(10)  4(1)
           74rem




                                         9
PROBLEM:

       A worker is exposed to 100 keV Nt flux of 2.5x105 Nt/cm2/sec for
three hours. Calculate the dose equivalent in rem.




SOLUTION:

            t = 3 hrs(3600 sec/hr)

            t = 10800 sec

            D=DR x t

            = 2.5x105 Nt/cm2/sec x 10800 sec

            = 2.7x107 Nt/cm2

            1 rem = 120x106 Nt/cm2

            D = 0.225 rem




                                     10
DOSE RATE CALCULATIONS:

                         ergs 
        DR   S    / A       
                         g 

        S = C (Ci)

          3.7 x1010 dps 
                         C Ci 
               Ci       

        = 3.7x1010C dps or gamma/sec

        = 3600 sec / hr x 3.7x1010C gamma/sec

        = 1.33x1014C gamma/hr

                                 E ( MeV ) 106 eV                ergs 
        1.33x1014C gamma/hr                         1.6 x1012
                                 gamma MeV                        eV 

                         erg
         2.13 x108 CE
                         hr




                                      11
      Radiation emitted by the source is distributed uniformly over the
surface area of a sphere of radius r.

               A  4r 2 ft 2
                                  2
                          12in   2.54cm 
                                                2

                4r ft 
                     2   2
                                         
                          ft   in 
                1.17 x104 r 2 cm 2

      For tissue over the gamma range 0.2 to 4.0 MeV an approximate
                    cm 2
value of     of 0.03      .
                     g


      Now, a rem of gamma radiation is absorbed when 100ergs are
absorbed per gram of body tissue.


                                           
                               1rem 
               DR  S   / A              
                               100ergs 
                                 
                                      g    
                                            
                               erg   0.03cm 2 
                 2.13 x108 CE                 
                               hr  
                                          g     
                                         ergs / g 
                                     
                1.17 x104 r 2 cm 2  100
                                          1rem   
                     CE
                5.46 2
                      r
                 6CE
                2
                  r

               C - Ci

               E - MeV

               r - ft




                                           12
     Table 7.5 Gamma Decay for Selected Radionuclides


                                    Percent     Dose Rate per Curie at
Radionuclide   Gamma Energy (MeV) Gamma Yield 1 Meter,G/10 (rem/hr)

Celsium-134       E1 0.57              23               0.84
                  E2 0.605             98
                  E3 0.796             99

Celsium-137       E1 0.662             85               0.31

Cobalt-58         E1 0.511             30               0.53
                  E2 0.810             99

Cobalt-60         E1 1.173             100              1.40
                  E2 1.332             100

Chromium-51       E1 0.315             9                0.016

Iodine-131        E1 0.364             82               0.20
                  E2 0.284             5.4
                  E3 0.637             6.8

Iron-59           E1 1.095             56               0.66
                  E2 1.295             44

Manganese-54      E1 0.835             100              0.47

Nickel-65         E1 1.48              25               0.31
                  E2 1.12              16




                               13
PROBLEM:

  Calculate the dose rate, rem/hr, three ft. from a source containing one Ci
of Mn-54.




SOLUTION:

             E = 0.835 MeV
             C = 1 Ci
             r = 3 ft


                    6CE
             DR 
                     r2
                                  MeV
              6  1Ci  0.835
                                  3 ft 
                                            2


              0.557 rem / hr




                                                14
PROBLEM:

    What happens when it emits two ’s?

    Calculate the does rate, rem/hr, 10 ft. from a 15 Ci Co-60 source.




SOLUTION:
          E  1.173 1  1.332 1
           2.505 MeV
          C  15Ci
          r  10 ft
          DR  6 15Ci  2.505 MeV  / 10 ft 
                                                   2


           2.25rem / hr




                                      15
PROBLEM:


       The dose rate 10 ft. from a pump is 10 rem/hr. Determine the dose
rate 25 ft. from the pump.




SOLUTION:


             DR10  10rem / hr
                                   2
                         r 
             DR25  DR10  10 
                          r25 
                             2
              10rem  10 
            
                hr  25 
                       
                  rem
             1.6
                   hr




                                       16
INTERNAL RADIATION EXPOSURE:


       Internal exposures can be caused by beta, gamma, or neutron sources
that are ingested, inhaled or enter the body by way of wounds.

       Internally deposited radionuclides are usually concentrated in
localized areas with in the body depending on the chemical characteristics
of the radioactive material involved.

The exact length of time which it remains in the body (organs) depends to a
  great extent on the organs involved and the form of the radionuclides.


           Table 8.3 Critical Organs for Selected Radionuclides


      Radioisotope                          Critical Organ

      Hydrogen-3 (tritium)                  Whole Body
      Phosphorous-32                        Bone
      Carbon-14                             Fat
      Sulfur-35                             Testes, whole body
      Chromium-51                           Lower Intestine
      Cobalt-60                             Lower Large Intestine
      Zinc-65                               Liver, prostate
      Rubidium-87                           Pancreas
      Technetium-99m                        Upper Large Intestine
      Iodine-131 (and I-125)                Thyroid
      Cesium-137                            Whole body, liver, spleen
      Gold-198                              Lower Large Intestine
      Mercury-203                           Kidney
      Iridium-192                           Lower Large Intestine
      Radon-222                             Lung
      Radium-226                            Bone
      Uranium-235                           Lower Large Intestine
      Plutonium-239                         Bone




                                   17
      The biological half-life for a particular radionuclide is the time
required to reduce the concentration of a radionuclide to 1/2.

      The effective half-life is the time during which a radionuclide may
cause damage, and is determined by combining the effects of physical and
biological half-lives:


                                  1    1   1
                                                         T = half-life
                                 Teff TP TB



                                 
                                     TB  TP 
                                       TBTP
                                           TBTP
                                 Teff 
                                          TB  TP




                                      18
       Table 8.4 Effective Half-Lives of Common Radionuclides

                      T2r               T2B               T2eff
                   Physical         Biological          Effective
                   Half-Life   Half-Life          Half-Life
Radionuclides       (Days)            (Days)       (Days)
Hydrogen-3            4.5x103           8                   8
Carbon-14             2.0x106           12                  12
Phosphorus-32         14.3              1155                14.1
Sulfur-35             87.1              90                  44.3
Chromium-51           27.8              616                 26.6
Manganese-54          300               25                  23.1
Iron-59               45.1              600                 41.9
Cobalt-58             72                9.5                 8.4
Cobalt-60             1.9x103           9.5                 9.5
Zinc-65               245               933                 194
Rubidium-87           1.8x1013          60                  60
Strontium-90          1.0x10 4          1.8x10 4            6.4x104
Technetium-99m        0.25              20                  0.25
Iodine-131            8                 138                 7.6
Cesium-134            840               70                  64.6
Cesium-137            1.1x104           70                  70
Iridium-192           74.5              20                  15.8
Gold-198              2.7               120                 2.6
Mercury-203           45.8              14.5                11
Radon-222             3.83       None (Inert Gas)           3.83
Radium-226            5.9x105           1.64x104            1.64x104
Uranium-235           2.6x1011          300                 300
Plutonium-239         8.9x106           7.3x104             7.2x104




                               19
PROBLEM:

    Calculate the Teff of Cs-137




SOLUTION:


          T
             1.1 x10 days   70days 
                        4


               1.1 x104 days  70days
            70days




PROBLEM:

    Calculate the effective half-life of S-35




SOLUTION:



          T
                87.1days  90days 
                87.1days  90days
            44.3days




                                        20
PROBLEM 1:

     Calculate the maximum critical dimensions of the core.
     A thermal homogeneous reactor has a cylindrical bare core:

                   •height equals its diameter
                   •1.3% enriched uranium metal
                   •light water as a moderator

                                                                Possible Data
             1.0558
                                              TR  0.45
             0.830                                                    D
Given:                                       LM  2.88           L2       (on tables)
           f  0.870                                                    a
                                             LSM  5.74
             1.40

                                                                Table in Problem Statement



SOLUTION:

           k  1.067
           L2   2.88   8.2944cm 2
                        2



           L2   5.74   32.95cm 2
                        2
            S

           M 2  L2  L2  41.24cm 2
                       S

           d E   0.71 0.45cm   0.32cm
                  k  1 1.0673  1                v  f  a
           B2                      0.00163 2 
                   M2      41.24                        D
                        2          2
                    2.405 
           B 
             2
                           
                 H e   Re 
           Re  R  d e
           H e  H  2d e  2 R  2d  2 Re
                             2               2
                         2.405 
           0.00163            
                      2 Re   Re 
           Re  71.14cm
           R  70.82cm
           H  2 R  141.64cm


                                        21
PROBLEM 2:

     Calculate the maximum critical dimensions of the core.
     A thermal homogeneous reactor has a cylindrical bare core:

                  •height equals its diameter
                  •1.3% enriched uranium metal
                  •light water as a moderator

                                                           Possible Data
             1.0558
                                              TR  0.45
             0.830                                               D
Given:                                       LM  2.88      L2       (on tables)
           f  0.870                                               a
                                             LSM  5.74
             1.40

                                                           Table in Problem Statement

SOLUTION:

           k  1.067
           L2   2.88  1  f   1.078cm 2
                        2



           L2  1.10  5.74   36.242cm 2
                            2
            S

           M 2  L2  L2  37.320cm 2
                       S

           d E   0.71 0.45cm   0.32cm
                 k  1 1.0673  1
           B2   2                   0.0018cm 1
                   M         37.320
                        2           2
                  2.405 
           B 
             2
                         
               H e   Re 
                            2            2
                        2.405 
           0.0018            
                     2 Re   Re 
           Re  67.705cm
           H  2 R  135.4cm




                                        22
PROBLEM:

    Calculate Slowing Down Length: LS2




SOLUTION:

                       1                                       D
                L2      N f   S  f  TR  f   or
                                                               a
                 S
                       3



                                                        Initial E
                        1  E Ni     
                Nf      ln                           Final E
                          E Nf
                            
                                     
                                     



                                              E
                                           ln     S  f
                                                         2
                                    S  f
                                           2

                                            
                                                E
                 L2  N f
                            3 1  Cos    3 1  Cos 
                    S




                                         23
PROBLEM:

      Determine k00 if the mass of U235 (f = 0.024 g/cc) in a homogenous
reactor ~6kg. The reactor core is a cube with water as moderator.




SOLUTION:


      Assume- critical dimentions
      Assume d = 0.71 to be small


                            2
                    
             Bg  3  
              2

                    S
                    k  1  v  f   a 
             Bm                       
                     m2          D      

            Critcal----> Bg = Bm
                                2
             k  1    
                     3 
                       S
                 2
              M
                        2
                   
            k  3   M 2  1
                   S




                                        24
PROBLEM:


   Calculate S and M2

   First determine S.

   Mass (g) = fS3


             6, 000 gram
                          S  63cm
         3            g
              0.024
                     cc



   Next, M2.
                                           33, Provided in Tables
         M  L
             2
                     L
                     2
                     S
                             2


                 Dt       Dt          0.18cm
         L2                   
                  a  af   am 0.02cm  0.037cm
         M 2  33  3  36
                         2
                
         k  3    36   1
                 63 
          1.27




                                      25
                         TABLE 6.1


Moderator     Density           Dt       L               M2

Water         1.00g/cc          0.18cm   2.88cm   33cm2   41cm2

Heavy Water   1.10              0.85     100      120     10,120

Beryllium     1.84              0.61     23.6     98      655

Graphite      1.62              0.92     50.0     350     2,850




                           26
EXTERNAL EXPOSURE:
    Neutrons - Energy Dependent
               Tabulated graphically

      Gamma’s

            for a beam with a single energy

                                                                      air
                   •  R                 8         a 
                  X    1. 83 *10             IE  
                    sec                            

                                                        photons                     's
                         where I - Intensity                                or
                                                      cm 2 * sec                 cm 2 * sec

                                  E - Energy MeV

                                  a                                    cm 2
                                            mass absorption coefficient
                                                                        g
in mR/hr
                                                            air
                   •  mR             
                  X      0. 0659IE  a 
                     h                

Dose from External Exposure

                                                            tis
                   •  mrad           
                  D      0. 0576I  a 
                     h               
or
                                                           tis
                                                  a 
                                                 
                  •  mrad                                •
                  D         0. 0874                          X
                     h                 a       
                                                        air
                                                    
                                                   

Equivalent Dose
                                  •         •
                               HfD
where f energy dependent function which depends on the type of tissue.


                                       27
INTERNAL EXPOSURE:

Gamma and Charged particle

                         •  rad         5. 92 *10 4 C  t  E
                     D   
                        sec                     M

             where C(t) Ci
                  M mass of the organ grams
                  E is energy in MeV

Equivalent dose
                         •       •
                     H  DQ

for a multi mode decay
                         •       •
                     H  D

Retention function

                    R  t   C 0 qe b t
             q is describes mode of internalization i.e. ingestion or
inhalation

Single intake

                                  51.1C d qe e t
                         •  rem 
                     H      
                       day          M

Continuous Intake


                                                                                                
                     t
                              e  t                                       Cd q
      C t   Cd q  e                                              Ct          1  e e t
                                                                               e
                    0




                                                 28
Then
       •  rem 
       H       
                                  
                       51.1C d q 1  e  et   
          day               M e




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